{"paper_id":"0b784090-7b75-4c06-a4f4-e96e09651a77","body_text":"Linking biochemical and cellular efficacy of\nMERS coronavirus main protease inhibitors\nVan N. T. La ,† Noa Lahav, ‡ Mario Rodriguez ,¶ Randy Diaz-Tapia,¶ Briana\nMcGovern ,¶ Jared Benjamin ,¶ Haim Barr ,‡ Kris M. White ,¶ Lulu Kang ,§\nJohn D. Chodera ,∥ and David D. L. Minh ∗,⊥\n†Department of Biology, Illinois Institute of Technology, Chicago, IL 60616, USA\n‡The Weizmann Institute of Science, Rehovot, 7610001, Israel\n¶Icahn School of Medicine at Mount Sinai, Department of Microbiology and Global Health\nand Emerging Pathogens Institute, New York, NY 10029, USA\n§Department of Mathematics and Statistics, University of Massachusetts Amherst,\nAmherst, MA, 01003, USA\n∥Computational and Systems Biology Program, Memorial Sloan Kettering Cancer Center,\nNew York, NY, USA\n⊥Department of Chemistry, Illinois Institute of Technology, Chicago, IL 60616, USA\nE-mail: dminh@illinoistech.edu\nAbstract\nCompoundsthatbindtotheMiddleEastRespiratorySyndromeCoronavirus(MERS-\nCoV)mainprotease(MPro)oftenproducebiphasicconcentration-responsecurves(CRCs)\nin biochemical assays; low concentrations activate the enzyme and high concentrations\ninhibit it. This biphasic behavior complicates data analysis. Here, we compare three\napproaches to data analysis: fitting the Hill equation to the activation phase, fitting it\n1\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nto the inhibition phase, and fitting an enzyme kinetics model that incorporates dimer-\nization and ligand binding to the complete CRC. In the latter case, cellular efficacy is\npredicted by extrapolating the model to high enzyme concentrations. For compounds\nin our drug lead series, all three procedures yield inhibitory concentrations that are\ncorrelated with live-virus antiviral assays. The latter procedure provides the most ac-\ncurate forecast of cellular efficacy rank. These data analysis procedures may be valuable\nfor antiviral drug discovery against MERS-CoV MPro and other enzymes with similar\nkinetics.\n1 Introduction\nThe Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is a serious threat to\nglobal health. The virus was first identified in Saudi Arabia in 20121 and has caused spo-\nradic outbreaks, predominantly in the Middle East, Africa, and South Asia. According to\nthe WHO, no vaccine or antiviral treatment has been approved for MERS-CoV.2 The virus\nhas evolved between 2015 and 20193 and further evolution could produce increased trans-\nmissibility. Given this possibility and the alarmingly high fatality rate of 35%,4 MERS-CoV\ncould lead to large-scale mortality.\nMany drug discovery efforts for coronaviruses have focused on identifying compounds that\ninhibit the main protease (MPro).5–11MPro is essential to the life cycle of coronaviruses. It\nis one of 16 non-structural proteins produced upon viral entry into host cells, forming part of\nthe replicase-transcriptase complex responsible for genomic RNA replication and subgenomic\nmRNA synthesis.12,13 Inhibiting MPro disrupts the viral replication cycle,5,9,14 facilitating\nits clearance by the immune system.\nIndrugdiscoverycampaignsfocusingonenzymeinhibitors, concentrationresponsecurves\n(CRCs) that measure the progress of a catalyzed reaction as a function of inhibitor concen-\ntration can be a key part of the assay cascade. Improving potency of enzymatic inhibition is\none of the most direct objectives of structure-based drug design. While it is possible to forego\n2\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nan enzyme inhibition assay and direct test inhibitors in a cell-based antiviral activity assay,\nthe former generally has fewer safety risks, is less expensive, and is less subject to biological\nvariability. Moreover, cell-based assays can introduce confounding factors, such as membrane\npermeability and active efflux pumps, that can confuse structure-activity relationships.\nUnfortunately, MERS-CoV MPro inhibition assays often show biphasic behavior that\ncomplicates their interpretation. MPro is most active as a dimer,15 but analytical ultracen-\ntrifugation shows that its dissociation constant (Kd) is 52 µM,16 weaker than MPro from\nSARS-CoV (6 µM)17 and SARS-CoV-2 (7 µM).18 Due to the high fraction of enzyme in\nthe relatively inactive monomeric form, ligand-induced dimerization16,19 produces biphasic\nCRCs, also known as activation-inhibition CRCs, in biochemical assays performed at low\nenzyme concentrations.16 Ligand binding to one monomer can trigger dimerization, locking\nthe catalytic site in an active conformation that stabilizes hydrogen bonding across the dimer\ninterface to the N-terminal serine of the opposite subunit (c.f. Fig. 6 of Nguyen et al.20). If\nligand concentrations are low, the other monomer is usually available to bind to substrate\nand produce product, leading to an overall increase in the catalytic rate. At high ligand\nconcentrations, both monomers are occupied by ligand and enzyme catalysis decreases. For\nsuch biphasic curves, the traditional four-parameter Hill equation - which includes bottom\nresponse, top response, IC50, and Hill slope - does not fit the complete curve. Thus, it has\nbeen unclear how to fit models to these data and how to interpret model parameters for\nthe evaluation of antiviral compounds targeting MERS-CoV MPro and other enzymes that\nproduce biphasic CRCs.\nHere, weevaluatethreepossibleprocedurestointerpretingthesebiphasicCRCs. Oneisto\nignore the activation phase and fit the Hill equation to the inhibition phase. This yields what\nwe will refer to as theinhibition pIC50. In another, the inhibition phase is also extracted,\nbut instead of fitting four parameters, the top response is set by the negative control (no\ninhibitor) and the three remaining parameters are estimated. This procedure essentially\nassumes that there is no ligand-induced dimerization. We refer to the pIC50 obtained from\n3\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nthis fit as thecontrol pIC50. A third procedure is based on fitting an enzyme kinetics model\nthat incorporates both dimerization and ligand binding that we recently introduced.21 This\nmodel produces biphasic CRCs that can be fit to the entire curve without ignoring any data.\nHere, we develop a protocol for fitting the model to a large number of CRCs. (Binding free\nenergies from this fitting procedure have been used as a benchmark in a blinded challenge for\nthe computational chemistry community.22) After fitting the model, we predict CRCs at high\nenzyme concentrations (reflecting cellular conditions), yielding thedimer pIC50. The three\nprocedures are evaluated based on the correlation between different pIC50s and pEC50s in\na live-virus antiviral assay.\n2 Methods\n2.1 Assays\nCRCs were measured in both biochemical enzymatic activity and live-virus antiviral as-\nsays, as reported in the AI-driven Structure-enabled Antiviral Platform (ASAP) Discovery\nConsortium (https://asapdiscovery.org/) protocols.io repository of experimental proto-\ncols.24\n2.1.1 Biochemical enzyme activity\nBiochemical CRCs were obtained by the MERS-CoV MPro fluorescence dose response for\nantiviral testing protocol25 and variants with different concentrations of enzyme, substrate,\nand inhibitor. The protocol is similar to that described for SARS-CoV-2 MPro,23 but ap-\nplied to MERS-CoV MPro. Two categories of experiments were performed. In the first\ncategory, the enzyme concentration was fixed and the response was measured as a function\nof substrate concentration. Datasets from this category are referred to as enzyme-substrate\n(ES) datasets, comprising three datasets with enzyme concentrations at 25, 50, and 100 nM,\nrespectively. Substrate concentrations were 50, 150, 350, 550, 750, 950, 1150, and 1350 nM.\n4\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nFor ES datasets, six replicates were measured at each substrate concentration. In the second\ncategory, both enzyme and substrate concentrations were fixed while inhibitor concentra-\ntions were varied. Datasets from this category are referred to as enzyme-substrate-inhibitor\n(ESI) datasets. For thirteen inhibitors, CRCs were measured under four conditions (ESI4c):\n50 nM enzyme, 150 nM substrate; 100 nM enzyme, 50 nM substrate; 100 nM enzyme, 750\nnM substrate; and 100 nM enzyme, 1350 nM substrate. Inhibitor concentrations were 50,\n100, 194, 388, 776, 1552, 2488, 7463, 12440, 24880, 49750, and 99500 nM. For 85 inhibitors,\nCRCs were measured with 50 nM of enzyme and 550 nM of substrate (ESI1c), while the\ninhibitor concentrations were 0.888, 2, 4, 15, 50, 133, 460, 1227, 2488, 9950, 32340, and 99500\nnM. In the ESI datasets, two replicates were measured at each inhibitor concentration. The\nESI1c data were obtained by the reported protocol25 and ES and ESI4c experiments were\nperformed analogously, but with different concentrations. Data are provided in Tables ES,\nESI4c, and ESI1c of the Supplementary Information.\nInhibitors were part of a drug discovery campaign for MPro inhibitors targeting both\nMERS CoV and SARS-CoV-2 conducted by ASAP. Compounds were synthesized by Enam-\nine (Ukraine). Complete CRCs and ASAP identifiers are available in Figure S21 and an Excel\nspreadsheet in the Supplementary Information. Chemical structures have been deposited to\nChEMBL 37, with public release anticipated in late Spring 2026.\n2.1.2 Live-virus antiviral assay\nThe Live-virus MERS-CoV Vero-TMPRSS2 with PgP Inhibitor Antiviral Screening Assay26\nwas performed at the Icahn School of Medicine at Mount Sinai. All assays were performed\nat Biosafety Level 3 (BSL-3) in the Emerging Pathogens Facility (EPF).\nVero-TMPRSS2 cells were seeded in 96-well plates at 2,000 cells per well in 10% growth\nmedia supplemented with puromycin the day before the assay and incubated at 37°C and\n5% CO2. Two hours before infection, cells were treated with 100µL of a 1 to 3 dilution\nseries of antiviral hits in 2% infection media supplemented with PgP-inhibitor. Dilutions\n5\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nwere performed using a Tecan D300e (Tecan). Concentrations of antiviral hits were 50%\nhigher than the target concentrations to account for infection volume. DMSO and uninfected\ncontrols were also included on each plate.\nPlates were then transferred to the BSL-3 and appropriate wells were infected with\nMERS-CoV/EMC/2012 at MOI 0.5 in 50 µL of 2% infection media supplemented with\nPgP-inhibitor, bringing the dilution series to the target concentrations. Plates were then\nincubated for 48 hours at 37C 5% CO2.\n48 hours post infection, supernatants were removed from the wells and replaced with\n100ul of 4% formalin and incubated for 15 minutes. Outer surfaces of the plates were\ndecontaminated; platesweredoublebagged, removedfromthefacilityandlefttofumigatefor\n48 hours. Plates were then immunostained using MERS-CoV nucleoprotein (NP) antibody\n(SinoBiological #40068-RP01) with a DAPI counterstain (Total Cells). Plates were analyzed\nusing a Cytation1 (Biotec). Infectivity was measured by the accumulation of viral N protein\n(Infected Cells; 488nm). Percent infection was quantified as ((Infected Cells/Total Cells)\n- Background) * 100, with DMSO control readouts as 100% infection. Data was fit using\nnonlinear regression and IC50s for each experiment were determined using GraphPad Prism\nv10.0.0 (San Diego, CA).\nAll data are included in the Supplementary Information.\n2.2 Bayesian regression for biochemical enzyme activity\nWe fit our enzyme kinetics model21 to the ES and ESI datasets. A schematic of the model,\ncomplete set of equations, and descriptions of numerical solutions to the equations are in-\ncluded in our previous publication.\n6\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\n2.2.1 Parameters\nThe objective of our Bayesian regression was to infer the following parameters,\nθ ≡ (∆Gd, ∆GS,M , ∆GS,D, ∆GS,DS, ∆GI,M , ∆GI,D , ∆GI,DI , ∆GS,DI ,\nkcat,M S, kcat,DS , kcat,DSI , kcat,DSS , [E]t, αp, σc). (1)\nThe enzyme kinetics model, which is based on a rapid equilibrium assumption, has thermo-\ndynamic (∆G) and kinetic (kcat) parameters as previously described.21 ∆G are the binding\nfree energies of species including the MPro monomer (M), MPro dimer (D), substrate (S),\ninhibitor (I): ∆Gd is a free energy of dimerization;∆GS,M is the binding free energy of the\nsubstrate to the monomer;∆GS,D is the binding free energy of the substrate to the dimer;\n∆GS,DS is the binding free energy of the substrate to the dimer-substrate complex;∆GI,M\nis the binding free energy of the inhibitor to the monomer;∆GI,D is the binding free en-\nergy of the inhibitor to the dimer; ∆GI,DI is the binding free energy of the inhibitor to\nthe dimer-inhibitor complex; and∆GS,DI is the binding free energy of the substrate to the\ndimer-inhibitor complex. kcat are enzyme velocities:kcat,M S is the velocity of the monomer-\nsubstrate complex; kcat,DS is the velocity of the dimer-substrate complex; andkcat,DSS is the\nvelocity of the dimer bound to two substrates.\nSome thermodynamic and kinetics parameters were treated as global, the same for every\ndataset, and others local, dependent on the inhibitor. The global parameters were the\nbinding free energy of dimerization∆Gd, binding free energies between the enzyme and the\nsubstrate ∆GS, and rate constantskcat,DS and kcat,DSS. The inhibitor-dependent parameters\nwere the binding free energies of the inhibitor binding to the enzyme∆GI, the binding free\nenergy of the substrate binding to the enzyme-inhibitor complex∆GS,DI, and the velocity\nof the enzyme-substrate-inhibitor complexkcat,DSI.\nIn addition to the thermodynamic and kinetic parameters, our model also uses several\nlocalparameters: [E]t, αp, andσc. [E]t isthetrueenzymeconcentration. Trueconcentrations\n7\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nmay differ from the stated concentrations due to dilution errors or protein degradation. We\nused one parameter[E]t for each of the three stated monomer concentrations of 25, 50, and\n100 nM; [E]25 is the true concentration for the solution with a stated concentration of 25\nnM, and analogously for 50 and 100.αp is a scaling factor for all velocities on a given plate\np. It accounts for differences in velocity calibration due to factors such as plate material\nor path length variation, instrument lamp intensity or detector sensitivity fluctuations, and\nsample variations such as pH or buffer evaporation. There was 1 plate for ES, 4 plates for\nESI4c, and 45 plates for ESI1c.σc is the standard error of the velocity, indexed byc, and is\nassumed to be constant for all points in a CRC.σc was also used in our previous work.21\n2.2.2 Likelihood\nFor each CRC, the dataD ∈ {y1, y2, ..., yn} are initial velocities (v, M/min) of the enzymatic\nreaction. Initial velocities were calculated based on linear regression and normalization\nto ensure that the same rates are obtained for the same reaction conditions. The total\nfluorescence response R was assumed to the sum of the response of the fluorescent substrate\nand product. For each species, the fluorescence response is the concentration of the species\n(cs for substrate and cp for product) and its molar response (rs for substrate and rp for\nproduct),\nR = csrs + cprp, (2)\nwhich has the time derivative,\ndR\ndt = rs\ndcs\ndt + rp\ndcp\ndt . (3)\nThus, as substrate is converted into product, the observed slope ism = (rp − rs)v, wherev is\nthe initial velocity of the reaction. For each well, the slopem was determined by measuring\nthe response from the biochemical assay every 2 minutes for 10 minutes after addition of sub-\n8\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nstrate and performing ordinary least squares linear regression (linalg.lstsq) as implemented\nin numpy.rs was determined by dividing the intercept by the initial substrate concentration.\nOn the master plate with the ES dataset,rp was calibrated by measuring fluorescence after\n21 hours, at which point the substrate was assumed to be completely converted to product.\nFor plates with the ESI4c datasets,rp for each plate was determined by solving a system\nof linear equations such that at the same enzyme and substrate concentrations, the initial\nvelocity of the plate and the master plate are equal. Velocities in the ESI1c dataset were\nnormalized to a velocity interpolated from the ES and ESI4c datasets. After fitting the veloc-\nities from the ES and ESI4c datasets by Bayesian regression, maximum a posteriori (MAP)\nparameters were used to estimate a reference velocityv0, the velocity at 50 nM enzyme and\n550 nM substrate; this condition was measured on all of the plates of the ESI1c dataset.\nDuring exploratory data analysis, we identified outliers, many which we attributed to\nlimited solubility at high compound concentrations. Before fitting the model, outliers were\nremoved using az-score test.27 A pooled standard deviation was calculated for each CRC in\nthe ESI datasets as,\nσ = 1\nN − 1\nX\nc\nX\ni\n(yc,i − ¯yc)2 , (4)\nwhere yc,i is a measured velocity at a given condition (enzyme, substrate, and inhibitor\nconcentration) and ¯yc is the sample mean of velocities at the condition. Sums are over the\nmeasurements and conditions andN is the number of measurements in all conditions (six\nfor ES datasets and two for ESI datasets.) Thez-score was calculated as,\nzc,i = yc,i − ¯yc\nσ . (5)\nAn observationyc,i is considered an outlier if the absolute value of its correspondingzc,i score\nexceeds 2.5. The thresholds of -2.5 and 2.5 correspond to the 2.5th and 97.5th percentiles of\nthe observations in the dataset, respectively. Any outliers present in each CRC were removed\n9\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nbefore fitting.\nMeasurements were assumed to follow a normal distribution centered around model-\npredicted values (scaled byαp), yn ∼ N (αpy∗\nn(θ), σ2). The likelihood of the dataD is given\nby,\np(D|θ) = 1\n(2π)N/2σN exp\n\"\n− 1\n2σ2\nNX\nn=1\n(yn − αpy∗\nn(θ))2\n#\n(6)\nin which the measurementy∗\nn(θ) is a function of all parameters inθ, except forαp.\n2.2.3 Prior\nAssuming that the parameters are independent, the priorp(θ) is a product of the prior for\nall parameters, p(θ) =Q\ni p(θi). Based on the reported value ofKd (52 ± 5 µM)16 and the\nrelationship betweenbinding free energyand dissociation constantthrough∆G = −RT ln K,\nthe prior of ∆Gd would follow a normal distribution with a mean of -5.9 and a standard\ndeviation of 0.06. However, to reduce the influence of this prior we chose a larger standard\ndeviation,\n∆Gd ∼ Normal(−5.9, 0.3) (kcal/mol). (7)\nBroad uniform priors were chosen for other binding free energies. The range of∆GS was\nbased onKS between 1 nM and 1 M. The range of∆GI was based onKI between 1 pM and\n10\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\n1 M.\n∆GS,M ∼ Uniform(−12.4, 0.0) (kcal/mol)\n∆GS,D ∼ Uniform(−12.4, 0.0) (kcal/mol)\n∆GS,DS ∼ Uniform(−12.4, 0.0) (kcal/mol)\n∆GI,M ∼ Uniform(−16.5, 0.0) (kcal/mol)\n∆GI,D ∼ Uniform(−16.5, 0.0) (kcal/mol)\n∆GI,DI ∼ Uniform(−16.5, 0.0) (kcal/mol)\n∆GS,DI ∼ Uniform(−16.5, 0.0) (kcal/mol). (8)\nBroad uniform priors were also selected for the kinetic parameters. Based on the reported\nvalue of kcat (0.2 ± 0.02 min−1),16 we chose,\nkcat,DS ∼ Uniform(0.0, 5.0).\nkcat,DSS ∼ Uniform(0.0, 5.0). (9)\n(10)\nDue to the biphasic behavior observed in CRCs,16 we set a higher upper limit forkcat,DSI ∼\nUniform(0.0, 10.0).\nFor prior ofαp, uniform distribution was used,\nαp ∼ Uniform(0.0, 2.0). (11)\nwhere p is the index for the plate. Because the uncertainty in concentration due to sample\npreparation in biochemical assays has been shown to be approximately 10%,28 we used a\n11\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nlog-normal prior with 10% uncertainty for the enzyme concentration,\n[E]t ∼ LN (µ = [E]s, σ = 0.1 ∗ [E]s), (12)\nwhere [E]s for s ∈ {25, 50, 100} nM is the stated value of the enzyme concentration and[E]t\nis the true value. The uninformative Jeffreys prior29 was used forσ of each CRC, as in our\nprevious work.21\n2.2.4 Sampling from the posterior\nAs the complexity of the model and large amount of data made global fitting computationally\nprohibitive with our limited computing resources, we divided the fitting process into several\nsteps, leveraging the posterior distribution from one step to limit the prior of the next.30\n1. AsimplifiedenzymekineticsmodelwithoutinhibitorwasfittotheESdatasettoobtain\nranges of ∆Gd, ∆GS,M, ∆GS,D, ∆GS,DS, kcat,DS, kcat,DSS, and [E]t. As we treated the\nES plate as a reference,αp was set to 1.\n2. The full enzyme kinetics model was fit to the ES dataset and curves fromeach inhibitor\nin the ESI4c dataset. The priors of∆Gd and ∆GS were defined based on the minimum\nand maximum values of these parameters observed in posteriors from step 1.\n3. The full enzyme kinetics model was globally fit to the ES dataset and thefull ESI4c\ndataset. The priors of ∆Gd, ∆GS, and αp were defined based on the minimum and\nmaximum values of these parameters observed in every posterior from step 2.\n4. The full enzyme kinetics model was globally fit to the ES dataset, the full ESI4c\ndataset, and three selected curves from the ESI1c dataset. Priors were defined as in\nStep 4. The three curves were selected based on criteria described below.\n5. When fitting to the ESI1c dataset, global parameters were fixed to the MAP of Step\n3 or 4 and local parameters were sampled from the conditional probability.\n12\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nThe three curves in Step 4 were selected based on using the MAP from Step 3 in Step 5.\nThe model from Step 5 did not fit to these three ESI1c curves. Therefore, we incorporated\nthe data in Step 4 in order to obtain a MAP capable of fitting not only ES and ESI4c data,\nbut also the selected ESI1c data.\nThe No-U-Turn sampler (NUTS) was used to sample from posterior distributions.31\nNUTS was run for 10,000 samples in steps 1 and 2. Because we observed that the posteriors\nwere already converged by 1,000 samples in steps 1 and 2, we collected 1,000 equilibrated\nsamples in steps 3 and 4. The equilibration time of all the parameters was detected using\nautomated equilibration detection32 as implemented in pymbar v4.0.3.33,34\n2.3 Estimating pIC50s and pIC90s\nInhibitory concentrations were estimated by fitting data with the Hill equation,\nyi(Ci, Rb, Rt, pIC50, H) = Rb + Rt − Rb\n1 + 10(pIC 50−pCi)∗H , (13)\nwhere Rb is the bottom response, Rt is the top response, pIC 50 is the negative base 10\nlogarithm of the half maximal inhibitory concentrationIC 50, and H is the Hill slope.\nAs outlined at the end of the introduction, we estimated inhibitory concentrations based\non three types of CRCs. For the inhibition pIC50, we first identified the concentration of\ninhibitor that yields the maximum response. The Hill equation was fit to data at this and\nhigher concentrations. For the control pIC50, the Hill equation was fit to data at this and\nhigher concentrations where the response is less than the negative control (Figure 1).\nFor the dimer pIC50, we simulated CRCs using the dimer-only kinetic model and fit the\nHill equation to the entire curve.21 Enzyme and substrate concentrations were drawn from\nlognormal distributions with a 10% uncertainty. The substrate concentration was selected\nto be saturating, 1000 times larger than the enzyme concentration. These concentrations\nwere selected by dividing the ESI1c dataset (85 curves) into a training set (45 curves) and\n13\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\na testing set (40 curves). Enzyme concentrations were optimized by minimizing the root\nmean square deviation between the dimer pIC50s and cellular pEC50s within the training\nset. This optimization was performed byscipy.optimize.minimize.35 Optimized concen-\ntrations were then applied to estimate dimer pIC50/pIC90 values in the testing set. The\nreported mean and standard deviation are results from repeating this procedure 100 times.\nVelocitiesweresimulatedat50geometricallydistributedinhibitorconcentrationsbetween\n1 pM to 1 mM and normalized to be between 0 and 100%.\nFigure 1: Representative inhibitionIC 50 and control IC 50.\nHill equation parameters were estimated using maximum likelihood estimation. For the\nbiochemical data, estimation was performed using our custom code.36 The EC50 is the\nhalf maximal effective concentration in cellular assays. Cellular pEC50s for antiviral assays\nwere estimated by fitting the Hill equation to the data using CDD Vault (https://www.\ncollaborativedrug.com/).\nBesides IC50, another commonly used metric for assessing the potency of a drug is the\nIC 90. This parameter denotes the concentration at which 90% of the enzyme is inhibited.\nGiven the IC 50, the Hill slope H, and a specific percentage F ranging between 0 to 100,\nrepresenting for the degree of enzymatic inhibition or cellular viability, theIC (F ) can be\n14\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\ncalculated using the formula 14,37\nIC (F ) =\n\u0012 F\n100 − F\n\u00131/H\nIC 50. (14)\nWith F set to 90, the formula simplifies to,\npIC 90 = pIC 50 − log(9)/H. (15)\nAnalogous formulae apply to pEC50 and pEC90 values for cellular assays.\n2.4 Correlation analysis\nCorrelation between the pIC50/pIC90 values obtained from different biochemical procedures\nand cellular pEC50/pEC90 were analyzed by a range of statistical measures, including the\nPearson R,38 Spearman ρ,39 Kendall τ,40 root mean square deviation (RMSD), and adjusted\nRMSD (aRMSD).41 Unlike the Pearson R, which measures linear correlation, the Spearman\nρ assesses the monotonic relationship between two variables by ranking data points and\nevaluating how well the ranks correspond, making it robust to nonlinearity. The Kendall\nτ evaluates whether pairs of data points move in the same or opposite directions. RMSD\nevaluates the absolute differences between predicted and observed values,\nRM SD =\nvuu\nt\n1\nN\nNX\nn=1\n(xn − yn)2. (16)\nThe adjusted RMSD (aRMSD) avoids the effect of systematic bias by normalizing RMSD\nusingthemeansofthedata, providingalocation-independentmeasureofpredictiveaccuracy,\naRM SD =\nvuu\nt\n1\nN\nNX\nn=1\n[xn − yn − (¯x − ¯y)]2. (17)\nFor the dimer pIC50/pIC90, the ESI4c 85 dataset was randomly split into a training set\n15\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\n(45 curves) and a test set (40 curves). Enzyme concentrations optimized using the training\nset were applied to estimate dimer pIC50/pIC90 values in the test set. This procedure was\nrepeated 100 times and the mean and standard deviation of results are reported.\n2.5 Code\nAll code is freely available athttps://github.com/vanngocthuyla/kinetic_mpro/tree/\nmain/mers.\n3 Results\n3.1 Bayesian credible intervals were converged\nThe convergence of sampling from Bayesian posteriors was evaluated based on the 5-th,\n25-th, 50-th, 75-th and 95-th percentiles of the marginal probability of parameters. In\nrepresentatives of all analyses (Figure S1, S4, S16, S20), these percentiles exhibited minimal\nchanges as the number of samples increases. Estimated standard errors were negligible. This\nconvergence indicates that the posterior distributions have been thoroughly sampled after a\nsmall number of samples from the posterior.\n3.2 Global fitting increases the precision of parameter estimates\nOverall, we observed that Bayesian posterior probability distributions became narrower with\nthe inclusion of additional data. In this section, we describe results from Steps 1 through 4.\nAll Step 2 results are with a representative compound, ASAP-0000214.\nMarginal distributions of all enzyme-substrate binding free energies are unimodal and\nnearly independent (Figures 2, S2, and S6). ∆Gd has a relatively small highest density\ninterval (HDI) that is unaffected by the amount of data analyzed. The other parameters\nare broader in Steps 1 and 2, with∆GS,M and ∆GS,DS approaching the upper limit of weak\n16\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\naffinity. All parameters are defined more precisely in Steps 3 and 4. For instance, the 95%\nHDI of∆GS,M in Steps 1 and 2 ranged between -7.5 and 0, whereas in Step 3 and 4, the HDI\nfell into a narrower range between -5.7 and -4.4. Between Steps 3 and 4, there is no significant\ndifference in posterior distributions of these parameters. In Steps 1 and 2, two-dimensional\nmarginal distributions suggest that pairs of enzyme-substrate binding free energies are nearly\nindependent (Figures S3 and S7). In Steps 3 and 4, however,∆GS,M is negatively correlated\nwith ∆GS,D (Pearson R = -0.75) and positively correlated with∆GS,DS (Pearson R = 0.94).\n∆GS,D and ∆GS,DS are negatively correlated with each other (Pearson R = -0.76) (Figures\nS13, S14, S17, and S18).\nWith additional data, the binding cooperativity of the substrate also becomes more\nclearly determined (Figure 3). In steps 1 and 2, the estimated difference between∆GS,DS\nand ∆GS,D is broad (step 1: median 6.5 and 95% HDI [1.7, 11.0] kcal/mol; step 2: median 6.6\nand 95% HDI [2.2, 10.0] kcal/mol). The median is positive, suggesting negative cooperativity\nof substrate binding, with the caveat of low precision. However, with additional data, the\nposterior is much narrower and the median indicates positive cooperativity of substrate\nbinding (step 3: median -0.99 and 95% HDI [-2.3, 0.57] kcal/mol; step 4 median -0.89; 95%\nHDI: [-1.9, 0.54] kcal/mol).\nMarginal distributions of all enzyme-inhibitor binding free energies are unimodal, and\nsome show significant correlations (Figure S7). In Step 2,∆GI,DI reaches the lower bound\nof strong affinity, indicating that the second binding of the inhibitor to the dimer-inhibitor\ncomplex is highly favorable. Correlations can be summarized via Pearson correlation co-\nefficients. In Step 2, the heatmap of the estimated parameters indicates that∆GS,DS and\n∆GI,M, which have broad posterior distributions, have no correlation with any other param-\neters (Figure S8). On the other hand,∆GI,D displays a strong negative correlation with both\n∆GI,DI and ∆GS,DI, but have no correlation with any other dissociation constants (Figures\nS8, S9a and S9b).∆GS,DI demonstrates a positive linear correlation with∆GI,DI, although\nthe difference between them is small (∆GS,DI=∆GI,DI+1.83, Figure S9c).\n17\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nFigure\n2: 1D marginal distributions of free energies (kcal/mol). Estimates were based on\n1,000 MCMC samples generated from the Bayesian posterior in Steps 1 (purple dotted\nline), 2 (green dashdot line), 3 (orange dashed line), and 4 (blue solid line). Red bars\nrepresent 95% HDIs from Step 4. The red triangle marks the median of that posterior.\nFigure\n3: Differences in binding free energies of substrate (kcal/mol). Estimates were based\non 1,000 MCMC samples generated from the Bayesian posterior in Steps 1 (purple dotted\nline), 2 (green dashdot line), 3 (orange dashed line), and 4 (blue solid line). Red bars\nrepresent 95% HDIs from Step 4. The red triangle marks the median of that posterior.\n18\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nBayesian posterior distributions of most rate constants are broad; data are insufficient to\nestimate these parameters accurately (Figure 4). For Steps 1 and 2, the marginal ofkcat,DSS\nhas a peak at low rates and a heavy tail that spans the range of the prior. In Steps 3 and 4,\nthe posterior of low rates is significantly decreased. The posterior ofkcat,DSS is flat in Steps\n1 and 2, but sharply defined after Steps 3 and 4. For the representative ligand, posteriors\nof kcat,DSI are flat despite the inclusion of more data (Figure S10). Additionally, 2D joint\nmarginal distributions show that there is no correlation between rate constants (Figure S11).\nFigure 4: 1D marginal distributions of rate constants (min−1). Estimates were based on\n1,000 MCMC samples generated from the Bayesian posterior in Steps 1 to 4. The posterior\ndistribution of kcat,DSS is shown zoomed in opposed to the full domain between 0 and 5\nobserved for Steps 1 and 2. Annotations are analogous to Figure 2.\nWhile individual rates are difficult to determine, the data are sufficient to estimate ratios\nof rate constants. The posterior distributions for kcat ratios are better defined compared\nto those for kcat themselves. In Step 4, the catalytic rate for the dimer bound to a single\nsubstrate (DS) is faster than the rate when bound to two substrates (DSS) (Figure S19).\nFor the representative inhibitor, both are considerably lower than the rate observed for the\ndimer-substrate-inhibitor complex (DSI) (Figure S10). In Step 5, for the majority of ligands\nin the dataset, kcat,DSI is comparable to or larger thankcat,DS (Figure 5). However, a few\nligands (ASAP-00008489-001, ASAP-00011343-001, ASAP-00011513-001, ASAP-00012331-\n001, ASAP-00012335-001, ASAP-00013263-001, ASAP-00013299-001, ASAP-00013301-001,\n19\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nASAP-00013407-001, ASAP-00013412-001, ASAP-00014551-001, ASAP-00014717-001, ASAP-\n00014750-001, ASAP-00014776-001, ASAP-00015517-001) clearly have lowkcat,DSI.\nFigure 5: Ratios of rate constants for all ligands from the ESI4c data set. Estimates were\nbased on 1,000 MCMC samples generated from the Bayesian posterior. Red bars represent\n95% HDIs, while green triangles mark the median of the posteriors. The vertical blue lines\nrepresented for the prior distributions.\nEnzyme concentration parameters are consistent with stated values except at the highest\nenzyme concentration (Figure 6). In Steps 1 and 2, there is still significant uncertainty in\nthe enzyme concentrations; marginal distributions are broad. In Steps 3 and 4, the 95% HDI\nof enzyme concentration parameters included the stated concentrations of 25 and 50nM,\nbut the median enzyme concentration parameter for 100nM is only 59.7nM. It is possible\nthat at high concentration, the enzyme precipitates or forms inactive higher-order oligomers,\nreducing the concentration of active enzyme.\n20\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nFigure\n6: 1D marginal distributions of enzyme concentrations (nM). Estimates were\nestimated based on 1,000 MCMC samples generated from the Bayesian posterior.\nAnnotations are analogous to Figure 2.\n3.3 The enzyme kinetics model closely fits nearly all data\nIn Step 4, the enzyme kinetics model is a close fit to nearly all of the data from the ES,\nESI4c, and three ESI1c datasets (Figure 7). For some ligands, the velocity is higher than\nthe model near the peak velocity and at the highest ligand concentration of 99.5µM. For\nhigh concentrations, ligands may have solubility limits that reduce the amount of ligand in\nsolution. Similar results are achieved in Step 5 (Figure S21). A small subset of compounds\n(ASAP-0000219-001, ASAP-0000375-001, ASAP-0010712-001, ASAP-0013397-001, ASAP-\n0013405-001, ASAP-0013407-001, ASAP-0013423-001) exhibit a significantly broader 95%\nposterior predictive interval of the velocity.\n21\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\n10 7\n 10 6\nSubstrate (M)\n0.0\n0.5\n1.0\n1.5Rate (nM min 1)\n10 7\n 10 6\n 10 5\nASAP-0000153-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0000214-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0000223-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0000272-001 (M)\n0\n1\n2\n3Rate (nM min 1)\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0000577-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0000654-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0000733-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0000773-001 (M)\n0\n1\n2\n3Rate (nM min 1)\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0008374-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0008401-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0008420-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0008452-001 (M)\n0\n1\n2\n3Rate (nM min 1)\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0008502-001 (M)\n0\n1\n2\n3\n10 7\n 10 6\n 10 5\n 10 4\nASAP-0008642-001 (M)\n0.0\n0.2\n0.4\n0.6\n10 8\n 10 6\n 10 4\nASAP-0011124-001 (M)\n0.0\n0.2\n0.4\n0.6\nFigure 7: Fit of the model to ES + all ESI4c + 3 ESI1c datasets. X axes are\nconcentrations (M). Dots are observed velocities. Velocities predicted by the model are\ny∗\nn(θM AP) (dashed line), whereθM AP is the MAP estimate, the mean of the posterior\nprediction (solid line), and the 95% posterior predictive interval (shaded region). Data are\ncolored by plate. For the upper left plot: 100 nM (brown), 50 nM (red), and 25 nM (black)\nof the enzyme. For other plots: enzyme 100 nM, substrate 1350 nM (blue); enzyme 100\nnM, substrate 750 nM (orange); enzyme 50 nM, substrate 150 nM (purple); enzyme 100\nnM, substrate 50 nM (green); enzyme 50 nM, substrate 550 nM (pink, olive, gray).\n3.4 MERS-CoV MPro undergoes substrate-induced dimerization\nWe modeled substrate-induced dimerization by calculating the effect on substrate on the\namount of enzyme in the monomeric versus the dimeric form. We computed the concentra-\ntions of monomeric ([M] and [MS]) and dimeric ([D], [DS], [DSS]) species given an initial\n22\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nenzyme concentration of 0.3µM and substrate concentration of 600µM, similar to a previous\nstudy,42 using thermodynamic and kinetic parameters drawn from the posterior. Monomeric\nand dimeric oncentrations were used to compute anapparent binding affinity,\n∆Gd,app ∼ −RT ln\n\u0012 ([M] + [M S])2\n[D] + [DS] + [DSS]\n\u0013\n. (18)\nThe 95% HDI of∆Gd,app is [-12, -9.2] kcal/mol with a mean of -10 kcal/mol. In contrast,\nthe 95% HDI of∆Gd is [-6.7,-5.4] kcal/mol with a mean of -5.9 kcal/mol. Thus, the model\npredicts strong substrate-induced dimerization under conditions similar to prior work.42\n3.5 The MERS-CoV MPro dimer binds most ligands with positive\ncooperativity\nMostinhibitorsexhibitedpositivecooperativitywiththeenzyme, asthefreeenergydifference\nbetween the second and first binding events was less than zero (Figure 8), except for ASAP-\n00013249-001, ASAP-00013301-001, ASAP-00013412-001, ASAP-00013894-001, and ASAP-\n00014900-001.\n3.6 Biochemical and cellular potencies of ASAP MERS-CoV MPro\ninhibitors are highly correlated\nCorrelations between inhibition, control, and dimer pIC50s are greater than 0.8 but there are\nweaker correlations with cellular pEC50s (Figure 9 and Table 1). The highest correlation\nis observed between inhibition and control pIC50s, with the Pearson R and Spearmanρ\nabove 0.93. Furthermore, the three pIC50s derived from the same biochemical CRC exhibit\na high level of correlation with each other. On the other hand, the coefficients between the\ncellular pEC50 and the other three pIC50s are less than 0.8, indicating a clear discrepancy\nbetween the biochemical and cellular assays. This discrepancy suggests that some factors in\nthe cellular environment, such as cellular permeability and metabolic stability, may not be\n23\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nFigure 8: Differences in binding free energies of inhibitors (kcal/mol). Estimates were\nbased on 1,000 MCMC samples generated from the Bayesian posterior from Step 5. Red\nbars represent 95% HDIs, while green triangles mark the median of the posteriors.\ncaptured in the biochemical assay.\nTable 1: Correlation matrix of biochemical pIC50 and cellular pEC50 by Pearson R,\nSpearman ρ, and Kendallτ\nPearson R Inhibition pIC50 Control pIC50 Dimer pIC50\nControl pIC 50 0.955 ± 1.493E-2\nDimer pIC 50 0.888 ± 7.541E-2 0.878 ± 6.918E-2\nCellular pEC50 0.720 ± 6.576E-2 0.712 ± 6.678E-2 0.711 ± 6.152E-2\nSpearman ρ Inhibition pIC50 Control pIC50 Dimer pIC50\nControl pIC 50 0.937 ± 2.156E-2\nDimer pIC 50 0.925 ± 4.765E-2 0.915 ± 4.493E-2\nCellular pEC50 0.677 ± 6.061E-2 0.659 ± 6.792E-2 0.718 ± 5.166E-2\nKendall τ Inhibition pIC50 Control pIC50 Dimer pIC50\nControl pIC 50 0.807 ± 3.352E-2\nDimer pIC 50 0.839 ± 4.543E-2 0.805 ± 4.485E-2\nCellular pEC50 0.501 ± 5.298E-2 0.492 ± 5.797E-2 0.530 ± 4.819E-2\nThe dimer pIC50 outperforms the inhibition and control pIC50 in forecasting the rank\n24\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nFigure 9: Correlogram of inhibition, control, dimer pIC50 and cellular pEC50.\nTable 2: Correlation matrix of biochemical pIC50 and cellular pEC50 by RMSD and\naRMSD\nRMSD Inhibition pIC50 Control pIC50 Dimer pIC50\nControl pIC 50 0.684 ± 1.565E-2\nDimer pIC 50 0.560 ± 5.985E-2 0.337 ± 1.173E-1\nCellular pEC50 0.568 ± 3.833E-2 0.415 ± 2.503E-2 0.415 ± 7.359E-2\naRMSD Inhibition pIC50 Control pIC50 Dimer pIC50\nControl pIC 50 0.132 ± 1.499E-2\nDimer pIC 50 0.261 ± 1.327E-1 0.267 ± 1.194E-1\nCellular pEC50 0.338 ± 2.350E-2 0.352 ± 2.434E-2 0.405 ± 7.405E-2\nof the cellular pEC50, but has similar Pearson R and higher error (Table 1). Assuming\nthat the statistical metrics are independent and follow a normal distribution, we evaluated\n25\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\np-values from the two-sample comparison of coefficients with the null hypothesis that there\nis no difference in the means of coefficients, then applied the Bonferroni adjustment for the\ncomparison of 4 procedures.43 With the threshold at 0.05, the adjusted p-values suggested\nstronger evidence to reject the null hypothesis for Spearmanρ and Kendall τ (Table S3). In\nother words, the correlation coefficients between dimer pIC50 and cellular pEC50 are higher\nthan the coefficients between other biochemical pIC50s and cellular pEC50 when evaluated\nby Spearmanρ and Kendallτ. This indicates that, according to rank order, the dimer model\nmay align more closely with cellular responses than the inhibition and control procedures.\n3.7 The dimer pIC90 better ranks cellular pEC90 than the dimer\npIC50 ranks cellular pEC50\nAs many of the CRCs from antiviral assays have a Hill slope distinct from one, we hypoth-\nesized that a high level of MPro inhibition is required to improve cell viability and that\nbiochemical pIC90 would better predict cellular pEC90 than biochemical pIC50 predicts cel-\nlular pEC50. Overall, correlation and error metrics for pIC90/pEC90 (Figure S22, Table S1,\nTable S2, and S4) were higher than those for pIC50/pEC50 (Figure 9, Table 1, and Table\n2) when evaluated by Spearmanρ and Kendall τ.\n4 Discussion\n4.1 Enzymekineticsexperimentsaresufficienttodetermineparam-\neters of a complex model\nWe have demonstrated that enzyme kinetics experiments with varying concentrations of\nenzyme, substrate, and multiple inhibitors are sufficient to precisely determine most pa-\nrameters of a complex enzyme kinetics model. When we recently introduced our enzyme\nkinetics model that incorporates both dimerization and ligand binding,21 we not only fit it\n26\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nto biochemical enzyme kinetics but also to analytical ultracentrifugation data for two vari-\nants of SARS-CoV-2 MPro: the wild-type enzyme and a mutant engineered to have a weaker\ndimerization affinity.44 Here we pursued an alternative strategy of fitting many CRCs for\none enzyme.\nWe have also addressed the computational challenge associated with globally fitting nu-\nmerous CRCs. We leveraged the structure of Bayesian posteriors to break down the fitting\nprocess into multiple steps and incrementally incorporate additional information into the\nmodel. Even with uninformative priors (besides the dimerization affinity), we observed that\nas the amount of data are increased from Steps 1 to 4, the binding free energies and ratios of\nspecies-specific rates are estimated more precisely. The success of global fitting extends be-\nyond the estimation of binding affinities for the inhibitors present in the fitted datasets; the\nshared parameters derived from this process can also be leveraged to fit additional datasets\nthat were not included in the original fitting procedure.\n4.2 Parameters are within ranges reported for MERS-CoV MPro\nand distinct from other MPro variants\nOur estimated parameters are consistent with values reported for MERS-CoV MPro enzyme\nkinetics. The 95% HDI ofKd in our paper is consistent with reported values from different\nmeasurements: 7.8 ± 0.3 µM by enzymatic assay;16 52 ± 5 µM by analytical ultracentrifu-\ngation;16 and 7.7 ± 0.3 µM by analytical ultracentrifugation.42 Based on the assumption\nthat only dimeric enzyme is catalytically active, Tomar et al.16 fit the observed rate as a\nfunction of the enzyme concentration to a model in which the apparent rate is proportional\non the dimer concentration. They reported kcat of 0.2 ± 0.02 min−1, which is faster than\nkcat,DSS but slower thankcat,DS. Given that the apparentkcat should be linear combination of\nturnover numbers from both species, the reported intermediate value does not raise concerns.\nMERS-CoV belongs to a group of RNA viruses that have caused several human outbreaks\nover the past two decades, including the severe acute respiratory syndrome (SARS) CoV and\n27\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nSARS-CoV-2.4,45 Based on phylogenetic analysis, MERS-CoV belongs toβ-CoV lineage C\nand is more closely related toTylonycteris bat CoV HKU4 andPipistrellus bat CoV HKU5,\nwhile SARS-CoV and SARS-CoV-2 are classified intoβ-CoV lineage B.46–48Our estimated\nKd for MERS-CoV MPro is weaker than for human SARS-CoV (0.7± 0.02 µM)42 and\nSARS-CoV-2 (1.32 ± 0.2 µM),44 as well as the enzymes from closely related bat CoVs such\nas HKU4-CoV (0.1± 0.03 µM) and HKU5-CoV (0.06± 0.01 µM).42 The dimerization free\nenergy is between what we reported for the SARS-CoV-2 MPro wild type (median: -8.9\nkcal/mol; 95% HDI: [-9.8, -7.0] kcal/mol) and slightly stronger than the mutant (median:\n-4.2 kcal/mol; 95% HDI: [-4.6, -1.7] kcal/mol).21\nDifferences in dimerization affinities between MPro from different CoVs may be largely\nattributed to dimerization interfaces. In the case of SARS-CoV MPro, there are intermolec-\nular polar interactions involving four amino acid pairs (Ser1-Glu166, Arg4-Glu290, Ser123-\nArg298, and Ser139-Gln299).42 For SARS-CoV-2 MPro, in addition to three of the pairs\n(Ser1-Glu166, Arg4-Glu290, and Ser139-Gln299), hydrogen bonding between the side chains\nof two Ser10, along with a long-distance ionic interaction between Lys12 and Glu14, were\nreported to contribute to this process.49 In contrast, only two pairs are found in MERS-CoV\nMPro: Ser1-Glu169 and Ser142-Gln299.42 The reduced number of intermolecular interac-\ntions likely cause MERS-CoV MPro to have a weakerKd compared to the enzymes from the\nother human CoVs. On the other hand, the differences in theKd values between MERS-\nCoV MPro and its closely related HKU4-CoV and HKU5-CoV can be attributed to the\nnon-conserved residues located in the N-terminal finger, the N-terminal helix, and domain\nIII.16\nComparing other enzyme kinetics parameters for SARS-CoV-2 MPro from our previous\nanalysis21 and MERS from our present analysis illustrates variations in how the enzyme can\nbehave and interact with ligands. The binding free energy of substrate to the monomer\n∆GS,M is comparable in MERS-CoV MPro (median: -5.1; 95% HDI: [-5.7, -4.4] kcal/mol)\nand SARS-CoV-2 MPro (median: -4.7; 95% HDI: [-4.8, -4.5] kcal/mol), but dimerization\n28\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nhas a much greater effect on substrate binding for MERS-CoV MPro. While the binding\naffinity of the substrate for the dimer∆GS,D is much lower than∆GS,M for MERS-CoV\nMPro (median: -9.0; 95% HDI: [-9.9, -8.4] kcal/mol), it is similar to∆GS,M for SARS-CoV-\n2 MPro (median: -4.7; 95% HDI: [-6.0, -4.0] kcal/mol). There is also a contrast in binding\ncooperativity behavior; while the binding free energy of the substrate to the dimer-substrate\ncomplex ∆GS,DS for MERS-CoV MPro (median -10.0; 95% HDI: [-10.1, -9.3] kcal/mol) is\nlower than∆GS,D, indicating positive cooperativity,∆GS,DS for SARS-CoV-2 MPro (median\n-0.8; 95% HDI: [-2.7, 0.] kcal/mol) is higher than∆GS,D, indicating negative cooperativity.\nRelative rate constants also differ between MPro variants. For wild-type SARS-CoV-2 MPro,\nall of the rates -kcat,DS, kcat,DSS, and kcat,DSI - are comparable.21 For the mutant,kcat,DSI\nand kcat,DSS are comparable to each other and larger thankcat,DS. Here, we report that\nkcat,DSI and kcat,DS are comparable to each other and larger thankcat,DSS for MERS-CoV\nMPro. These comparisons suggest that coronaviruses could employ different strategies for\nthe regulation of enzyme activity. Compared to SARS-CoV-2 MPro, MERS-CoV MPro\nrequires more enzyme to dimerize and become active, but the dimer binds more tightly to\nthe substrate.\nAs a word of caution, differences in enzyme kinetics parameters may not be due the pro-\nteins themselves, but can be affected by assay conditions such as the choice of substrate. Our\nstudy used the substrate [5-FAM]-AVLQSGFR-[Lys(Dabcyl)]-K-amide. In contrast, Nashed\net al.44 used Dabsyl-KTSAVLQ/SGFRKM-E(Edans)-NH2, a longer peptide that could have\ngreater difficulty occupying both binding sites. Additional data and analyses would be re-\nquired to dissect whether parameter differences originate from the protein sequence or the\nassay conditions.\n29\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\n4.3 FullCRCfittinganddimerpIC90calculationsarerecommended\nfor drug discovery targeting MERS-CoV MPro and similar en-\nzymes\nWe recommend interpreting CRCs of MERS-CoV enzyme inhibition by fitting an enzyme\nkinetics model and calculating dimer pIC90s. We compared three data analysis procedures\nusing Pearson R, Spearmanρ, and Kendallτ correlation metrics based on two assumptions:\nthe null hypothesis for multiple-sample comparisons that there are no differences in the\nmeans of the coefficients; and the correlation coefficients follow a normal distribution. While\nbounded metrics cannot strictly follow a normal distribution, these assumptions are a rea-\nsonable approximation. Based on these assumptions, all three data analysis procedures that\nwe evaluated yielded inhibition constants that are correlated with cellular efficacy. While\nall three biochemical procedures have similar Pearson R, dimer pIC50/90 generally have a\nhigher Spearman ρ and Kendall τ rank correlation with cellular pEC50/90. Additionally,\nthe pIC90 was found to be more predictive than the pIC50. In the context of a drug dis-\ncovery campaign, the major objective of performing biochemical assays is to prioritize a\nsubset of compounds to test in more expensive and challenging antiviral assays. Rank order\ncorrelations are the most relevant metrics for prioritization decisions.\nBeyond achieving the highest rank correlations with cellular efficacy, fitting the enzyme\nkinetics model provides insight into the mechanism of specific inhibitors. MPro enzyme\nkinetics can be altered by inhibitor binding free energies to different species including the\nmonomer, dimer, and dimer-ligand complexes. Determining these parameters can help eval-\nuate whether a compound promotes dimerization or binds cooperativity to the target. The\nparameters can also quantify whether inhibitor binding to one catalytic site increases activ-\nity of the opposite site. Finally, determined parameters can be used to validate results from\nmolecular simulations. Because molecular simulations are performed with specific species,\ninhibitor binding free energies to specific species can be directly compared to forecasts from\n30\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\nthese calculations. Parameters from our fitting procedure have been used as benchmarks to\nvalidate an ASAP computational workflow Castellanos et al.50 and in a blind challenge for\nthe computational chemistry community MacDermott-Opeskin et al.22.\nThe main drawback of full CRC fitting is its relative complexity. Fortunately, we have\nmade our code freely available at https://github.com/vanngocthuyla/kinetic_mpro/\ntree/main/mers. In service of the ASAP drug discovery campaign targeting SARS-CoV-\n2/MERS-CoV MPro, the procedure was integrated into an automated data analysis pipeline\nthat presents results on CDD Vault (https://www.collaborativedrug.com/).\nBeyond MERS-CoV MPro, substrate/ligand-induced dimerization has been observed in\nmultiple serine proteases.51,52 Biphasic CRCs have been reported for the cysteine protease\ncaspase-1,53 and may be a factor in other enzymes.\n5 Conclusion\nWe have developed a multi-step statistical analysis procedure to fit an enzyme kinetics model\nthat incorporates dimerization and ligand binding to many CRCs with multiple inhibitors\nfrom a drug discovery campaign. The analysis precisely determines many binding parameters\nand ratios of rate constants and quantifies substrate-induced dimerization and ligand binding\ncooperativity. For the leads in the ASAP drug discovery campaign targeting MERS-CoV\nand SARS-CoV-2, inhibition constants from multiple data analysis procedures are highly\ncorrelated with cellular efficacy. pIC90s estimated by simulating CRCs at high enzyme\nconcentration are have higher rank correlation with cellular pEC90 than the other tested\nprocedures. Code implementing the procedure is freely available and is recommended for the\ninterpretationofbiphasicCRCsfromMERS-CoVMProandenzymeswithsimilarproperties.\n31\n.CC-BY 4.0 International licenseavailable under a \n(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made \nThe copyright holder for this preprintthis version posted February 21, 2026. ; https://doi.org/10.64898/2026.02.20.707097doi: bioRxiv preprint \n\n6 Disclosures\nJDC is a current member of the Scientific Advisory Board of OpenEye Scientific, and has\nequity in and serves as the Chief Executive Officer of Achira, Inc. which is engaged in\nthe creation of open foundation simulation models for drug discovery. A complete history\nof all entities that have provided funding for the Chodera lab can be found athttp://\nchoderalab.org/funding. DDLM is a founder of Biagon Inc. Biagon is not doing work\nrelated to this paper.\nAcknowledgement\nThisprojectwassupportedinpartbyNIAIDoftheNationalInstitutesofHealthunderaward\nno. U19AI171399 (JDC) and the NIH/NCI Cancer Center Support Grant P30 CA008748\n(JDC).\nThis work used the Jetstream2 cloud-based environment at Indiana University through\nallocation MCB150144 from the Advanced Cyberinfrastructure Coordination Ecosystem:\nServices & Support (ACCESS) program, which is supported by National Science Foundation\ngrants #2138259, #2138286, #2138307, #2137603, and #2138296.\nThe content is solely the responsibility of the authors and does not necessarily represent\nthe official views of the National Science Foundation or the National Institutes of Health.\nSupporting Information A vailable\nReferences\n(1) Zaki, A. M.; van Boheemen, S.; Bestebroer, T. M.; Osterhaus, A. D. M. E.; Fouchier, R.\nA. M. 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