Synthetic Generation of Dynamic Omics Data Demonstrates Aspergillus nidulans BrlA Paradoxical Wall Stress Response

Synthetic Generation of Dynamic Omics Data Demonstrates Aspergillus nidulans BrlA Paradoxical Wall Stress Response | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (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];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Synthetic Generation of Dynamic Omics Data Demonstrates Aspergillus nidulans BrlA Paradoxical Wall Stress Response View ORCID Profile Joseph Zavorskas , View ORCID Profile Harley Edwards , Walker Huso , View ORCID Profile Alexander G. Doan , View ORCID Profile Mark R. Marten , Steven Harris , View ORCID Profile Ranjan Srivastava doi: https://doi.org/10.1101/2025.03.02.638868 Joseph Zavorskas 1 Department of Chemical and Biomolecular Engineering, University of Connecticut Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Joseph Zavorskas Harley Edwards 2 Department of Chemical, Biochemical, and Environmental Engineering, University of Maryland, Baltimore County Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Harley Edwards Walker Huso 2 Department of Chemical, Biochemical, and Environmental Engineering, University of Maryland, Baltimore County Find this author on Google Scholar Find this author on PubMed Search for this author on this site Alexander G. Doan 2 Department of Chemical, Biochemical, and Environmental Engineering, University of Maryland, Baltimore County Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Alexander G. Doan Mark R. Marten 2 Department of Chemical, Biochemical, and Environmental Engineering, University of Maryland, Baltimore County Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Mark R. Marten Steven Harris 3 Department of Plant Pathology, Entomology, and Microbiology, Iowa State University Find this author on Google Scholar Find this author on PubMed Search for this author on this site Ranjan Srivastava 1 Department of Chemical and Biomolecular Engineering, University of Connecticut Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Ranjan Srivastava For correspondence: rs{at}uconn.edu Abstract Full Text Info/History Metrics Supplementary material Preview PDF Abstract We propose a method to generate additional dynamic omics trajectories which could support pathway analysis methods such as enrichment analysis, genetic programming, and machine learning. Using long short-term memory neural networks, we can effectively predict an organism’s dynamic response to a stimulus based on an initial dataset with relatively few samples. We present both an in silico proof of principle, based on a model that simulates viral propagation, and an in vitro case study, tracking the dynamics of Aspergillus nidulans’ BrlA transcript in response to antifungal agent micafungin. Our silico experiment was conducted using a highly noisy dataset with only 25 replicates. This proof of principle shows that this method can operate on biological datasets, which often have high variance and few replicates. Our in silico validation achieved a maximum R 2 value of approximately 0.95 on our highly noisy, stochastically simulated data. Our in vitro validation achieves an R 2 of 0.71. As with any machine learning application, this method will work better with more data; however, both of our applications attain acceptable validation metrics with very few biological replicates. The in vitro experiments also revealed a novel paradoxical dose-response effect: transcriptional upregulation by Aspergillus nidulans BrlA is highest at an intermediate dose of 10 ng/mL and is reduced at both higher and lower concentrations of micafungin. Introduction Multi-omics methods amalgamate multiple sources of biological “big data,” each of which often describe the organism-wide dynamics of some part of the central dogma of biology: DNA -> RNA -> protein. 1 For example, a multi-omics study might consider a regulatory network containing transcription factors, kinases/phosphatases, repressor proteins, etc. all responding to a certain stimulus. To collect transcriptomic data, for example, one could use RNA sequencing (RNA-seq) to understand the dynamics of all transcripts in an organism. 2 Alternatively, DNA microarrays 3 or quantitative polymerase chain reaction (qPCR) 4 can be used to study the dynamics of a small subset of transcripts. To perform studies from a protein lens, one can use mass-spectrometry based proteomics to collect data on all proteins present in the cell at the time of sampling. 5 This analysis can be extended to understand protein regulation via post translational modifications by searching for additions such as phosphorylation, methylation, etc. 6 Interactions between genes and signaling pathways are both complicated and interconnected. Commonly, researchers will select pathways of interest to focus their data analysis and reduce complexity. To glean connections without a pathway basis, techniques such as pathway enrichment analysis, 7 , 8 genetic programming (GP), 9 – 11 and machine learning (ML) can be used. 12 , 13 Each of these data analysis methods benefits from greater quantities of quality data, especially GP and ML. However, many of the data collection methods mentioned previously require significant time and energy to generate quality replicates. In addition, several time points are required to accurately capture the dynamics of an organism’s response to a stimulus, each of which requires both biological and technical replicates. 14 This work seeks to generate synthetic, multi-omics replicates which could be used to further biological pathway understanding, such as GP algorithms or machine learning. We used a long short-term memory (LSTM) neural network 15 to capture the dynamic response of Aspergillus nidulans BrlA to varying doses of the echinocandin antifungal agent micafungin. 16 , 17 Before this case study, we conducted proof of concept studies for the LSTM on a viral propagation model. 18 In this model system, significant noise was introduced via stochastic simulation of the differential equations, to simulate the high variance of true biological data. Long Short-Term Memory Neural Networks To create mechanistic models for dynamic gene expression, it is more important that the technique used to generate synthetic -omics replicates consider the temporal dynamics between points than the individual points themselves. These requirements can be satisfied using machine learning techniques that perform sequence learning 19 such as recurrent neural networks (RNNs), and their extension, LSTMs. 15 RNNs are layered algorithms which process sequential information by taking one point as input in each layer and producing a single output. 20 RNNs’ strength is their built-in memory, where hidden nodes of the current layer pass information to the hidden nodes of the subsequent layer. 21 However, RNNs have a few fundamental flaws that make them unsuitable to apply to large problems with long time scales. Most importantly, RNNs face an issue known as the vanishing gradient problem. 22 This problem is caused by the consistent scaling of information by each layer’s activation function by values between -1 and 1. 23 Therefore, the longer the sequence an RNN is considering, the more extreme the vanishing gradient problem is expected to become. 24 The exact opposite effect, exploding gradients, is also possible depending on the activation function and scaling type used. 25 LSTMs are a subset of RNNs that were created by Hochreiter and Schmidhuber 15 to address the shortcomings of traditional RNNs. A typical LSTM, as shown in Figure 1 , contains two streams of data, the “cell” stream and the “hidden state” stream. The cell stream contains the long-term memory of the network, while the hidden state directly handles the input of the current time point. LSTMs typically contain three “gates” which apply activation functions to the data streams: the forget gate, input gate, and output gate. The forget gate decides what information from the cell memory stream to delete based on what it has learned is important to current and future time points and discards less needed information. 2627 The input gate uses multiple activation functions to store the current hidden state information in the memory stream. Finally, the output gate combines information from memory and the current input to generate the output at the current time point. An activation function is never permanently applied to the memory stream, only to a copy of its value in the output gate, solving the vanishing gradient problem. Case Studies Viral Propagation First, we validate our LSTM approach by using the simple biological model proposed by Srivastava et al . (2002), which represents the infection and propagation dynamics of a generalized virus. 18 Their model simplifies the viral infection process into three general stages: 1) tem , the free, translated genetic template responsible for creating the physical components of the virus; 2) gen , the genomic nucleic acid sequence that is packaged within new viruses to infect other cells; 3) struct , the structural proteins such as capsid proteins or envelope proteins that form the physical virus. 18 Most importantly, gen produces tem , which can produce both gen and struct . A complete virus is created by the export of gen and struct together. This system can be represented by three coupled differential equations, as shown in Equation 2 : The parameters in these equations and the processes they represent are included in Table 1 . This viral propagation model tests the LSTM’s ability to simulate a system with a dynamic phase which eventually leads to a stable steady state. This steady state occurs at tem, gen , and struct values of 20, 200, and 10000, respectively. 18 Our goal for the LSTM is to generate accurate dynamic trajectories representing differing initial infection quantities by adjusting the initial condition for tem . View this table: View inline View popup Download powerpoint Table 1. The rate constants for each viral propagation reaction are included below. The corresponding process for each consumption or production term is also included. Rate constants were chosen by Srivastava et al . (2002) to result in a stable steady state. Aspergillus nidulans BrlA Various species from the genus Aspergilli are widespread in nature and are used prevalently in the bioprocess industry. For example, A. oryzae and A. niger are used for many bioproduction processes such as the fermentation of sake and soy sauce, production of citric and gluconic acids, and the production of many useful enzymes. 28 – 30 However, other Aspergilli are opportunistic human pathogens, the most virulent of which is A. fumigatus . This fungus can cause aspergillosis, especially in hosts which are already immunocompromised. 31 A. fumigatus is so virulent due to its aggressive spore production and dissemination, which when breathed in are quickly cleared by the immune system. 32 However, these ubiquitous spores can easily infect immunocompromised individuals who are frequently exposed to them in everyday life. In Aspergilli , fungal spores are produced through an asexual reproduction process called conidiation. This process is regulated by a genetic pathway that responds to both light and air to decide when to initiate spore production. 33 The signaling pathways that initiate conidiation all feed into and activate the central transcription factor of asexual reproduction, BrlA, which is the first of three central transcription factors in the asexual reproduction pipeline, organized as follows: brlA → abaA → wetA . 34 Each transcription factor is responsible for a different phase of conidial development, which is evidenced by differing morphological defects in their respective deletion mutations. 35 , 36 Understanding the role of BrlA, and the central conidiation pathway, is very important to understand fungal reproduction, aspergillosis, and other pathogenic fungi. However, according to literature sources 37 , 38 and our previous findings 39 , 40 , BrlA appears to have functions outside of the asexual reproduction pathway. Notably, BrlA appears to play a role in cell wall stress response. This function is particularly significant because echinocandins, one of the most potent classes of antifungal agents, specifically target the fungal cell wall. 16 , 17 Interestingly, in Aspergillus species, echinocandins produce only a fungistatic effect rather than a fungicidal one, suggesting these organisms possess inherent resistance mechanisms against these drugs. 41 There is a significant amount of evidence that BrlA participates in the cell wall stress response. First, the brlA transcript was found to be significantly upregulated in response to micafungin exposure in our previous work. 39 Additionally, this transcriptional upregulation occurred without the upregulation of the transcription factors abaA and wetA , which are commonly thought to act together. 36 Second, the terminal MAP kinase of the cell wall integrity (CWI) signaling pathway, MpkA, has been shown to physically associate with, and have transcriptional effects, on BrlA. Kovacs et al . found that brlA transcription changed significantly in an mpkA deletion mutant. 38 Rocha et al . found that MpkA and BrlA were “physically associated” during asexual reproduction via coimmunoprecipitation (Co-IP). 37 Considering that MpkA is a serine/threonine kinase, this physical association may indicate that BrlA is being phosphorylated by MpkA to carry out cell wall integrity-related processes. A final piece of evidence supporting the hypothesis that BrlA participates in the cell wall stress response is that the transcriptional upregulation of brlA in response to micafungin does not occur in an mpkA deletion mutant. 42 Our group has also explored possible downstream gene targets that brlA may regulate as part of the cell wall stress response we are proposing. Because of our interest in brlA transcriptional dynamics, we use it as an experimental case study in this paper. We collected detailed dynamic data of brlA ’s transcriptional response to micafungin exposure for use in a proof-of-concept for generating synthetic dynamic -omics trajectories. Ultimately, these data and any synthetic trajectories could be used in a genetic programming approach to understand the upstream regulation of brlA in either a conidiation or cell-wall stress context. Future work may include computational analysis of brlA ’s transcriptional network using this new tool. Methods Viral Propagation Proof of Principle We generate a noisy, sparse solution to Srivastava et al .’s viral propagation model by generating a stochastically simulated dynamic trajectory and sampling it at evenly spaced time intervals. Biological data is often extremely noisy and does not have good time resolution due to the high cost of an individual biological replicate. To stress test the LSTM on more biologically realistic data, we introduced noise by performing stochastic simulation of the differential equations using the Gillespie stochastic simulation algorithm (SSA). 43 In addition, we created sparse dynamic trajectories by removing all but a few small “sampling” events from the data. Sampling the generated noisy trajectories at evenly spaced time intervals In a single step of the Gillespie simulation, the following occurs: 1) the “propensity” of each reaction is calculated, essentially the likelihood that the reaction will occur given the current conditions; 2) a random number is generated and subjected to the following equation to calculate the size of the current time-step. 3) based on the calculated propensities, the first reaction to fire is calculated. Gillespie assumes that this reaction is the only one that fires in the short timespan calculated above and updates the values according to the stoichiometry of that equation. The Gillespie SSA is stochastic both with respect to the timestep used and calculation of the first reaction to fire, as shown in Equation 3 . Because the first reaction to fire is found via cumulatively summing the probabilities of each reaction, Gillespie is somewhat dependent on the order in which reactions are defined. and Gillespie simulation requires a defined stoichiometric matrix for each individual reaction and a vector of propensities that determine the probability of each reaction firing. Based on the system of differential equations shown in Equation 2 and the rate constants displayed in Table 1 , the Gillespie formulation is shown in Equation 4 . When a reaction is determined to “fire”, the counts for each species (i.e. tem, gen, struct ) are updated according to that reaction’s stoichiometry only. Gillespie simulation was used to generate 25 stochastic viral propagation trajectories, each with a randomly selected initial tem concentration. We chose to simulate very few replicates to emulate the reality of performing -omics experimentation. These varying initial conditions represent a varying severity of initial infection. Two initial tem concentrations were used, the first varying between 6 and 10, and the second between 4 and 14. Gillespie simulation will produce different trajectories depending on the part of the range the initial value is selected from, with the larger range producing a greater variance in trajectory. These 25 replicates are used to train an LSTM, with hyperparameters as shown in Table 2 , and training x and y values as shown in Equation 5 . Training x values include one row representing the time points for each training y value, with three rows which repeat the initial x conditions for each entry. The training y values are simply the simulated counts of tem, gen , and struct at each time point. View this table: View inline View popup Download powerpoint Table 2. Hyperparameter values used to train the viral propagation LSTM neural network. After training the LSTM network, validation was performed in multiple ways. First, the root mean squared error (RMSE) of the LSTM’s prediction of the average initial tem concentration (8 tem molecules) was calculated. The numerical solution of the viral propagation model was calculated given 8 initial tem molecules were used as a point of comparison. In addition, we extended this analysis by applying the elbow rule to determine the lowest number of replicates required for the LSTM to achieve acceptable accuracy. 25 LSTM networks were trained on five random subsets of data selected without replacement. These datasets contain begin containing a single replicate and one addition replicate is added for each subsequent iteration, until all 25 replicates were used. We used this technique to identify the point of diminishing returns, when adding more replicates is not a worthwhile investment. Each of these LSTM networks uses the same hyperparameters values as shown in Table 2 . Aspergillus nidulans brlA Case Study Strains and Media Aspergillus nidulans A1405 (Fungal Genetics Stock Center; FGSC) was used as the control strain. Frozen stocks were spread on MAGV plates (2% malt extract, 1.5% agar, 2% glucose, 2% peptone, and 1ml/L Hutner’s trace elements and vitamin solution) and incubated for 2 days at 28 °C (29). 1E7 spores were harvested and inoculated into 50 ml of YGV (pH 3.3) (0.5% yeast extract, 1% glucose, and 1 ml/L Hutner’s trace elements and vitamin solution). Seed cultures were grown in a 250 ml baffled flask at 250 rpm and 28 °C. After 12 h growth, this flask was used to seed 1.2L YGV in a 2.8L Fernbach flask. All strains used in this study are all available from FGSC. Micafungin Treatment and Extraction After 20 h of growth (mid-exponential growth phase as determined by growth curve), various quantities of micafungin were added to the 2.8L Fernbach flask. The critical concentration of micafungin was previously determined to be 7 ng/mL in Chelius et al . (2020). To sample above and below this value, cultures were grown at 0, 5, 10, 15, and 20 ng/mL. 25 ml of culture from the shake flask was extracted after 0, 10, 20, 30, 60, and 90 minutes after micafungin exposure. Fungal biomass was recovered from the liquid via filtration through cheesecloth, squeezed dry, and then transferred into 25 mL centrifuge tubes by spatula. Biomass in the centrifuge tubes were flash frozen by liquid nitrogen and placed in a liquid nitrogen bath while samples were collected. Samples were placed in -80°C for at least one hour to ensure even freezing and brittleness. Frozen mycelia were crushed with mortar and pestle into a fine powder. RNA extraction, purification, and cDNA conversion were completed as described by Chelius et al . (2019). Based on the results of our in silico proof of concept using the viral model, five biological replicates and three technical replicates were collected at each time point. Each replicate’s converted cDNA was run using a BioRad C1000 Touch Thermal Cycler with CFX96Real-Time System. The target transcript brlA was quantified with respect to the reference gene, histone (H2B)’s transcript, and fold change was determined with respect to the zero-time point following the Ct method (52). Primers were designed using Benchling and are included in Supplementary Material LSTM Structure and Parameters A similar training procedure was used for the brlA LSTM and the viral propagation one. An LSTM neural network was trained on the brlA transcriptomic data which takes micafungin concentration as input and predicts the dynamic response of brlA . Table 3 displays the LSTM hyperparameters, which are the same for both of our brlA LSTM models. View this table: View inline View popup Download powerpoint Table 3. Hyperparameter values used to train the brlA transcriptomics LSTM neural network. Biological data is extremely noisy, so validation is paramount to assess the accuracy of our trained LSTMs. First for the dynamic trajectories, 75 dynamic trajectories were available among five biological replicates, three technical replicates, and five micafungin concentrations. Five-fold cross-validation was used to stress-test the network. Removing large quantities of data (15 points in each fold) was expected to lead to breakdowns in performance. For our in vitro case study, we selected five biological replicates based on our application of the elbow method 44 to our in-silico proof of concept. Links to all code and data used to train each LSTM is included in the Supplementary Material . Surface Plotting Once the network predicting dynamic trajectories was validated, it was used to generate in silico transcriptomic replicates within the range of micafungin concentration from which the dataset was generated. To do so, the network was queried from 0 to 20 ng/mL micafungin concentration in 1 ng/mL intervals. These 21 replicates were used to generate a surface plot whose z -axis represents brlA ’s transcriptomic response with respect to both micafungin concentration and time after exposure. In addition to visualization via surface plot, these additional replicates could be used alongside other modeling techniques. For example, these additional replicates could be used to help fit parameters within a kinetic model, or even de novo generate a model via a technique such as genetic programming. Results and Discussion Viral Propagation Despite introducing stochasticity and providing very scarce viral propagation data for training, an LSTM can accurately predict trajectories within the range of initial concentrations used for training. In addition, the LSTM shows reasonable extrapolation capability outside of the training range of initial concentrations. For the viral propagation data, an LSTM was trained on two stochastically generated datasets, one with low variation of the initial tem concentration, and one significantly more variation. Each LSTM was tested by generating analytical solutions for tem concentrations within the training range and without and calculating the error and correlation coefficient (R 2 ) between analytical and LSTM-predict solutions. Table 3 displays this analysis for both the small initial condition range (6-10 tem molecules) and large (4-14 tem molecules). Figures 2 and 3 display representative trajectories from the small and large initial condition ranges, respectively, with each considering two close extrapolations and an interpolation. Download figure Open in new tab Figure 2. Given a small initial range of possible template ( tem ) molecules, between 6 and 10, an LSTM can predict the infection’s dynamics very accurately. To assess the accuracy of the LSTM and choose an appropriate number of replicates for our in vitro case study, subsets of the full dataset were selected, containing between 1 replicate and all data. For each number of replicates, five random subsets were selected without replacement and used to train an LSTM neural network. A time course at the center value of the range, 8 tem molecules, was generated analytically and via the LSTM, and the accuracy is reported via: a) R 2 , and b) root-mean-squared errors for tem, gen , and struct . We suggest that an elbow occurs at five replicates, indicating that additional replicates beyond this point provide diminishing return. Download figure Open in new tab Figure 3. Given a larger initial range of possible template ( tem ) molecules, between 4 and 12, an LSTM can predict the dynamics of infection accurately but requires more replicates to do so. This exercise is likely more realistic to the amount of noise present in biological data, and what can be expected in the in vitro case study. As in Figure 2 , a time course at the center value of the range, 8 tem molecules, was generated analytically and via the LSTM, and the accuracy is reported via: a) R 2 , and b) root-mean-squared errors for tem, gen , and struct . We suggest that an elbow occurs at six replicates, indicating that additional replicates beyond this point provide diminishing return. For the small initial condition range, LSTM shows good performance for all interpolation cases, including those at the edge of the possible initial conditions. However, the LSTM shows significantly worse performance extrapolating solutions with initial conditions greater than the training dataset, with smaller initial conditions retaining high R 2 values. A possible cause for this imbalance is that the randomly selected initial tem values in the training dataset were skewed toward small values. However, with 25 replicates, it is highly unlikely that such a large skew exists. A more likely cause is that higher initial viral loads lead to different infection and propagation dynamics, confusing the LSTM which has not been exposed to those dynamics. Compare the extrapolated trajectories in Figure 2(b) and (c) , in which high initial tem concentrations lead to significantly less lag time in both gen and struct , as well as a faster and more intense initial dip in tem concentration. For the large initial condition range, the LSTM has lower R 2 values and worse RMSE for all trajectories. This result is expected, especially due to the known significant difference in dynamics between severe and mild infections. In addition, the large initial tem range has a more pronounced asymmetry with regard to validation R 2 and RMSE at low and high initial conditions, as shown in Table 4 . The extrapolation ability of the LSTM is diminished in the larger initial tem range. This effect is expected both due to using a wider range with the same number of replicates, and the fact that expanding the extremes introduces more varied dynamics. View this table: View inline View popup Download powerpoint Table 4. An error assessment for interpolated and extrapolated time-courses for LSTMs trained on datasets generated with small (6-10) and large (4-12) initial template concentration ranges. Italicized values represent extrapolations, bold values represent the center value of the initial condition range. The final section reports the error for the large (4-12) initial range but seeded with five extra replicates in the top half (8-12) of the range. To address the asymmetry in error, we seeded the dataset with five additional stochastically generated replicates with initial conditions in the top half of the range. Seeding additional replicates within this problem region drastically improved its predictive performance through the entire range of initial conditions. In fact, as seen in Table 4 , just five additional replicates drastically improve error at the extremes of the initial condition range. The LSTM still struggles to predict the complex dynamics at high initial conditions, but additional steps such as applying weights to these initial conditions during training could further improve accuracy. Most interestingly, adding five additional high initial tem replicates drastically improved and extended the accuracy of the LSTM when predicting low initial tem replicates. This effect suggests that addressing the weakest link can benefit prediction among the entire dataset. We applied the elbow rule to both initial condition ranges both to further validate the LSTMs and also the number of replicates required to reach satisfactory performance. 44 The purpose of the elbow rule is to identify the “point of diminishing returns,” which is essentially the minimum number of biological replicates required to get acceptable predictive performance should this type of experiment be performed in vitro . Figures 4 and 5 display elbow rule visualizations for both the small and large initial condition ranges, respectively. We have identified the “elbow” or point of diminishing returns for each range to be five and six replicates, respectively. The error metrics decrease in variance and improve at a significantly slower rate beyond five and six replicates, respectively. While the elbow rule is largely qualitative, it is a valuable first pass to help decide how many replicates are necessary for accurate in vitro experimentation and modeling. Based on the results of this proof of concept, we decided to collect five biological replicates for our in vitro case study using Aspergillus nidulans BrlA. Download figure Open in new tab Figure 4. Given a smaller initial range of possible template ( tem ) molecules, between 6 and 10, an LSTM can predict the dynamics of infection accurately. Each row represents LSTM time course predictions for tem, gen , and struct at initial tem values of a) 6 tem molecules, b) 8 tem molecules, c) 10 tem molecules. The predictions at 6 and 10 are just at the edge of the available training range. Near the bottom of the training dataset range, prediction remains highly accurate, while predictions near the top of the range result in significant errors. This is likely because infections with high initial tem concentration result in more extreme dynamics early in the trajectory, which differs from lower initial concentrations. Download figure Open in new tab Figure 5. Given a larger initial range of possible template ( tem ) molecules, between 4 and 12, an LSTM is less accurate in predicting propagation time courses. Each row represents LSTM time course predictions for tem, gen , and struct at initial tem values of a) 4 tem molecules, b) 8 tem molecules, c) 12 tem molecules. The predictions at 4 and 12 are just at the edge of the available training range. Near the bottom of the training dataset range, prediction remains more accurate than top of the range, as in Figure 4 . By seeding the neural network with five additional replicates in the top of the range, shown in d) , the prediction at 12 tem molecules drastically improves. Aspergillus nidulans brlA Case Study For noisy biological data with a wide range of micafungin concentrations, the LSTM’s validation R 2 value is acceptable and in line with expected accuracy based on our viral propagation proof of concept. In five-fold cross-validation, the average R 2 achieved by the dynamic trajectory LSTM is approximately 0.71, as displayed in Table 5 . The relatively low R 2 value is likely due to the inconsistent outlier nature of the data at 10 ng/mL, discussed later. This behavior confounds our LSTM’s prediction capability, especially when replicates that would reinforce this paradoxical behavior are left out during validation. These results at the point of greatest paradoxical behavior are still a drastic improvement over linear interpolation. Interpolation techniques would likely completely miss this peak, but LSTMs trained on full time-course trajectories can somewhat capture the true dynamics. The main focus of this paper is on the development of an LSTM technique for modeling dynamic -omics trajectories and extracting additional data for use in model development. However, our transcriptomic data also reveal a paradoxical trend in brlA transcriptional regulation in response to micafungin exposure. As a point of clarification, there is already a well-known “paradoxical effect” between Aspergilli and echinocandin antifungals. 45 Aspergilli paradoxically recover the ability to grow effectively at high echinocandin concentrations, which has been shown in many echinocandins. 46 – 49 The paradoxical effect we will reference for the rest of the paper is transcriptomic, not related directly to growth rate; however, these two effects may be linked. The paradoxical transcriptomic response of brlA is further exemplified by the surface plot generated from additional in-silico replicates from our LSTM. The expected dose-response behavior is that higher doses elicit a higher response, unless the dose is lethal. Based on our previously published data 39 , 40 , no concentration within our range of micafungin doses is lethal. We generated a surface plot to visualize this paradoxical effect by querying our LSTM with many micafungin concentrations as input, which is shown in Figure 6 . The surface plot illustrates the paradoxical behavior of A. nidulans BrlA, in which 10 ng/mL micafungin elicits the greatest transcriptional response. Download figure Open in new tab Figure 6. An LSTM trained on all brlA transcriptomic data was used to generate the following surface plot, by querying at 1 ng/mL intervals from 0 to 20 ng/mL of micafungin. This surface plot illustrates micafungin’s “paradoxical effect” on brlA expression. Medium doses of micafungin elicit the strongest brlA response, while higher doses cause a weaker response. In addition, medium micafungin concentrations elicit an initial spike in brlA transcription, followed by the more typical exponential rise seen in all other concentrations. In previous work, Chelius et al . (2020), the lowest concentration at which micafungin caused visual impairment was between 7 and 10 ng/mL. It is possible that the fungistatic effect of micafungin kicks in very quickly and hinders the fungi, or that the brlA response is only effective at low micafungin concentrations. Additionally, all dynamic trajectories have a steady, exponential increase in fold change with respect to time after micafungin exposure. Again, 10 ng/mL appears to have the highest average transcription response at each time point. However, at 20 minutes after exposure, 10 ng/mL micafungin elicits a secondary spike in brlA transcript which then quickly fades as shown in Figure 6 . Both the overall dose-response behavior and the dynamic transcriptomic trajectory of 10 ng/mL display paradoxical and/or counterintuitive responses. Namely, 10 ng/mL is consistently at higher regulation levels, and shows a unique, intense spike at 20 minutes. Finally, we wish to address our use of the elbow method to inform usage of five biological replicates. Within scientific literature, there is no concrete measure for how many biological replicates are enough to capture a biological effect and accurately draw conclusions. Many researchers operate with the rule of thumb of two to three biological replicates and three technical replicates. Due to high variance, we found that applying this machine learning technique to -omics data requires at least five biological replicates. We will not claim that our treatment is a concrete rule for all biological research, but we do suggest that researchers following the common rule of thumb may not yet have reached the point of diminishing returns with regards to the number of replicates used. Researchers collecting only two or three biological replicates may be losing valuable information about the systems they are studying. Conclusion The long short-term memory neural network is an effective method to capture and amplify trends within noisy and/or sparse biological data. We have successfully conducted an in silico proof of concept and an in vitro case study, both of which demonstrate an LSTM’s ability to generate additional in silico time-resolved replicates for -omics studies. Synthetic -omics time courses can be generated on-demand by querying the trained neural network. Both the biological and synthetic time courses can be used to generate mechanistic models, such as in genetic programming. 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