Elucidating the pathological axis of hIAPP-mediated β-cell toxicity: A MATLAB-based network modelling

Elucidating the pathological axis of hIAPP-mediated β-cell toxicity: A MATLAB-based network modelling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Elucidating the pathological axis of hIAPP-mediated β-cell toxicity: A MATLAB-based network modelling Komal Kharat, Aditya Pansare, Rajesh Gacche This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7722499/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Human islet amyloid polypeptide (hIAPP) oligomers are increasingly recognized as central mediators of β-cell dysfunction and toxicity in type 2 diabetes mellitus (T2DM). Islet amyloidosis is a chronic condition developed during the course of T2DM and it is characterized by the deposition of toxic hIAPP aggregates in pancreatic β-cells. Although, islet amyloidosis in not a condition that has gone unaddressed however, the intricate mechanisms that the toxic hIAPP oligomers intervene with to mediate β-cell toxicity are yet to be fully elucidated. In this study, we employed systems metabolism and computational biology approach to mathematically reconstruct and investigate the dynamics and hIAPP-mediated β-cell toxicity axis using SimBiology MATLAB. The signalling network was reconstructed using a number of enzyme kinetics and parameters which provided a computable framework of all the signalling components giving us valuable insights to predict and replicate the best behavioural outcomes. Sensitivity analysis, Principal Component Analysis (PCA), Flux analysis, Model reduction and cross-talk point determination accurately captured the dynamics of the entire system and identified key components (RAGE, PKC, ROS, CytoC, PERK, IRE1, ATF6, Ca 2+ influx), interactions, and processes (insulin resistance, glycation, autophagy defect, ER and mitochondrial stress, apoptosis) driving its pathogenic behaviour. Biological sciences/Biochemistry Biological sciences/Biological techniques Biological sciences/Cell biology Biological sciences/Computational biology and bioinformatics Health sciences/Diseases Biological sciences/Systems biology hIAPP Islet amyloidosis T2DM β-cell dysfunction SimBiology MATLAB Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 1. Introduction Islet amyloidosis is a chronic condition developed during the course of prolonged hyperglycaemia in Type II Diabetes Mellitus (T2DM). It is characterized by the accumulation of amyloid deposits formed through aggregation of amyloidogenic peptide known as Islet Amyloid Poly-Peptide (IAPP) within the Islets of Langerhans causing their loss of function and mass. IAPP aggregates are attributed to defective glucose regulation, mitochondrial and endoplasmic reticulum (ER) stress, increased β-cell toxicity, dysfunction and apoptosis; and are best characterized by their physiological role in being able to inhibit insulin secretion causing insulin resistance through a direct paracrine effect on the β-cells [ 1 ]. IAPP deposits in the pancreas of a T2DM patient were first described in 1901 as hyaline lesions [ 2 ] however, were later described as proteinaceous amyloid plaques in 1961 [ 3 ]. Proteinaceous plaques are mainly formed due to aberrations in protein folding mechanisms leading to misfolded protein aggregates and deposits in the cells causing severe damage to the organs and surrounding areas [ 4 ]. IAPP exhibits endocrine, paracrine and autocrine functions. Human IAPP (hIAPP) is expressed as an 89 amino acid pre-pro-peptide and post-translationally 22 amino acids are cleaved from the N-terminus to give a 67-amino acid peptide called proIAPP. proIAPP is then altered in the lumen of ER by forming a disulphide bond between cysteines at position 2 and 7. This altered peptide is transported to the Golgi Complex to be packed in the secretory granules and further be cleaved into a final 37 amino acid peptide modified by amidation at the C-terminus [ 5 ]. Under normal physiological conditions this active form of hIAPP is co-expressed, co-processed and co-secreted with insulin in a molar ratio of 1:100 to regulate blood glucose levels; however, during chronic hyperglycaemic conditions this ratio is heavily altered [ 6 ]. Aggregation or oligomerization of hIAPP has been associated with histidine and tyrosine residues present at 18 and 37 positions respectively. Hydrophobic and aromatic interactions between amyloidogenic areas 15–20 and 22–29 have been demonstrated to induce the structural rearrangement of random coil structures to pentameric β-sheet oligomers, with residues 23–27 playing a significant role [ 7 ]. Extensive evidences suggest that hIAPP oligomerizes intracellularly as a result of incorrect processing of proIAPP in the secretory granules and released as deposits into extracellular space when β-cells degenerate. Apart from the physicochemical alterations, perturbations in the biological processes also hold a significant weight in the oligomerization of hIAPP leading to loss of β-cell mass. To maintain the homeostatic blood glucose levels during hyperglycaemic conditions the insulin secreted by the pancreatic β-cells initiate the glucose metabolism process via insulin signalling pathway. This pathway is triggered when the glucose uptake by GLUT2 transporters has increased intracellularly; the glucose is metabolised increasing the ATP levels which close the K + channels and escalates Ca 2+ influx which prompts the secretory granules to release the stored insulin. Once, secreted this insulin binds the insulin receptors facilitating autophosphorylation. Insulin receptor substrate-1 (IRS1) is recruited by activated insulin receptors and phosphorylated at the Tyr residue. This allows phosphatidylinositol 3-kinase (PI3K) to dock and further catalyse the conversion of PIP2 to PIP3, which induces AKT activation. GLUT4 translocation for glucose uptake is facilitated by activated AKT, and its metabolism is supported through processes such as glycolysis, TCA cycle and glycogen synthesis through inhibition of glycogen synthase kinase-3 (GSK3β). In β-cells, this signalling is tightly coupled with nutrient sensing to insulin exocytosis, ensuring that increased circulating glucose triggers enhanced hormone release [ 8 ]. Persistently elevated blood glucose levels place a heavy metabolic burden on β-cells creating glycolytic overload. As a compensatory mechanism excess glucose is rapidly metabolized to meet insulin synthesis demands and by default synthesizing hIAPP along with insulin. The proteostatic environment is usually maintained when the secretory granules release their contents, however, when there is a higher demand for insulin, the cytosolic pool of hIAPP will also rise and there will be greater chance of aggregation and deposition of aggregates around β-cells. This metabolic strain promotes diversion of glucose into secondary metabolic pathways generating glycotoxic byproducts that again accelerate the misfolding and oligomerization of already produced hIAPP. Despite the considerable research available linking hIAPP with T2DM, hIAPP misfolding, deposits as plaques throughout different parts of the body little amount of research is available on the integrative role of toxic hIAPP oligomers as central regulators of β-cell toxicity. In this study we elaborate and corroborate the role that toxic hIAPP oligomers may have in contributing towards aberrant functioning of several biological processes that lead to insulin resistance, ER and mitochondrial stress, autophagy failure, inflammation and β-cell death during T2DM. The perturbations in these signalling pathways are subject to two major events firstly the changes in the blood glucose levels and its influence on the oligomerization of hIAPP. Understanding the impact of these events on the tempering of various metabolic and biological processes will prove to be crucial in following the evolution and reach of the disease. Our study mainly focuses on deciphering the hIAPP mediated β-cell toxicity axis in islet amyloidosis during T2DM, which could offer new insights in developing precision and targeted therapies for this condition. 1.1. The hIAPP mediated β-cell toxicity axis Once, the glucose uptake is levelled up through the GLUT4 transporters it is rapidly converted to pyruvate through sequential enzymatic steps of glycolysis. Pyruvate is an essential node that connects the mitochondrial TCA cycle and glycolysis. The pyruvate dehydrogenase complex in mitochondria transforms pyruvate into acetyl-CoA, through the production of metabolic intermediates from citrate to oxaloacetate the TCA cycle advances and produces ATP and NADH during oxidative phosphorylation [ 9 ]. Additional regulatory features of this metabolic signalling are initiated by continuous glucose influx where anaplerotic flux converts back oxaloacetate to phosphoenolpyruvate via phosphoenolpyruvate carboxylase. This phosphoenolpyruvate can re-enter glycolysis cycle producing pyruvate in a feedback loop where recurrent cycling of oxaloacetate-PEP-pyruvate feeds into α-ketoglutarate production. Increased production of α-ketoglutarate acts as a metabolic signal for secretory granules to promote the release of stored insulin and hIAPP monomers [ 9 , 10 ]. Apart from this under conditions of chronic metabolic burden excessive glucose is shunted into secondary metabolic pathways most notably the polyol pathway where the aldose reductase reduces glucose to sorbitol which is then oxidized to fructose pushing it back into the glycolysis cycle. During this reaction methylglyoxal a highly reactive dicarbonyl molecule is generated as a byproduct. As a glycation agent methylglyoxal functions in altering the structural conformations of hIAPP monomers speeding up its oligomerization. As a result, soluble hIAPP monomers are transformed into insoluble toxic oligomeric assemblies characterized by β-sheets [ 11 , 12 ]. Notably, the hIAPP oligomers rather than the mature fibrils are the prominent mediators of cellular toxicity and their formation can be influenced not only by the intrinsic amyloidogenic properties but also extrinsic molecular factors and non-canonical processes that promote protein misfolding [ 4 ]. Once formed these hIAPP oligomers engage in cellular toxicity by two mechanisms including receptor mediated interactions and non-receptor mediated events (Fig. 1 ). The receptor for advanced glycation end products (RAGE) can bind hIAPP oligomers due to its oligomerization being enhanced by glycation. RAGE is not only involved in eliciting signalling responses leading to inflammation and apoptosis but also plays a crucial role in causing insulin resistance during T2DM. Interaction of hIAPP oligomers with RAGE leads to the recruitment and activation of protein kinase C (PKC), which carries out IRS1 phosphorylation at serine/threonine residues. This impairs normal IRS1 functioning and damages the insulin mediated PI3K/AKT signalling inhibiting glucose uptake and metabolism, thus, leading to insulin resistance in β-cells [ 13 , 14 ]. Parallelly, β-cell apoptosis characterized by release of cytochrome C (CytoC) and activation of caspases is mediated by hIAPP-RAGE signalling. PKC activates NADPH oxidase (NOX), which takes up hydrogen from NADPH formed in mitochondria and releases a reactive oxygen species (ROS) harmful to the cells. ROS production mostly occurs through the electron transport chain in mitochondria however, activated PKC triggers the stress-related JNK/p38 signalling pathway which stimulates NOX for ROS generation in β-cells [ 15 ]. The activated JNK mediates β-cell apoptosis by activating a range of events leading to mitochondrial and ER stress, ROS formation and production of pro-inflammatory cytokines. Reactive oxygen species formed permeabilizes the outer mitochondrial membrane to release CytoC into the cytosol which further initiates the intrinsic apoptotic cascade by binding to the APAF1 forming the apoptosome assembly activating caspase 9 for cell death [ 12 ]. Additionally, it also acts as signalling molecules that participates in the activation of NLRP3 inflammasome. Inflammasome formation triggers the activation and release of pro-inflammatory cytokines such as IL-1β, IL-6, IL-18 and TNFα. Systemic release of these cytokines induces islet inflammation that plays a major role in β-cell dysfunction and apoptosis activation [ 16 , 17 ]. Further through NF-κB-mediated transcription pro-inflammatory cytokine expression is amplified, recruiting immune responses that worsen β-cell injury. These cytokines initiate an inflammatory response that does not act in isolation; rather, it primes β-cells for apoptosis by enhancing Fas receptor expression on their surface. Thus, inflammation, oxidative stress, and failed proteostasis converge to channel β-cells toward programmed cell death, making apoptosis an inevitable point. Apart from this constant exposure of β-cells to increased nutrient levels demands and increase in insulin biosynthesis as discussed earlier. As this demand becomes chronic, the biosynthesis and secretion process may eventually overload the protein folding capacity of the ER leading to the saturation of chaperon BiP and activation of the unfolded protein response (UPR) which senses the activation of PERK, IRE1α, and ATF6. Chronic nutrient stress will uncouple translational control from protein folding capacity of the ER leading to its dysfunction, miss-processing of proIAPP and proInsulin and accumulation of misfolded protein cargo in the β-cells [ 12 , 18 ]. These misfolded proteins are targeted for polyubiquitination and degradation by autophagy under physiologically normal conditions. hIAPP oligomers have the ability to engage with calcitonin receptor (CTR) which recruits receptor activity-modifying protein 3 (RAMP3) and activate the GPCR signalling via Gαs/Gαq intermediates. This elevates the levels of cyclic AMP (cAMP) that initiates the closure of K + channels and depolarizes the membrane to open voltage-gated Ca 2+ channels. Increased Ca 2+ concentrations lead to disruption of lysosomal membranes preventing its fusion with the autophagosomes for degradation of misfolded protein cargos. Under physiologically normal circumstances, autophagy maintains β-cell proteostasis by degrading excess proInsulin and IAPP monomers through lysosomal clearance. Polyubiquitinated proteins are destined for degradation by autophagy through ubiquitin binding p62/sequestosome 1 (SQSTM1) which itself gets degraded in autophagosome along with the cargo. However, during islet amyloidosis defective autophagy in β-cells results in accumulation of p62 forming cytoplasmic inclusions as an indicator of impaired autophagic flux [ 4 , 19 , 20 ]. Ultimately, the toxicity of hIAPP oligomers establishes a pathological cascade converging various metabolic and biological processes. The fate of the hIAPP mediated β-cell toxicity axis in islet amyloidosis during T2DM is β-cell dysfunction and loss of β-cell mass culminating to a decline of insulin secretory capacity. These events not only contribute to the degeneration of pancreatic functions but also intensifies the systemic insulin resistance and chronic hyperglycaemic conditions. Based on existing biological data to get a greater insight into this intricate pathological axis, we reconstructed a kinetic model interpreting this signalling network using a systems and computational biology approach which emphasizes its key molecular interactions [ 21 ]. For this purpose, we have used Systems Biology Markup Language – based MATLAB SimBiology Toolbox R2024b. Through the mathematical model we have thus, worked two extremely important objectives: firstly, to contribute to a deeper understanding of the biological events under study in a manner that is simple to be replicated in silico and conveyed; secondly, to make it possible in the future to design in vitro and in vivo experiments that specifically track the predicted features (vital cross-talks) of this biological system in order to follow the reach of the pathological network. 2. Methodology 2.1. Data Preparation: To decipher and reconstruct the hIAPP mediated β-cell toxicity axis fragmented data was gathered through thorough literature reviews and signalling database searches such as KEGG and GEO Dataset [ 4 , 12 , 13 , 18 , 19 , 22 , 23 , 24 ]. 2.2. Quantitative Modelling and Simulations: Quantitative modelling of biological reactions was done using SimBiology Model Builder; it involves the application of appropriate kinetic rate laws, parameter estimation, and initial component concentration ( https://in.mathworks.com/help/simbio/ ). The kinetic rate laws implemented in the SimBiology Toolbox for the reconstructed models were as follows: 1) The Law of Mass Action, was applied to association and dissociation reactions. 2) The Henri-Michaelis-Menten equation, was employed for phosphorylation, dephosphorylation, and ubiquitination reactions. 3) Hill's kinetic equation was applied for gene expression reactions. Initial concentrations of signalling components were determined considering experimentally known concentrations from the literature, indicating that a cell can secrete 10 3 -10 6 signalling molecules [ 25 ]. The parameter estimation and model simulations were regulated in such a manner that the mathematical model could mimic the behaviour of the signalling events taking place in the β-cell during the course of islet amyloidosis in T2DM. Simulations of the mathematical model were performed using the Stiff Deterministic ODE15s solver type for 100 seconds time units in SimBiology Model Analyzer, which generates the first-order non-linear ODEs, that provides a state versus time graph for each node (molecule/species) to determine their dynamic behaviour in the system over time defining the mathematical framework used in SimBiology [ 26 , 27 , 28 ]. This discrete transition depends on the conditions applied i.e., the reaction rate (V max ), and the concentration of the substrate (K max ) at a given time. 2.3. Trigger Events: A per the SimBiology User Guide documentation provided by Mathworks, in addition to simulations, species in the model can be assigned trigger events such that they demonstrate a discrete transition in their concentration regulating the final outcome of the system ( https://in.mathworks.com/help/simbio/ug/event-object.html ). In mathematical modelling of biological networks an event describes a particular process discretely transitioning from its normal functioning and progresses towards an abnormality. These transitions occur when a customized time and concentration condition becomes true. Such conditions are defined as Event objects in the model as they have the trigger property that must be true for an event to execute. For instance, if a specific simulation time is considered as a triggering object, then at that time the amounts/values/parameters of a particular species are changed in such a way that an event occurs. In response to the dynamics of the events in the system certain other species are affected even though they are not tied to the triggering time or concentration. The reactions or species participating in triggering events are of great importance as they ultimately govern the fate of the biological processes causing it to switch or transition between normal and pathological forms during disease condition. In SimBiology we need to use a combination of relational and logical operators to execute a trigger event. In addition to Event objects an EventFcns property needs to be specified which occurs when an event is triggered. The EventFcns property of an event specifies a condition that is time – dependent or time – independent. For example, at a time > = 25 seconds, and at a species concentration of X = 150 molecule per second will trigger an event where post 25 seconds the axis with switch from its normal functioning depending on the change in concentration of the species X. In our model we have employed time – dependent simulation of trigger events which allowed us to specify the EventFcns property with respect to change in concentration and parameters associated with the species at given time = 20 seconds or 50 seconds. 2.4. Sensitivity Analysis: In order to determine the interdependence of the components and robustness of the biological network, sensitivity analysis of the mathematical model was carried out. According to various factors, including the biochemical process they are involved in, the kinetic law used, and the set of parameters the components are subjected to, the sensitivity analysis of the model provides information about the most important signalling species that have a significant impact on the output of the entire system. Sensitivity analysis provides in-depth understanding of how mathematical models should be operated to best mimic the behaviour of biological networks and events, where each component of the signalling cascade is sensitive to the action of others [ 29 , 30 ]. In our current work, we have performed Local Sensitivity Analysis (LSA) for the reconstructed model. SimBiology computes time-dependent sensitivities of all species depending on their initial concentration and parametric values. The SimBiology Toolbox uses the Sundails solver type to perform the LSA by integrating the primary ODE of the model with the auxiliary differential equations to determine the sensitivity coefficient for every species/component in the system. Thus, the time-dependent sensitivities for a species, say x, with regard to its parameters y and z, are expressed as dx/dy and dx/dz, where the numerator denotes sensitivity output and the denominator denotes sensitivity input ( https://in.mathworks.com/help/simbio/ug/global-local-sensitivity-analysis-gsa-lsa-simbiology.html ). 2.5. Principal Component Analysis: Principal Component Analysis (PCA) is a well-known method for simplifying large multi-component biological networks by eliminating background noise and randomness from the network. PCA was calculated using sensitivity scores for each signalling component with respect to another in the system using the MATLAB function "score coefficient = princomp A," where A = m*n matrix. The variance in sensitivities of each signalling component in the system is represented by the principal component score. Highly linked species in biological networks are those that tend to convey the most information from one end to the other. Thus, because of their importance in establishing the phenotype of the biological system, removing the principal components from the biological network might cause the network as a whole to collapse [ 31 ]. 2.6. Flux Analysis: One of the best methods for identifying most important reactions in the system that could be involved in disease aetiology is through comparative flux analysis. The flux analysis determines the productivity of each reaction, and their contribution to the outcome of the biological system. It demonstrates the rate at which a metabolite or a signalling component is synthesized. In light of the fact that the pace at which the metabolite is produced will ultimately determine the outcome of the biological system, a higher rate of the reaction implies greater flux therefore is important for the axis to maintain its goal. In our study, we have used COPASI (4.45) a biochemical network simulator to compute the flux [ 31 , 32 ]. 2.7. Model Reduction: Model reduction is a method for streamlining biological networks by removing biochemical reactions that don't significantly affect the dynamics of the whole system. By minimizing extraneous parameters that are not contributing maximally to enrich the phenotype of the biological axis, model reduction makes it easier to anticipate the final outcome of the system by making the mathematical model more comprehensible [ 33 ]. In order to accomplish this in a systematic approach, we have combined the results of flux analysis and sensitivity analysis for filtering out reactions with low flux and sensitivity levels that have negligible impact on the output of the network. 2.8. Crosstalk Point Determination: A cross-talk point is a bridge between two or more biological signalling pathways that have been reconstructed. It is created when a single component or metabolite of the biological axis can regulate or is regulated by various signalling cascades. Cross-talk points facilitate the inter-communication among different biological networks and shape the dynamic outcomes of the system depending on their activity [ 34 ]. The cross-talk point in our study was computed for the reconstructed biological axis of hIAPP-mediated β-cell toxicity, by subtracting the in-degree of a node (species) across the overall network from the out-degree of a node (species) in a specific signalling pathway, producing a positive non-zero value. 3. Results The reconstructed mathematical model elucidated that the interactions between hIAPP oligomers and β-cell receptors prompted the activation of various metabolic and biological processes in the hIAPP-mediated β-cell toxicity axis. The pathogenicity of this axis was mediated through the generation of methylglyoxal, ROS and activation of PKC, cAMP, CytoC, NLRP3 and p62. This led the entire axis through events that facilitated the β-cell toxicity, dysfunction and loss of β-cell mass. 3.1. Reconstruction of signalling cascade and simulations The signalling cascade was reconstructed using SimBiology Model Builder. The mathematical model represented four compartments: β-cell, nucleus, mitochondria and endoplasmic reticulum (Table 1 ). Each compartment consisted of a set of reactions influenced by receptor-ligand interaction of insulin as well as hIAPP oligomers (Fig. 2 ). To simulate the entire signalling cascade, SimBiology Model Analyzer and the Ordinary Differential Equation (ODE15s) solver were used. This solver generated first-order non-linear ordinary differential equations (ODEs) to depict the pathogenicity and toxicity induced by hIAPP oligomers in β-cells over a duration of 100 seconds. The same solver was used to simulate the trigger events. The simulation generated concentration-versus-time graphs to visualize the dynamic changes in the concentrations of various molecular components within the hIAPP-mediated β-cell toxicity axis. The axis yielded significant outputs that corresponded to key biological features of β-cell dysfunction and toxicity in T2DM. These outputs including insulin resistance, altered glucose metabolism, mitochondrial and ER stress, defective autophagy, inflammation and apoptosis were governed by key signalling intermediates and transcription factors such as AP1, PDX1, NF-κB and STAT3. Table 1 Summary of compartments, species and their respective parameters. Sr. No. Compartment Components 1 Beta Cell 98 2 Endoplasmic Reticulum 11 3 Nucleus 7 4 Mitochondria 21 5 Total Number of Species 137 6 Total Number of Reactions 97 7 Total Number of Parameters 195 3.2. Trigger Events The trigger events were applied to track the evolutionary behaviour of biological processes and the reach of pathological effects of hIAPP oligomers mediating β-cell toxicity. In total five crucial reactions of the axis were subjected to trigger events which played a major role in the control of disease state. This helped us track the parametric alterations of various species affected by the event as well as the species undergoing the event itself. The list of reactions subjected to trigger events are summarized in Table 2 . These reactions were associated with the processes like insulin resistance, glycogen breakdown, autophagy defect, glycation and ER stress. Regulation of PKC at physiologically normal conditions does not affect insulin signalling and glucose metabolism. However, hyperactivation of PKC through RAGE and hIAPP oligomer interactions plays an important role in escalating insulin resistance eventually hindering the uptake of glucose in β-cells. On the other hand, since the body is under nutrient stress due to hyperglycaemic conditions β-cells are signalled to increase the production and secretion of insulin, this puts the endoplasmic reticulum through unfolded protein response signals that upregulate ER stress associated ATF6, PERK and IRE1α. Due to hyperglycaemic conditions alternates pathways such as polyol signalling is activated to metabolise glucose leading to the formation of sorbitol which further helps in regulating hIAPP glycation and oligomerization. Additionally, AKT blocks the GSK3B which facilitates inhibition of glycogen breakdown putting the islets through starvation. Autophagy, one of the critical processes involved in hIAPP regulation is impaired due to defects in lysosomal biogenesis via mTORC1 expression. All these events culminate to remodel the normal physiological signalling to work in a pathological manner. Table 2 List of reactions subjected to trigger events Sr. No. Trigger Event Reactions 1 GLUCOSE + Aldose Reductase ->Sorbitol 2 PKC & MAPK + IRS1 ->Insulin Resistance 3 proIAPP & proInsulin + Chaperon BiP ->PERK + ATF6 + IRE1α 4 mTORC1 + TFEB ->Depletion of Lysosome 5 AKT + GSK3B ->Inhibition of Glycogen Breakdown 3.3. Principal Component Analysis: Principal Component Analysis helps in identifying key molecular species that have the greatest impact on the overall dynamics and behaviour of the signalling system disregarding those species with background noise as they are involved in reactions with least effect. By considering the sensitivity profiles and score coefficients of all components in the interconnected axis principal components were identified having significant fluctuations. In addition to recognized T2DM hallmarks such as insulin resistance, PCA detected several elements that are likely to exert substantial effect on the regulation of pathogenicity of hIAPP oligomers in inducing β-cell toxicity. Notably, we observed the involvement of hIAPP monomers and intermediates of metabolic signalling such as methylglyoxal and αketoglutarate which facilitated oligomerization kinetics. PKC, IRS1, REDD1 and XBP1 involved in insulin resistance and ER stress response were also highlighted. Processes and events like GPCR signalling, Ca 2+ influx relating to autophagic defect, inflammation and β-cell death were corroborated with to the identification of GαS/GαQ, calpain, p62, NLRP3 and caspases as principal component species in the axis (Fig. 3 ). Besides the standard components, our analysis revealed numerous model-specific molecules depending on trigger events and sensitivities, that emerged as significant principal components that enhanced the interpretability of their roles played in governing the system, ensuring minimal loss of information. 3.4. Flux Analysis: In order to have a closer look at every reaction in the axis with respect to its kinetics (V max , K max ) and what role it plays in shaping the biological system we have computed molecular flux for every reaction. Amongst the total number of reactions involved in the biological network we considered reactions with high molecular flux to be crucial as these usually play a vital role in defining the outcome of the system having a substantial impact on the dynamics and behaviour of biological processes. By identifying these high flux reactions, we gained insights into the key molecular processes and interactions that drive the network towards pathogenicity and inevitable disease progression. Reactions with molecular flux ranging from 500 mol/s to 1200 mol/s were observed for processes like apoptosis through activation of caspases and APAF1, inflammation, autophagic defect through lysosomal depletion and p62 inclusions, glycation, mitochondrial and ER stress through generation of ROS and activation of cytoC (Table 3 ). Table 3 List of high flux reactions in the system governing the fate of the axis. Sr. No. Reactions Molecular Flux (mol/s) 1 PARP ->BC Death 1191.96 2 Caspase 3/6/7 ->PARP 895.472 3 Depletion of Lysosome ->p62 893.121 4 NOX1 + NADPH ->ROS + NOX1 746.004 5 p62 ->AUTOPHAGY DEFECT 697.195 6 Secretory Granules ->hIAPP monomer + Insulin 697.129 7 CytoC ->APAF1 696.833 8 hIAPP monomer + Methylglyoxal ->Amyloid Fibrils 696.467 9 APAF1 ->Caspase 9 696.467 10 Caspase 9 ->Caspase 3/6/7 696.467 11 Adenylyl Cyclase + ATP ->cAMP + Closure of K + Channels 695.823 12 DHAP + Methylglyoxal synthase ->Methylglyoxal 695.035 13 BID ->CytoC 596.311 14 mTORC1 + TFEB ->Depletion of Lysosome 502.855 3.5. Model Reduction: Model reduction is aimed at simplifying the system for better comprehensibility and understanding. The goal of model reduction is to retain essential species and interactions to achieve a robust and concise model for precisely replicating and predicting the outcome of a biological system. The model reduction was thus, adopted for the reconstructed hIAPP-mediated β-cell toxicity axis to eliminate extraneous elements and parameters aiding its precise prediction. The 3D Quasi-potential landscape graph was generated considering the molecular flux, sensitivity and concentration of species over the time duration of 100s (Fig. 4 ). The graph exhibited a peak-like pattern, which effectively demonstrated the concentration of high flux reactions and principal components at the top of the peak. The species with low molecular flux, sensitivity and concentration descended from the peak and were distributed at the bottom of the plot. The model reduction peak thus, represented the focal point of the network's dynamics and the most influential components within the system. 3.6. Crosstalk Point Determination: Cross-talk points serve as critical hubs where various signalling pathways converge through molecular components, allowing for extensive communication and coordination across distinct biological processes. Within the reconstructed mathematical model for hIAPP-mediated β-cell toxicity axis, a total of eight cross-talk points were identified communicating across crucial signalling pathways. These cross-talk points include caspases, cytoC, IL1β, PKC, NLRP3, ATF6, PERK and IRE1 (Fig. 5 ). Each of these species represents a point of convergence or intersection of insulin signalling, glycolysis, polyol signalling, TCA cycle, GPCR signalling, RAGE signalling, autophagy, ER stress, and Mitochondrial stress and apoptosis in the hIAPP-mediated β-cell toxicity axis culminating to facilitate the pathogenicity of the disease. 4. Discussion Type 2 Diabetes Mellitus remains a significant global health issue due to its widespread occurrence, as well as its morbidity and mortality rates. The rapid pace of economic growth, urbanization, and abrupt lifestyle shifts have contributed to the increasing global burden of T2DM. Current estimates suggest that over 530 million adults are affected, with projections indicating that this number could exceed 780 million by 2045 if effective prevention and treatment strategies are not implemented [ 35 ]. T2DM extends beyond hyperglycemia, representing a complex multisystem disorder associated with cardiovascular, neural, renal, and hepatological complications. These collectively contribute to increased global disability and premature mortality rates [ 36 ]. A hallmark of T2DM is the progressive reduction in pancreatic β-cell function and mass, primarily driven by the advancement of islet amyloidosis. Islet amyloidosis is characterized by the accumulation of amyloid fibrils, predominantly composed of human islet amyloid polypeptide. It is estimated that amyloid deposits are present in over 90% of patients with longstanding T2DM, highlighting their critical role in the disease pathology [ 12 ]. Far from merely being inert aggregates, hIAPP oligomers are cytotoxic species that disrupt β-cell membranes, induce oxidative and ER stress, cause insulin resistance, and initiate apoptotic cascades [ 37 , 38 ]. The toxic effects of hIAPP oligomers on β-cells are multidimensional. Their interaction with receptors activates toxic signalling intermediates that facilitate calcium influx, leading to autophagy defects and mitochondrial dysfunction through ROS generation. Additionally, in line with metabolic overload, oligomers induce ER stress by overwhelming its protein folding capacity and activating unfolded protein response signalling through PERK, IRE1, and ATF6 [ 22 ]. In our present study we have investigated the hIAPP-mediated β-cell toxicity axis through mathematical modelling using computational tool – MATLAB SimBiology ToolBox. The MATLAB SimBiology Toolbox is a potent tool widely used in systems and computational biology for mathematical modelling and simulation of complex biological systems. It offers a comprehensive platform to replicate, reconstruct, analyse and capture the multifaceted dynamics of intricate biological processes [ 39 ]. The hIAPP-mediated β-cell toxicity axis in T2DM is characterized by the dysregulation of several biological processes that culminate to apoptosis and contribute to loss of β-cell mass. Our data focusing on the reconstructed signalling axis highlights the activation and aberrant expression of crucial signalling intermediates such as PKC, IRS1, REDD1, XBP1, PERK, IRE1, ROS, cytoC, GαS/GαQ, calpain, p62, NLRP3, interleukins and caspases that augment the pathogenic effects of hIAPP oligomers. Additionally, the trigger event reactions incorporated into the system signifies the control of the disease state and fucntion as bottleneck reactions that heavily influence network stability. The use of trigger events helped in tracking the evolutionary behaviour of biological processes and the reach of pathological effects of hIAPP oligomers mediating β-cell toxicity. The trigger event reactions were associated with the processes like sorbitol production, PKC hyperactivation and insulin resistance, activation of UPR intermediates, autophagic defect and β-cell starvation representing critical switches that drive the β-cells from adaptation to dysfunction during the course of disease. Further, sensitivity analysis and principal component analysis of the model identified molecular species with strongest influence of methylglyoxal-induced fibril formation, ER stress sensors (PERK, IRE1, ATF6), mitochondrial amplifiers (cytochrome c, ROS), metabolic intermediates (methylglyoxal, α-ketoglutarate), lysosomal depletion and autophagy-associated molecules (p62, Gαs/Gαq, calpain, NLRP3, caspases) as key pathogenic regulators driving disease progression. This was validated through computing molecular flux for every reaction in the system. Flux analysis thus, provided a quantitative rationale for the dysregulated expression of signalling intermediates emphasized in critical biological processes. Next, the quasi-potential landscape graph for model reduction demonstrated a peak-like structure which indicated the concentration of high flux reactions and principal components at the peak of the dome. The entire model was reduced by 86% retaining only the essential components and interactions, involved in facilitating the dynamic outcome of the biological system (Fig. 4 ). The systems-level reconstruction further pointed to critical cross-talk molecules such as IL-1β, NLRP3, cytochrome c, caspases, and RAGE as nodal regulators that integrate signals from multiple pathways, involved in the axis thus, highlighting the reach of pathogenic effects of hIAPP oligomers. Although, islet amyloidosis in not a condition that has gone unaddressed however, the intricate mechanisms that the toxic hIAPP oligomers intervene with to mediate β-cell toxicity are yet to be fully elucidated. Certain reports suggest that hIAPP oligomers can cross the blood-brain barrier and have been shown to deposit in the brain, kidneys, heart, and liver of individuals with T2DM, where they contribute to neuroinflammation, nephropathy, cardiomyopathy, and hepatic dysfunction [ 40 , 41 , 42 ]. These extraprancreatic effects explain the high mortality risk associated with T2DM highlighting the importance of developing new therapeutic approaches that address amyloid toxicity at its origin, rather than focusing solely on insulin sensitization in diabetic patients. Despite advances in diabetes management, current therapies largely fail to address the hIAPP aggregation or proteostasis defects. While the therapies like metformin improve insulin sensitivity and reduces hepatic glucose production, it does not effectively prevent amylin fibril formation or restore autophagic function, which may explain the continued progression of β-cell loss in patients despite receiving therapeutic care [ 43 ]. This broader perspective aligns with our systems-level analysis, which integrates pancreatic consequences into a unified model of disease progression. Our findings provide a comprehensive framework that consolidates diverse experimental observations into a single mechanistic narrative. The mathematical model for the hIAPP-mediated β-cell toxicity axis was reconstructed using a number of enzyme kinetics and parameters which provided a computable framework of all the signalling components giving us valuable insights to predict the best behavioural outcomes of the system. The findings point toward potential combinatorial therapeutic strategies employed to modulate the receptor activities of RAGE and GPCR pathways. RAGE blockade has shown protective effects in models of atherosclerosis, neurodegeneration, and other diabetic complications [ 44 , 45 ], suggesting that similar benefits may be achievable in the context of β-cell amyloidosis. Restoring autophagic flow and preventing lysosomal biogenesis errors can be one of the approaches used to modulate calcium influx by targeting the calcitonin receptor or GPCR signalling. The growing prevalence of this chronic condition, coupled with the underappreciated role of hIAPP deposits and toxic oligomers, highlights the urgent need for innovative strategies that can protect β-cell functionality and improve long-term outcomes. Our study lays the groundwork for the next generation of therapeutic interventions for the hIAPP- mediated β-cell toxicity. The fine-tuning of the mathematical model will require a step wise validation of crucial points and processes through in vitro and in vivo studies. Once the appropriate level of optimization has been achieved, the model may be used to tweak therapeutic targets and reproduce the physiological response. Declarations Conflicts of interest The authors have no conflicts of interest to declare. Funding This research was funded by Science and Engineering Research Board (SERB), Government of India (File No. EEQ/2023/000151). Author Contribution RNG designed the project, KK performed in silico experiments and drafted the manuscript. AP helped in data mobilization manuscript improvement. Acknowledgment: RNG sincerely acknowledges the financial assistance from SERB (File No. EEQ/2023/000151) and RUSA Phase 2 grant of SPPU Pune. KK acknowledges SERB for providing project assistance fellowship. Data Availability Data generated is provided within the manuscript and supplementary information files. References Silvestre, R. A. et al. Inhibitory effect of rat amylin on the insulin responses to glucose and arginine in the perfused rat pancreas. Regul. Pept. 31 (1), 23–31 (1990). Opie, E. L. The relation Oe diabetes mellitus to lesions of the Pancreas. Hyaline degeneration of the Islands Oe Langerhans. J. Exp. Med. 5 (5), 527 (1901). Ehrlich, J. C. & Irving, M. Ratner. Amyloidosis of the islets of Langerhans: a restudy of islet hyalin in diabetic and nondiabetic individuals. Am. J. Pathol. 38 (1), 49 (1961). 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Circulation 106 , 2827–2835 (2002). Bierhaus, A. et al. Understanding RAGE, the receptor for advanced glycation end products. J. Mol. Med. 83 (11), 876–886 (2005). Additional Declarations No competing interests reported. Supplementary Files SupplementaryData.xlsx SupplemntarydataT2DMAxis.sbproj Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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1","display":"","copyAsset":false,"role":"figure","size":594900,"visible":true,"origin":"","legend":"\u003cp\u003eOverview of the hIAPP-mediated β-cell toxicity axis during T2DM.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7722499/v1/c6ace25dbf30d69ccd4557f7.png"},{"id":94107931,"identity":"c9c5c2d5-cc3c-43cc-b01b-c3f7c1bff300","added_by":"auto","created_at":"2025-10-22 12:45:54","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":554799,"visible":true,"origin":"","legend":"\u003cp\u003eReconstructed mathematical model depicting the hIAPP-mediated β-cell toxicity signalling axis during T2DM. The model consists of four compartments including Beta Cell, Nucleus, Endoplasmic Reticulum and Mitochondria. All the signalling components/species are connected across these compartments.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7722499/v1/bd351687c90ca0f4a484da6c.png"},{"id":94107929,"identity":"ae1da987-dc5f-41a5-a4af-a1da94768a45","added_by":"auto","created_at":"2025-10-22 12:45:54","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":539780,"visible":true,"origin":"","legend":"\u003cp\u003ePrincipal Component Analysis depicting components with high sensitivities and PCA score coefficients.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7722499/v1/050fd5ddf70a9aba5065792f.png"},{"id":94109303,"identity":"10bc9d72-bcdf-4c82-9b81-191c9dbf12a7","added_by":"auto","created_at":"2025-10-22 13:01:54","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":453639,"visible":true,"origin":"","legend":"\u003cp\u003e3D Quasi-potential landscape graph representing Model Reduction. The peak-like pattern reflects concentration of high flux reactions and principal components at the top of the peak. X-axis = sensitivity score, Y-axis = molecular concentration and Z-axis = molecular flux.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7722499/v1/ef6d3bf35beb9bff07aa509c.png"},{"id":94107935,"identity":"eef15f07-5b25-4973-9098-dc287b805a86","added_by":"auto","created_at":"2025-10-22 12:45:54","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":33655,"visible":true,"origin":"","legend":"\u003cp\u003eCrosstalk points\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-7722499/v1/c4c24263e054a3573a8131b5.png"},{"id":102746588,"identity":"f0f3c03b-7ae0-4e6a-8bd5-a1cdb69536b2","added_by":"auto","created_at":"2026-02-16 08:58:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2689542,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7722499/v1/f0381126-0c84-440c-9b8b-70f506ea409e.pdf"},{"id":94108757,"identity":"b83a57d3-d2a4-4319-aa37-7803e62310b2","added_by":"auto","created_at":"2025-10-22 12:53:54","extension":"xlsx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":540779,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryData.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-7722499/v1/8e80656f634bb9f7a6521a1c.xlsx"},{"id":94108754,"identity":"40040a5d-23f1-4a8e-b8ea-a261d8cc4473","added_by":"auto","created_at":"2025-10-22 12:53:54","extension":"sbproj","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":966179,"visible":true,"origin":"","legend":"","description":"","filename":"SupplemntarydataT2DMAxis.sbproj","url":"https://assets-eu.researchsquare.com/files/rs-7722499/v1/92d8ca92558ecae52c36b08e.sbproj"}],"financialInterests":"No competing interests reported.","formattedTitle":"Elucidating the pathological axis of hIAPP-mediated β-cell toxicity: A MATLAB-based network modelling","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIslet amyloidosis is a chronic condition developed during the course of prolonged hyperglycaemia in Type II Diabetes Mellitus (T2DM). It is characterized by the accumulation of amyloid deposits formed through aggregation of amyloidogenic peptide known as Islet Amyloid Poly-Peptide (IAPP) within the Islets of Langerhans causing their loss of function and mass. IAPP aggregates are attributed to defective glucose regulation, mitochondrial and endoplasmic reticulum (ER) stress, increased β-cell toxicity, dysfunction and apoptosis; and are best characterized by their physiological role in being able to inhibit insulin secretion causing insulin resistance through a direct paracrine effect on the β-cells [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]. IAPP deposits in the pancreas of a T2DM patient were first described in 1901 as hyaline lesions [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] however, were later described as proteinaceous amyloid plaques in 1961 [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]. Proteinaceous plaques are mainly formed due to aberrations in protein folding mechanisms leading to misfolded protein aggregates and deposits in the cells causing severe damage to the organs and surrounding areas [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIAPP exhibits endocrine, paracrine and autocrine functions. Human IAPP (hIAPP) is expressed as an 89 amino acid pre-pro-peptide and post-translationally 22 amino acids are cleaved from the N-terminus to give a 67-amino acid peptide called proIAPP. proIAPP is then altered in the lumen of ER by forming a disulphide bond between cysteines at position 2 and 7. This altered peptide is transported to the Golgi Complex to be packed in the secretory granules and further be cleaved into a final 37 amino acid peptide modified by amidation at the C-terminus [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Under normal physiological conditions this active form of hIAPP is co-expressed, co-processed and co-secreted with insulin in a molar ratio of 1:100 to regulate blood glucose levels; however, during chronic hyperglycaemic conditions this ratio is heavily altered [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]. Aggregation or oligomerization of hIAPP has been associated with histidine and tyrosine residues present at 18 and 37 positions respectively. Hydrophobic and aromatic interactions between amyloidogenic areas 15\u0026ndash;20 and 22\u0026ndash;29 have been demonstrated to induce the structural rearrangement of random coil structures to pentameric β-sheet oligomers, with residues 23\u0026ndash;27 playing a significant role [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Extensive evidences suggest that hIAPP oligomerizes intracellularly as a result of incorrect processing of proIAPP in the secretory granules and released as deposits into extracellular space when β-cells degenerate. Apart from the physicochemical alterations, perturbations in the biological processes also hold a significant weight in the oligomerization of hIAPP leading to loss of β-cell mass.\u003c/p\u003e\u003cp\u003eTo maintain the homeostatic blood glucose levels during hyperglycaemic conditions the insulin secreted by the pancreatic β-cells initiate the glucose metabolism process via insulin signalling pathway. This pathway is triggered when the glucose uptake by GLUT2 transporters has increased intracellularly; the glucose is metabolised increasing the ATP levels which close the K\u003csup\u003e+\u003c/sup\u003e channels and escalates Ca\u003csub\u003e2+\u003c/sub\u003e influx which prompts the secretory granules to release the stored insulin. Once, secreted this insulin binds the insulin receptors facilitating autophosphorylation. Insulin receptor substrate-1 (IRS1) is recruited by activated insulin receptors and phosphorylated at the Tyr residue. This allows phosphatidylinositol 3-kinase (PI3K) to dock and further catalyse the conversion of PIP2 to PIP3, which induces AKT activation. GLUT4 translocation for glucose uptake is facilitated by activated AKT, and its metabolism is supported through processes such as glycolysis, TCA cycle and glycogen synthesis through inhibition of glycogen synthase kinase-3 (GSK3β). In β-cells, this signalling is tightly coupled with nutrient sensing to insulin exocytosis, ensuring that increased circulating glucose triggers enhanced hormone release [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e].\u003c/p\u003e\u003cp\u003ePersistently elevated blood glucose levels place a heavy metabolic burden on β-cells creating glycolytic overload. As a compensatory mechanism excess glucose is rapidly metabolized to meet insulin synthesis demands and by default synthesizing hIAPP along with insulin. The proteostatic environment is usually maintained when the secretory granules release their contents, however, when there is a higher demand for insulin, the cytosolic pool of hIAPP will also rise and there will be greater chance of aggregation and deposition of aggregates around β-cells. This metabolic strain promotes diversion of glucose into secondary metabolic pathways generating glycotoxic byproducts that again accelerate the misfolding and oligomerization of already produced hIAPP. Despite the considerable research available linking hIAPP with T2DM, hIAPP misfolding, deposits as plaques throughout different parts of the body little amount of research is available on the integrative role of toxic hIAPP oligomers as central regulators of β-cell toxicity. In this study we elaborate and corroborate the role that toxic hIAPP oligomers may have in contributing towards aberrant functioning of several biological processes that lead to insulin resistance, ER and mitochondrial stress, autophagy failure, inflammation and β-cell death during T2DM. The perturbations in these signalling pathways are subject to two major events firstly the changes in the blood glucose levels and its influence on the oligomerization of hIAPP. Understanding the impact of these events on the tempering of various metabolic and biological processes will prove to be crucial in following the evolution and reach of the disease. Our study mainly focuses on deciphering the hIAPP mediated β-cell toxicity axis in islet amyloidosis during T2DM, which could offer new insights in developing precision and targeted therapies for this condition.\u003c/p\u003e\u003cdiv id=\"Sec2\" class=\"Section2\"\u003e\u003ch2\u003e1.1. The hIAPP mediated β-cell toxicity axis\u003c/h2\u003e\u003cp\u003eOnce, the glucose uptake is levelled up through the GLUT4 transporters it is rapidly converted to pyruvate through sequential enzymatic steps of glycolysis. Pyruvate is an essential node that connects the mitochondrial TCA cycle and glycolysis. The pyruvate dehydrogenase complex in mitochondria transforms pyruvate into acetyl-CoA, through the production of metabolic intermediates from citrate to oxaloacetate the TCA cycle advances and produces ATP and NADH during oxidative phosphorylation [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Additional regulatory features of this metabolic signalling are initiated by continuous glucose influx where anaplerotic flux converts back oxaloacetate to phosphoenolpyruvate via phosphoenolpyruvate carboxylase. This phosphoenolpyruvate can re-enter glycolysis cycle producing pyruvate in a feedback loop where recurrent cycling of oxaloacetate-PEP-pyruvate feeds into α-ketoglutarate production. Increased production of α-ketoglutarate acts as a metabolic signal for secretory granules to promote the release of stored insulin and hIAPP monomers [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. Apart from this under conditions of chronic metabolic burden excessive glucose is shunted into secondary metabolic pathways most notably the polyol pathway where the aldose reductase reduces glucose to sorbitol which is then oxidized to fructose pushing it back into the glycolysis cycle. During this reaction methylglyoxal a highly reactive dicarbonyl molecule is generated as a byproduct. As a glycation agent methylglyoxal functions in altering the structural conformations of hIAPP monomers speeding up its oligomerization. As a result, soluble hIAPP monomers are transformed into insoluble toxic oligomeric assemblies characterized by β-sheets [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Notably, the hIAPP oligomers rather than the mature fibrils are the prominent mediators of cellular toxicity and their formation can be influenced not only by the intrinsic amyloidogenic properties but also extrinsic molecular factors and non-canonical processes that promote protein misfolding [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eOnce formed these hIAPP oligomers engage in cellular toxicity by two mechanisms including receptor mediated interactions and non-receptor mediated events (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The receptor for advanced glycation end products (RAGE) can bind hIAPP oligomers due to its oligomerization being enhanced by glycation. RAGE is not only involved in eliciting signalling responses leading to inflammation and apoptosis but also plays a crucial role in causing insulin resistance during T2DM. Interaction of hIAPP oligomers with RAGE leads to the recruitment and activation of protein kinase C (PKC), which carries out IRS1 phosphorylation at serine/threonine residues. This impairs normal IRS1 functioning and damages the insulin mediated PI3K/AKT signalling inhibiting glucose uptake and metabolism, thus, leading to insulin resistance in β-cells [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]. Parallelly, β-cell apoptosis characterized by release of cytochrome C (CytoC) and activation of caspases is mediated by hIAPP-RAGE signalling. PKC activates NADPH oxidase (NOX), which takes up hydrogen from NADPH formed in mitochondria and releases a reactive oxygen species (ROS) harmful to the cells. ROS production mostly occurs through the electron transport chain in mitochondria however, activated PKC triggers the stress-related JNK/p38 signalling pathway which stimulates NOX for ROS generation in β-cells [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. The activated JNK mediates β-cell apoptosis by activating a range of events leading to mitochondrial and ER stress, ROS formation and production of pro-inflammatory cytokines.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003eReactive oxygen species formed permeabilizes the outer mitochondrial membrane to release CytoC into the cytosol which further initiates the intrinsic apoptotic cascade by binding to the APAF1 forming the apoptosome assembly activating caspase 9 for cell death [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Additionally, it also acts as signalling molecules that participates in the activation of NLRP3 inflammasome. Inflammasome formation triggers the activation and release of pro-inflammatory cytokines such as IL-1β, IL-6, IL-18 and TNFα. Systemic release of these cytokines induces islet inflammation that plays a major role in β-cell dysfunction and apoptosis activation [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Further through NF-κB-mediated transcription pro-inflammatory cytokine expression is amplified, recruiting immune responses that worsen β-cell injury. These cytokines initiate an inflammatory response that does not act in isolation; rather, it primes β-cells for apoptosis by enhancing Fas receptor expression on their surface. Thus, inflammation, oxidative stress, and failed proteostasis converge to channel β-cells toward programmed cell death, making apoptosis an inevitable point.\u003c/p\u003e\u003cp\u003eApart from this constant exposure of β-cells to increased nutrient levels demands and increase in insulin biosynthesis as discussed earlier. As this demand becomes chronic, the biosynthesis and secretion process may eventually overload the protein folding capacity of the ER leading to the saturation of chaperon BiP and activation of the unfolded protein response (UPR) which senses the activation of PERK, IRE1α, and ATF6. Chronic nutrient stress will uncouple translational control from protein folding capacity of the ER leading to its dysfunction, miss-processing of proIAPP and proInsulin and accumulation of misfolded protein cargo in the β-cells [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. These misfolded proteins are targeted for polyubiquitination and degradation by autophagy under physiologically normal conditions. hIAPP oligomers have the ability to engage with calcitonin receptor (CTR) which recruits receptor activity-modifying protein 3 (RAMP3) and activate the GPCR signalling via Gαs/Gαq intermediates. This elevates the levels of cyclic AMP (cAMP) that initiates the closure of K\u003csup\u003e+\u003c/sup\u003e channels and depolarizes the membrane to open voltage-gated Ca\u003csub\u003e2+\u003c/sub\u003e channels. Increased Ca\u003csub\u003e2+\u003c/sub\u003e concentrations lead to disruption of lysosomal membranes preventing its fusion with the autophagosomes for degradation of misfolded protein cargos. Under physiologically normal circumstances, autophagy maintains β-cell proteostasis by degrading excess proInsulin and IAPP monomers through lysosomal clearance. Polyubiquitinated proteins are destined for degradation by autophagy through ubiquitin binding p62/sequestosome 1 (SQSTM1) which itself gets degraded in autophagosome along with the cargo. However, during islet amyloidosis defective autophagy in β-cells results in accumulation of p62 forming cytoplasmic inclusions as an indicator of impaired autophagic flux [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eUltimately, the toxicity of hIAPP oligomers establishes a pathological cascade converging various metabolic and biological processes. The fate of the hIAPP mediated β-cell toxicity axis in islet amyloidosis during T2DM is β-cell dysfunction and loss of β-cell mass culminating to a decline of insulin secretory capacity. These events not only contribute to the degeneration of pancreatic functions but also intensifies the systemic insulin resistance and chronic hyperglycaemic conditions. Based on existing biological data to get a greater insight into this intricate pathological axis, we reconstructed a kinetic model interpreting this signalling network using a systems and computational biology approach which emphasizes its key molecular interactions [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. For this purpose, we have used Systems Biology Markup Language \u0026ndash; based MATLAB SimBiology Toolbox R2024b. Through the mathematical model we have thus, worked two extremely important objectives: firstly, to contribute to a deeper understanding of the biological events under study in a manner that is simple to be replicated in silico and conveyed; secondly, to make it possible in the future to design in vitro and in vivo experiments that specifically track the predicted features (vital cross-talks) of this biological system in order to follow the reach of the pathological network.\u003c/p\u003e\u003c/div\u003e"},{"header":"2. Methodology","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.1. Data Preparation:\u003c/h2\u003e\u003cp\u003eTo decipher and reconstruct the hIAPP mediated β-cell toxicity axis fragmented data was gathered through thorough literature reviews and signalling database searches such as KEGG and GEO Dataset [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Quantitative Modelling and Simulations:\u003c/h2\u003e\u003cp\u003eQuantitative modelling of biological reactions was done using SimBiology Model Builder; it involves the application of appropriate kinetic rate laws, parameter estimation, and initial component concentration (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://in.mathworks.com/help/simbio/\u003c/span\u003e\u003cspan address=\"https://in.mathworks.com/help/simbio/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). The kinetic rate laws implemented in the SimBiology Toolbox for the reconstructed models were as follows: 1) The Law of Mass Action, was applied to association and dissociation reactions. 2) The Henri-Michaelis-Menten equation, was employed for phosphorylation, dephosphorylation, and ubiquitination reactions. 3) Hill's kinetic equation was applied for gene expression reactions. Initial concentrations of signalling components were determined considering experimentally known concentrations from the literature, indicating that a cell can secrete 10\u003csup\u003e3\u003c/sup\u003e -10\u003csup\u003e6\u003c/sup\u003e signalling molecules [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. The parameter estimation and model simulations were regulated in such a manner that the mathematical model could mimic the behaviour of the signalling events taking place in the β-cell during the course of islet amyloidosis in T2DM. Simulations of the mathematical model were performed using the Stiff Deterministic ODE15s solver type for 100 seconds time units in SimBiology Model Analyzer, which generates the first-order non-linear ODEs, that provides a state versus time graph for each node (molecule/species) to determine their dynamic behaviour in the system over time defining the mathematical framework used in SimBiology [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. This discrete transition depends on the conditions applied i.e., the reaction rate (V\u003csub\u003emax\u003c/sub\u003e), and the concentration of the substrate (K\u003csub\u003emax\u003c/sub\u003e) at a given time.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Trigger Events:\u003c/h2\u003e\u003cp\u003eA per the SimBiology User Guide documentation provided by Mathworks, in addition to simulations, species in the model can be assigned trigger events such that they demonstrate a discrete transition in their concentration regulating the final outcome of the system (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://in.mathworks.com/help/simbio/ug/event-object.html\u003c/span\u003e\u003cspan address=\"https://in.mathworks.com/help/simbio/ug/event-object.html\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). In mathematical modelling of biological networks an event describes a particular process discretely transitioning from its normal functioning and progresses towards an abnormality. These transitions occur when a customized time and concentration condition becomes true. Such conditions are defined as Event objects in the model as they have the trigger property that must be true for an event to execute. For instance, if a specific simulation time is considered as a triggering object, then at that time the amounts/values/parameters of a particular species are changed in such a way that an event occurs. In response to the dynamics of the events in the system certain other species are affected even though they are not tied to the triggering time or concentration. The reactions or species participating in triggering events are of great importance as they ultimately govern the fate of the biological processes causing it to switch or transition between normal and pathological forms during disease condition. In SimBiology we need to use a combination of relational and logical operators to execute a trigger event. In addition to Event objects an EventFcns property needs to be specified which occurs when an event is triggered. The EventFcns property of an event specifies a condition that is time \u0026ndash; dependent or time \u0026ndash; independent. For example, at a time\u0026thinsp;\u0026gt;\u0026thinsp;=\u0026thinsp;25 seconds, and at a species concentration of X\u0026thinsp;=\u0026thinsp;150 molecule per second will trigger an event where post 25 seconds the axis with switch from its normal functioning depending on the change in concentration of the species X. In our model we have employed time \u0026ndash; dependent simulation of trigger events which allowed us to specify the EventFcns property with respect to change in concentration and parameters associated with the species at given time\u0026thinsp;=\u0026thinsp;20 seconds or 50 seconds.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.4. Sensitivity Analysis:\u003c/h2\u003e\u003cp\u003eIn order to determine the interdependence of the components and robustness of the biological network, sensitivity analysis of the mathematical model was carried out. According to various factors, including the biochemical process they are involved in, the kinetic law used, and the set of parameters the components are subjected to, the sensitivity analysis of the model provides information about the most important signalling species that have a significant impact on the output of the entire system. Sensitivity analysis provides in-depth understanding of how mathematical models should be operated to best mimic the behaviour of biological networks and events, where each component of the signalling cascade is sensitive to the action of others [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e, \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. In our current work, we have performed Local Sensitivity Analysis (LSA) for the reconstructed model. SimBiology computes time-dependent sensitivities of all species depending on their initial concentration and parametric values. The SimBiology Toolbox uses the Sundails solver type to perform the LSA by integrating the primary ODE of the model with the auxiliary differential equations to determine the sensitivity coefficient for every species/component in the system. Thus, the time-dependent sensitivities for a species, say x, with regard to its parameters y and z, are expressed as dx/dy and dx/dz, where the numerator denotes sensitivity output and the denominator denotes sensitivity input (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://in.mathworks.com/help/simbio/ug/global-local-sensitivity-analysis-gsa-lsa-simbiology.html\u003c/span\u003e\u003cspan address=\"https://in.mathworks.com/help/simbio/ug/global-local-sensitivity-analysis-gsa-lsa-simbiology.html\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e\u003ch2\u003e2.5. Principal Component Analysis:\u003c/h2\u003e\u003cp\u003ePrincipal Component Analysis (PCA) is a well-known method for simplifying large multi-component biological networks by eliminating background noise and randomness from the network. PCA was calculated using sensitivity scores for each signalling component with respect to another in the system using the MATLAB function \"score coefficient\u0026thinsp;=\u0026thinsp;princomp A,\" where A\u0026thinsp;=\u0026thinsp;m*n matrix. The variance in sensitivities of each signalling component in the system is represented by the principal component score. Highly linked species in biological networks are those that tend to convey the most information from one end to the other. Thus, because of their importance in establishing the phenotype of the biological system, removing the principal components from the biological network might cause the network as a whole to collapse [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e2.6. Flux Analysis:\u003c/h2\u003e\u003cp\u003eOne of the best methods for identifying most important reactions in the system that could be involved in disease aetiology is through comparative flux analysis. The flux analysis determines the productivity of each reaction, and their contribution to the outcome of the biological system. It demonstrates the rate at which a metabolite or a signalling component is synthesized. In light of the fact that the pace at which the metabolite is produced will ultimately determine the outcome of the biological system, a higher rate of the reaction implies greater flux therefore is important for the axis to maintain its goal. In our study, we have used COPASI (4.45) a biochemical network simulator to compute the flux [\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e].\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e2.7. Model Reduction:\u003c/h2\u003e\u003cp\u003eModel reduction is a method for streamlining biological networks by removing biochemical reactions that don't significantly affect the dynamics of the whole system. By minimizing extraneous parameters that are not contributing maximally to enrich the phenotype of the biological axis, model reduction makes it easier to anticipate the final outcome of the system by making the mathematical model more comprehensible [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. In order to accomplish this in a systematic approach, we have combined the results of flux analysis and sensitivity analysis for filtering out reactions with low flux and sensitivity levels that have negligible impact on the output of the network.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e2.8. Crosstalk Point Determination:\u003c/h2\u003e\u003cp\u003eA cross-talk point is a bridge between two or more biological signalling pathways that have been reconstructed. It is created when a single component or metabolite of the biological axis can regulate or is regulated by various signalling cascades. Cross-talk points facilitate the inter-communication among different biological networks and shape the dynamic outcomes of the system depending on their activity [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e]. The cross-talk point in our study was computed for the reconstructed biological axis of hIAPP-mediated β-cell toxicity, by subtracting the in-degree of a node (species) across the overall network from the out-degree of a node (species) in a specific signalling pathway, producing a positive non-zero value.\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eThe reconstructed mathematical model elucidated that the interactions between hIAPP oligomers and β-cell receptors prompted the activation of various metabolic and biological processes in the hIAPP-mediated β-cell toxicity axis. The pathogenicity of this axis was mediated through the generation of methylglyoxal, ROS and activation of PKC, cAMP, CytoC, NLRP3 and p62. This led the entire axis through events that facilitated the β-cell toxicity, dysfunction and loss of β-cell mass.\u003c/p\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Reconstruction of signalling cascade and simulations\u003c/h2\u003e\u003cp\u003eThe signalling cascade was reconstructed using SimBiology Model Builder. The mathematical model represented four compartments: β-cell, nucleus, mitochondria and endoplasmic reticulum (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). Each compartment consisted of a set of reactions influenced by receptor-ligand interaction of insulin as well as hIAPP oligomers (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). To simulate the entire signalling cascade, SimBiology Model Analyzer and the Ordinary Differential Equation (ODE15s) solver were used. This solver generated first-order non-linear ordinary differential equations (ODEs) to depict the pathogenicity and toxicity induced by hIAPP oligomers in β-cells over a duration of 100 seconds. The same solver was used to simulate the trigger events. The simulation generated concentration-versus-time graphs to visualize the dynamic changes in the concentrations of various molecular components within the hIAPP-mediated β-cell toxicity axis. The axis yielded significant outputs that corresponded to key biological features of β-cell dysfunction and toxicity in T2DM. These outputs including insulin resistance, altered glucose metabolism, mitochondrial and ER stress, defective autophagy, inflammation and apoptosis were governed by key signalling intermediates and transcription factors such as AP1, PDX1, NF-κB and STAT3.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eSummary of compartments, species and their respective parameters.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSr. No.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCompartment\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eComponents\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBeta Cell\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e98\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eEndoplasmic Reticulum\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNucleus\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eMitochondria\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e21\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTotal Number of Species\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e137\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTotal Number of Reactions\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e97\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTotal Number of Parameters\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e195\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e3.2. Trigger Events\u003c/h2\u003e\u003cp\u003eThe trigger events were applied to track the evolutionary behaviour of biological processes and the reach of pathological effects of hIAPP oligomers mediating β-cell toxicity. In total five crucial reactions of the axis were subjected to trigger events which played a major role in the control of disease state. This helped us track the parametric alterations of various species affected by the event as well as the species undergoing the event itself. The list of reactions subjected to trigger events are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. These reactions were associated with the processes like insulin resistance, glycogen breakdown, autophagy defect, glycation and ER stress. Regulation of PKC at physiologically normal conditions does not affect insulin signalling and glucose metabolism. However, hyperactivation of PKC through RAGE and hIAPP oligomer interactions plays an important role in escalating insulin resistance eventually hindering the uptake of glucose in β-cells. On the other hand, since the body is under nutrient stress due to hyperglycaemic conditions β-cells are signalled to increase the production and secretion of insulin, this puts the endoplasmic reticulum through unfolded protein response signals that upregulate ER stress associated ATF6, PERK and IRE1α. Due to hyperglycaemic conditions alternates pathways such as polyol signalling is activated to metabolise glucose leading to the formation of sorbitol which further helps in regulating hIAPP glycation and oligomerization. Additionally, AKT blocks the GSK3B which facilitates inhibition of glycogen breakdown putting the islets through starvation. Autophagy, one of the critical processes involved in hIAPP regulation is impaired due to defects in lysosomal biogenesis via mTORC1 expression. All these events culminate to remodel the normal physiological signalling to work in a pathological manner.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eList of reactions subjected to trigger events\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"2\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSr. No.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTrigger Event Reactions\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eGLUCOSE\u0026thinsp;+\u0026thinsp;Aldose Reductase -\u0026gt;Sorbitol\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePKC \u0026amp; MAPK\u0026thinsp;+\u0026thinsp;IRS1 -\u0026gt;Insulin Resistance\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eproIAPP \u0026amp; proInsulin\u0026thinsp;+\u0026thinsp;Chaperon BiP -\u0026gt;PERK\u0026thinsp;+\u0026thinsp;ATF6\u0026thinsp;+\u0026thinsp;IRE1α\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003emTORC1\u0026thinsp;+\u0026thinsp;TFEB -\u0026gt;Depletion of Lysosome\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAKT\u0026thinsp;+\u0026thinsp;GSK3B -\u0026gt;Inhibition of Glycogen Breakdown\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e\u003ch2\u003e3.3. Principal Component Analysis:\u003c/h2\u003e\u003cp\u003ePrincipal Component Analysis helps in identifying key molecular species that have the greatest impact on the overall dynamics and behaviour of the signalling system disregarding those species with background noise as they are involved in reactions with least effect. By considering the sensitivity profiles and score coefficients of all components in the interconnected axis principal components were identified having significant fluctuations. In addition to recognized T2DM hallmarks such as insulin resistance, PCA detected several elements that are likely to exert substantial effect on the regulation of pathogenicity of hIAPP oligomers in inducing β-cell toxicity. Notably, we observed the involvement of hIAPP monomers and intermediates of metabolic signalling such as methylglyoxal and αketoglutarate which facilitated oligomerization kinetics. PKC, IRS1, REDD1 and XBP1 involved in insulin resistance and ER stress response were also highlighted. Processes and events like GPCR signalling, Ca\u003csub\u003e2+\u003c/sub\u003e influx relating to autophagic defect, inflammation and β-cell death were corroborated with to the identification of GαS/GαQ, calpain, p62, NLRP3 and caspases as principal component species in the axis (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). Besides the standard components, our analysis revealed numerous model-specific molecules depending on trigger events and sensitivities, that emerged as significant principal components that enhanced the interpretability of their roles played in governing the system, ensuring minimal loss of information.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec16\" class=\"Section2\"\u003e\u003ch2\u003e3.4. Flux Analysis:\u003c/h2\u003e\u003cp\u003eIn order to have a closer look at every reaction in the axis with respect to its kinetics (V\u003csub\u003emax\u003c/sub\u003e, K\u003csub\u003emax\u003c/sub\u003e) and what role it plays in shaping the biological system we have computed molecular flux for every reaction. Amongst the total number of reactions involved in the biological network we considered reactions with high molecular flux to be crucial as these usually play a vital role in defining the outcome of the system having a substantial impact on the dynamics and behaviour of biological processes. By identifying these high flux reactions, we gained insights into the key molecular processes and interactions that drive the network towards pathogenicity and inevitable disease progression. Reactions with molecular flux ranging from 500 mol/s to 1200 mol/s were observed for processes like apoptosis through activation of caspases and APAF1, inflammation, autophagic defect through lysosomal depletion and p62 inclusions, glycation, mitochondrial and ER stress through generation of ROS and activation of cytoC (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eList of high flux reactions in the system governing the fate of the axis.\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"3\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSr. No.\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eReactions\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMolecular Flux (mol/s)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ePARP -\u0026gt;BC Death\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e1191.96\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCaspase 3/6/7 -\u0026gt;PARP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e895.472\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDepletion of Lysosome -\u0026gt;p62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e893.121\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNOX1\u0026thinsp;+\u0026thinsp;NADPH -\u0026gt;ROS\u0026thinsp;+\u0026thinsp;NOX1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e746.004\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ep62 -\u0026gt;AUTOPHAGY DEFECT\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e697.195\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eSecretory Granules -\u0026gt;hIAPP monomer\u0026thinsp;+\u0026thinsp;Insulin\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e697.129\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCytoC -\u0026gt;APAF1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e696.833\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ehIAPP monomer\u0026thinsp;+\u0026thinsp;Methylglyoxal -\u0026gt;Amyloid Fibrils\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e696.467\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAPAF1 -\u0026gt;Caspase 9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e696.467\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eCaspase 9 -\u0026gt;Caspase 3/6/7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e696.467\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eAdenylyl Cyclase\u0026thinsp;+\u0026thinsp;ATP -\u0026gt;cAMP\u0026thinsp;+\u0026thinsp;Closure of K\u003csup\u003e+\u003c/sup\u003e Channels\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e695.823\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eDHAP\u0026thinsp;+\u0026thinsp;Methylglyoxal synthase -\u0026gt;Methylglyoxal\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e695.035\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBID -\u0026gt;CytoC\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e596.311\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003emTORC1\u0026thinsp;+\u0026thinsp;TFEB -\u0026gt;Depletion of Lysosome\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e502.855\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec17\" class=\"Section2\"\u003e\u003ch2\u003e3.5. Model Reduction:\u003c/h2\u003e\u003cp\u003eModel reduction is aimed at simplifying the system for better comprehensibility and understanding. The goal of model reduction is to retain essential species and interactions to achieve a robust and concise model for precisely replicating and predicting the outcome of a biological system. The model reduction was thus, adopted for the reconstructed hIAPP-mediated β-cell toxicity axis to eliminate extraneous elements and parameters aiding its precise prediction. The 3D Quasi-potential landscape graph was generated considering the molecular flux, sensitivity and concentration of species over the time duration of 100s (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The graph exhibited a peak-like pattern, which effectively demonstrated the concentration of high flux reactions and principal components at the top of the peak. The species with low molecular flux, sensitivity and concentration descended from the peak and were distributed at the bottom of the plot. The model reduction peak thus, represented the focal point of the network's dynamics and the most influential components within the system.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec18\" class=\"Section2\"\u003e\u003ch2\u003e3.6. Crosstalk Point Determination:\u003c/h2\u003e\u003cp\u003eCross-talk points serve as critical hubs where various signalling pathways converge through molecular components, allowing for extensive communication and coordination across distinct biological processes. Within the reconstructed mathematical model for hIAPP-mediated β-cell toxicity axis, a total of eight cross-talk points were identified communicating across crucial signalling pathways. These cross-talk points include caspases, cytoC, IL1β, PKC, NLRP3, ATF6, PERK and IRE1 (Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Each of these species represents a point of convergence or intersection of insulin signalling, glycolysis, polyol signalling, TCA cycle, GPCR signalling, RAGE signalling, autophagy, ER stress, and Mitochondrial stress and apoptosis in the hIAPP-mediated β-cell toxicity axis culminating to facilitate the pathogenicity of the disease.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eType 2 Diabetes Mellitus remains a significant global health issue due to its widespread occurrence, as well as its morbidity and mortality rates. The rapid pace of economic growth, urbanization, and abrupt lifestyle shifts have contributed to the increasing global burden of T2DM. Current estimates suggest that over 530\u0026nbsp;million adults are affected, with projections indicating that this number could exceed 780\u0026nbsp;million by 2045 if effective prevention and treatment strategies are not implemented [\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. T2DM extends beyond hyperglycemia, representing a complex multisystem disorder associated with cardiovascular, neural, renal, and hepatological complications. These collectively contribute to increased global disability and premature mortality rates [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. A hallmark of T2DM is the progressive reduction in pancreatic β-cell function and mass, primarily driven by the advancement of islet amyloidosis. Islet amyloidosis is characterized by the accumulation of amyloid fibrils, predominantly composed of human islet amyloid polypeptide. It is estimated that amyloid deposits are present in over 90% of patients with longstanding T2DM, highlighting their critical role in the disease pathology [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. Far from merely being inert aggregates, hIAPP oligomers are cytotoxic species that disrupt β-cell membranes, induce oxidative and ER stress, cause insulin resistance, and initiate apoptotic cascades [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e]. The toxic effects of hIAPP oligomers on β-cells are multidimensional. Their interaction with receptors activates toxic signalling intermediates that facilitate calcium influx, leading to autophagy defects and mitochondrial dysfunction through ROS generation. Additionally, in line with metabolic overload, oligomers induce ER stress by overwhelming its protein folding capacity and activating unfolded protein response signalling through PERK, IRE1, and ATF6 [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e\u003cp\u003eIn our present study we have investigated the hIAPP-mediated β-cell toxicity axis through mathematical modelling using computational tool \u0026ndash; MATLAB SimBiology ToolBox. The MATLAB SimBiology Toolbox is a potent tool widely used in systems and computational biology for mathematical modelling and simulation of complex biological systems. It offers a comprehensive platform to replicate, reconstruct, analyse and capture the multifaceted dynamics of intricate biological processes [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. The hIAPP-mediated β-cell toxicity axis in T2DM is characterized by the dysregulation of several biological processes that culminate to apoptosis and contribute to loss of β-cell mass. Our data focusing on the reconstructed signalling axis highlights the activation and aberrant expression of crucial signalling intermediates such as PKC, IRS1, REDD1, XBP1, PERK, IRE1, ROS, cytoC, GαS/GαQ, calpain, p62, NLRP3, interleukins and caspases that augment the pathogenic effects of hIAPP oligomers. Additionally, the trigger event reactions incorporated into the system signifies the control of the disease state and fucntion as bottleneck reactions that heavily influence network stability. The use of trigger events helped in tracking the evolutionary behaviour of biological processes and the reach of pathological effects of hIAPP oligomers mediating β-cell toxicity. The trigger event reactions were associated with the processes like sorbitol production, PKC hyperactivation and insulin resistance, activation of UPR intermediates, autophagic defect and β-cell starvation representing critical switches that drive the β-cells from adaptation to dysfunction during the course of disease.\u003c/p\u003e\u003cp\u003eFurther, sensitivity analysis and principal component analysis of the model identified molecular species with strongest influence of methylglyoxal-induced fibril formation, ER stress sensors (PERK, IRE1, ATF6), mitochondrial amplifiers (cytochrome c, ROS), metabolic intermediates (methylglyoxal, α-ketoglutarate), lysosomal depletion and autophagy-associated molecules (p62, Gαs/Gαq, calpain, NLRP3, caspases) as key pathogenic regulators driving disease progression. This was validated through computing molecular flux for every reaction in the system. Flux analysis thus, provided a quantitative rationale for the dysregulated expression of signalling intermediates emphasized in critical biological processes. Next, the quasi-potential landscape graph for model reduction demonstrated a peak-like structure which indicated the concentration of high flux reactions and principal components at the peak of the dome. The entire model was reduced by 86% retaining only the essential components and interactions, involved in facilitating the dynamic outcome of the biological system (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). The systems-level reconstruction further pointed to critical cross-talk molecules such as IL-1β, NLRP3, cytochrome c, caspases, and RAGE as nodal regulators that integrate signals from multiple pathways, involved in the axis thus, highlighting the reach of pathogenic effects of hIAPP oligomers.\u003c/p\u003e\u003cp\u003eAlthough, islet amyloidosis in not a condition that has gone unaddressed however, the intricate mechanisms that the toxic hIAPP oligomers intervene with to mediate β-cell toxicity are yet to be fully elucidated. Certain reports suggest that hIAPP oligomers can cross the blood-brain barrier and have been shown to deposit in the brain, kidneys, heart, and liver of individuals with T2DM, where they contribute to neuroinflammation, nephropathy, cardiomyopathy, and hepatic dysfunction [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e]. These extraprancreatic effects explain the high mortality risk associated with T2DM highlighting the importance of developing new therapeutic approaches that address amyloid toxicity at its origin, rather than focusing solely on insulin sensitization in diabetic patients. Despite advances in diabetes management, current therapies largely fail to address the hIAPP aggregation or proteostasis defects. While the therapies like metformin improve insulin sensitivity and reduces hepatic glucose production, it does not effectively prevent amylin fibril formation or restore autophagic function, which may explain the continued progression of β-cell loss in patients despite receiving therapeutic care [\u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e43\u003c/span\u003e]. This broader perspective aligns with our systems-level analysis, which integrates pancreatic consequences into a unified model of disease progression. Our findings provide a comprehensive framework that consolidates diverse experimental observations into a single mechanistic narrative. The mathematical model for the hIAPP-mediated β-cell toxicity axis was reconstructed using a number of enzyme kinetics and parameters which provided a computable framework of all the signalling components giving us valuable insights to predict the best behavioural outcomes of the system. The findings point toward potential combinatorial therapeutic strategies employed to modulate the receptor activities of RAGE and GPCR pathways. RAGE blockade has shown protective effects in models of atherosclerosis, neurodegeneration, and other diabetic complications [\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e], suggesting that similar benefits may be achievable in the context of β-cell amyloidosis. Restoring autophagic flow and preventing lysosomal biogenesis errors can be one of the approaches used to modulate calcium influx by targeting the calcitonin receptor or GPCR signalling. The growing prevalence of this chronic condition, coupled with the underappreciated role of hIAPP deposits and toxic oligomers, highlights the urgent need for innovative strategies that can protect β-cell functionality and improve long-term outcomes. Our study lays the groundwork for the next generation of therapeutic interventions for the hIAPP- mediated β-cell toxicity. The fine-tuning of the mathematical model will require a step wise validation of crucial points and processes through \u003cem\u003ein vitro\u003c/em\u003e and \u003cem\u003ein vivo\u003c/em\u003e studies. Once the appropriate level of optimization has been achieved, the model may be used to tweak therapeutic targets and reproduce the physiological response.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003ch2\u003eConflicts of interest\u003c/h2\u003e\u003cp\u003eThe authors have no conflicts of interest to declare.\u003c/p\u003e\u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e\u003cp\u003eThis research was funded by Science and Engineering Research Board (SERB), Government of India (File No. EEQ/2023/000151).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eRNG designed the project, KK performed in silico experiments and drafted the manuscript. AP helped in data mobilization manuscript improvement.\u003c/p\u003e\u003ch2\u003eAcknowledgment:\u003c/h2\u003e\u003cp\u003eRNG sincerely acknowledges the financial assistance from SERB (File No. EEQ/2023/000151) and RUSA Phase 2 grant of SPPU Pune. KK acknowledges SERB for providing project assistance fellowship.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eData generated is provided within the manuscript and supplementary information files.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eSilvestre, R. A. et al. Inhibitory effect of rat amylin on the insulin responses to glucose and arginine in the perfused rat pancreas. \u003cem\u003eRegul. Pept.\u003c/em\u003e \u003cb\u003e31\u003c/b\u003e (1), 23\u0026ndash;31 (1990).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOpie, E. L. The relation Oe diabetes mellitus to lesions of the Pancreas. Hyaline degeneration of the Islands Oe Langerhans. \u003cem\u003eJ. Exp. Med.\u003c/em\u003e \u003cb\u003e5\u003c/b\u003e (5), 527 (1901).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEhrlich, J. C. \u0026amp; Irving, M. Ratner. 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Islet amyloidosis is a chronic condition developed during the course of T2DM and it is characterized by the deposition of toxic hIAPP aggregates in pancreatic β-cells. Although, islet amyloidosis in not a condition that has gone unaddressed however, the intricate mechanisms that the toxic hIAPP oligomers intervene with to mediate β-cell toxicity are yet to be fully elucidated. In this study, we employed systems metabolism and computational biology approach to mathematically reconstruct and investigate the dynamics and hIAPP-mediated β-cell toxicity axis using SimBiology MATLAB. The signalling network was reconstructed using a number of enzyme kinetics and parameters which provided a computable framework of all the signalling components giving us valuable insights to predict and replicate the best behavioural outcomes. Sensitivity analysis, Principal Component Analysis (PCA), Flux analysis, Model reduction and cross-talk point determination accurately captured the dynamics of the entire system and identified key components (RAGE, PKC, ROS, CytoC, PERK, IRE1, ATF6, Ca\u003csub\u003e2+\u003c/sub\u003e influx), interactions, and processes (insulin resistance, glycation, autophagy defect, ER and mitochondrial stress, apoptosis) driving its pathogenic behaviour.\u003c/p\u003e","manuscriptTitle":"Elucidating the pathological axis of hIAPP-mediated β-cell toxicity: A MATLAB-based network modelling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-22 12:45:49","doi":"10.21203/rs.3.rs-7722499/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ef48c6b1-4cf3-4fc5-b004-69601e7adebe","owner":[],"postedDate":"October 22nd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":56244986,"name":"Biological sciences/Biochemistry"},{"id":56244987,"name":"Biological sciences/Biological techniques"},{"id":56244988,"name":"Biological sciences/Cell biology"},{"id":56244989,"name":"Biological sciences/Computational biology and bioinformatics"},{"id":56244990,"name":"Health sciences/Diseases"},{"id":56244991,"name":"Biological sciences/Systems biology"}],"tags":[],"updatedAt":"2026-02-12T16:55:33+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-22 12:45:49","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7722499","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7722499","identity":"rs-7722499","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}