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LLM - Digital Humanities 15

ERROR: type should be string, got "https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Abstract The treatment of SARS-CoV-2 can be accomplished by an effective suppression of its 3CL \nprotease (3CLpro), also known as the main protease (Mpro) and nonstructural protein 5 (nsp5). Covalent inhibitors can irreversibly and selectively disable the protease, particularly when they are \nhighly exothermic. Herein we delve into the distinct kinetic behaviors exhibited by two covalently \nlinked SARS-CoV-2 inhibitors. One of these inhibitors features a nitrile reactive group, while the \nother has this group replaced by an alkyne group, a less reactive electrophile. Our investigations \ninvolve the assessment of pertinent free energy surfaces through the utilization of both ab initio \nand empirical valence bond (EVB) simulations. The calculated free energy profiles show that \nsubstituting the nitrile group with alkyne significantly increases the overall reaction exothermicity. This leads to an efficient inhibition, even though the reaction of the nitrile group has a substantially \nlower barrier than the alkyne group. We examine the time-dependence of IC50 inhibition by \napplying a novel kinetic simulation approach, which is particularly important in studies of covalent \ninhibitors with a very exothermic bonding step. Our computational approach reproduces the \nobserved binding kinetics and appears to provide a powerful tool for studies of covalent inhibitors. This leads to an efficient inhibition, even though the reaction of the nitrile group has a substantially \nlower barrier than the alkyne group. We examine the time-dependence of IC50 inhibition by \napplying a novel kinetic simulation approach, which is particularly important in studies of covalent \ninhibitors with a very exothermic bonding step. Our computational approach reproduces the \nobserved binding kinetics and appears to provide a powerful tool for studies of covalent inhibitors. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Introduction The coronavirus disease 2019 (COVID-19), caused by the severe acute respiratory syndrome \ncoronavirus 2 (SARS-CoV-2), has been one of the most devastating pandemics of recent times. There has been significant effort to develop antiviral therapeutics targeting two proteases of SARS-\nCoV-2: the main protease (Mpro) and papain-like protease (PLpro).1–3 Out of these targets, Mpro, also \nknown as 3-chymotrypsin-like protease (3CLpro), has received significant attention in the \ndevelopment of antivirals, i.e., protease inhibitors, to combat COVID-19,4–7 with the fundamental \naim to disrupt the function and life cycle of SARS-CoV-2.8 Several small-molecule inhibitors of \nSARS-CoV-2 Mpro have been discovered, with a few progressing into early-phase human clinical \ntrials.9,10 Covalent enzyme inhibitors are of significant interest as biochemical tools and therapeutic \ndrugs. Previous authors have summarized the distinctive advantages and disadvantages of covalent \nenzyme inhibition in drug and inhibitor design.11–13 As the treatment of COVID-19 requires \ndisabling the activity of Mpro, covalent inhibitors with high exothermicity and irreversible binding \nto Mpro can be important candidates for antiviral treatments. A notable therapeutic strategy for \nCOVID-19 is to design inhibitors with an electrophilic reactive group (“warhead”) that binds to \nthe nucleophilic target cysteine 145 (Cys145) in Mpro. Cys145 is essential for the catalytic activity \nof Mpro, so blockage or modification of this residue is detrimental to the virus.14–18 Nirmatrelvir is \na new FDA-approved medication developed for the treatment of COVID‑1919 that has a nitrile \nwarhead and binds covalently and reversibly to Cys145. There are several known derivatives of \nnirmatrelvir, some of which are reversible, while others lead to irreversible catalytic reactions. Recently, Zhang and co-workers have demonstrated the effectiveness of latent electrophilic \nwarheads,20, such as terminal alkynes, in inhibiting Mpro compared to more reactive electrophiles \nlike acrylamides. These terminal alkyne warheads demonstrate marked specificity for Mpro due to \ntheir lack of intrinsic reactivity, which circumvents nonspecific binding to other cellular proteins. Upon activation within Mpro's active site, these warheads have shown potent inhibition, as \nconfirmed through biochemical assays and structural analysis via X-ray crystallography. Notably, \nthese terminal alkyne-based inhibitors have also exhibited promising antiviral activity in cellular \nmodels of COVID-19, indicating their potential as effective therapeutic agents. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 System Equilibration Our study began with the utilization of a co-crystal structure of the main protease (Mpro) of SARS-\nCoV-2 and the drug nirmatrelvir. The specific structure employed was sourced from the Protein \nData Bank (PDB), under the identifier 7RFS.24 In this structure, nirmatrelvir is observed to be \ncovalently bonded to the cysteine residue at position 145 (Cys145) of the protease. To investigate \nthe effects of an alkyne derivative, we referenced a similar co-crystal structure wherein the \nderivative forms a covalent bond at the same cysteine residue, as detailed in the study by Zhang et \nal. (PDB 8FY6).20 Following the selection of the initial structures, we performed molecular \ndynamics simulations using the GROMACS software suite (version 2021)25 with 40 ns trajectories. The Amber force field (ff14sb) was employed to model the interactions within the system. Subsequently, we carefully selected suitable initial configurations from the simulation trajectories \nto serve as starting points for the subsequent calculations involving the empirical valence bond \n(EVB) method. In order to define the force field parameters for the ligand atoms, we referred to \nthe generalized Amber force field (GAFF) using AmberTools 21.26 Introduction License: CC BY 4.0 Our prior computational investigations into covalent inhibitors targeting Mpro explored the \nmechanism of α-ketoamide inhibitors18 and the estimation of their absolute binding free energies.21 \nThis study centers on a comparative analysis between nirmatrelvir and its alkyne-substituted \ncounterpart, where the nitrile group is substituted with an alkyne group22,23 (see Figure 1). Our \nobjective is to elucidate the underlying factors responsible for the disparate behavior exhibited by \nthese inhibitors, particularly with regard to the time-dependent inhibition process. To achieve this \ngoal, we conducted a comprehensive exploration of the reaction mechanisms associated with each \ninhibitor through ab initio and empirical valence bond (EVB) simulations. A prior experimental \nstudy20 has shown that the alkyne derivative inhibits Mpro approximately five times less effectively \nthan nirmatrelvir, with an IC50 value of ~0.76 μM for nirmatrelvir and IC50 ≥ 0.063 μM for the \nalkyne derivative, following a preincubation period of three hours.22,24 Our simulations have not \nonly substantiated the exothermic nature of the alkyne substitution but also replicated the \ncorresponding time-dependent IC50 trend, corroborating the assertion that the alkyne derivative is \na more potent inhibitor compared to nirmatrelvir. Figure 1: Chemical structure for nirmatrelvir (a) and its alkyne derivative (b), in which the nitrile reactive \ngroup is substituted with an alkyne group. a\nb b b a a Figure 1: Chemical structure for nirmatrelvir (a) and its alkyne derivative (b), in which the nitrile reactive \ngroup is substituted with an alkyne group. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 EVB Simulations The EVB methodology utilizes a hybrid quantum mechanics/molecular mechanics (QM/MM) \nframework to model chemical reactions through a combination of relevant diabatic states. This \nenables an efficient exploration of reaction processes,33,34 as detailed in the Supplementary \nInformation. Prior studies have validated the utility of EVB in analyzing protease inhibition \nthermodynamics.18,35–38 Our EVB calculations were executed with the Q6 simulation software package.39 Within these \nsimulations, the active site of the reaction—comprising the inhibitor's reactive groups, Cys145, \nHis41, and a catalytic water molecule in nitrile—was designated as region 1. The remainder of the \nenzyme-solvent system was categorized as region 2. Electrostatic potential (ESP) charges for \natoms in region 1 were derived from Gaussian 16 calculations,27 which were then transformed into \nRestrained Electrostatic Potential (RESP) charges using the Antechamber tool from AmberTools \n21.26 The initial position of the sulfur in cysteine was used to set the center of the simulations \nsphere. The system was immersed in a water sphere with a diameter of 25 Å, where the water \nmolecules were described by the TIP3P model40 and subjected to the SCAAS boundary \nconditions,41 where the long-range effects were treated by the local reaction field.42 The multi-stage optimization of each reaction step commenced with a local energy minimization, \nconstraining all heavy atoms with a force constant of 20 kcal/ (mol Å2), followed by a gradual \nrelaxation of these restraints and a temperature increase from 5 to 300 K over 1 ns for system \nequilibration. Subsequent to this, free-energy perturbation/umbrella sampling (FEP/US)43 \nsimulations were conducted on the equilibrated systems to obtain the free-energy profiles. Ab \ninitio activation and reaction energy data from reference solution reactions were then employed to \nfine-tune the EVB Hamiltonian for each step of the reaction mechanism. For comprehensive \nsampling, we performed five umbrella sampling replicas, each comprising 100 frames with a 5 ps \nduration per frame to ensure statistical reliability and robustness of the results. Ab initio Calculations The reaction mechanisms pertinent to the aqueous phase, crucial for the calibration of EVB study \n(see below) were explored using ab initio computational methods. The study entailed modifying \nthe inhibitor molecules under consideration by truncating their reactive groups and capping the \nresulting sites with a methane moiety, as depicted in Figures S1 and S2 in the Supplementary \nInformation section. For the computational analysis, we employed the Gaussian 16 software \npackage.27 The quantum mechanical calculations were executed using Density Functional Theory \n(DFT), specifically applying the M06-2X functional combined with the 6-311+G(d,p) basis set to \nensure a balance of computational efficiency and accuracy.28–31 Additionally, the conductor-like \npolarizable continuum model (CPCM)32 was utilized to simulate solvent effects within these \ncalculations. Both the geometry optimizations and energy evaluation were conducted under this \ntheoretical framework. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Time-dependent kinetic simulations In the case of very exothermic covalent inhibitors, the justification of the use of the standard kinetic \nassay equations is far from obvious. Thus we used a kinetic simulation to evaluate the time https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 dependence of the competitive inhibition of Mpro in the experimental assay conditions by solving \nthe first-order system of equations as described in ref35, with the exception that the inhibitor may \nbe reversible. That is, competitive inhibition is described by the scheme, where E is the enzyme, S is the substrate, P is the product, I and I* are the free and bound inhibitors, \nand EI is the covalently bound enzyme-inhibitor complex. The equilibrium constant 𝐾! = 𝑘\"#/𝑘#, \nand catalytic rate 𝑘#,%&' of the substrate are determined by experimental characterization of the \nenzyme. The equilibrium constant 𝐾( = 𝑘\")/𝑘) is determined from the calculated PDLD/S-LRA/β \nbinding affinity,44 ∆𝐺*!+, by 𝐾( = 𝑒-.!\"#$/0%1 M, while the rates 𝑘2 and 𝑘\"2 are determined from \nthe barrier and reverse barrier, respectively, in the EVB profile using the Arrhenius relation. As \nthe second step of the inhibition scheme is the covalent and possibly irreversible step, 𝑘2 is \nequivalently denoted as 𝑘!+&%'. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Results and Discussion The key residues of Mpro include Cys145, His41, His163, His172, Glu166, and Ser144 (Figure 2) \nin its active site, which together form the oxyanion hole for the covalent and non-covalent binding \ninteractions. The catalytic dyad Cys145-His41, in which the N𝜀2 atom of His41 is 3.6Å away from \nthe SG atom of Cys145, participates in the first proton transfer. We initially observed that the \nprotonation state of His163 plays a crucial role in catalytic activity and binding affinity. One \npossible rationale is that the position of carbonyl oxygen in pyrrolidin-2-one of the inhibitors is \nstabilized by hydrogen bonding with His163. Thus, we proceeded with our calculations assuming \nN𝜀2 in His163 is protonated. We explored different ionizable states of His164 and His172 and \noverall, we found no significant changes in the EVB energy barrier when changing the protonated \nnitrogen from N𝜀2 to N𝛿1 or to both. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Figure 2: Structure of Mpro covalently bound with the alkyne derivative of nirmatrelvir (PDB 8FY6). Surrounding key residues for binding and catalytic activity are also shown. The binding pose and the \nconformers of the catalytic residue are essentially identical to the structure of Mpro covalently bound with \nnirmatrelvir (PDB 7RFS). GLU166\nHIS172\nSER144\nHIS163\nCYS145\nHIS164\nHIS41\nASP187 GLU166\nHIS172\nSER144\nHIS163\nCYS145\nHIS164\nHIS41\nASP187 Figure 2: Structure of Mpro covalently bound with the alkyne derivative of nirmatrelvir (PDB 8FY6). Surrounding key residues for binding and catalytic activity are also shown. The binding pose and the \nconformers of the catalytic residue are essentially identical to the structure of Mpro covalently bound with \nnirmatrelvir (PDB 7RFS). Figure 2: Structure of Mpro covalently bound with the alkyne derivative of nirmatrelvir (PDB 8FY6). Surrounding key residues for binding and catalytic activity are also shown. The binding pose and the \nconformers of the catalytic residue are essentially identical to the structure of Mpro covalently bound with \nnirmatrelvir (PDB 7RFS). https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Ab Initio Calculations As a starting point, we explored potential reaction pathways for the covalent binding of nitrile and \nalkyne functional groups to cysteine in a solution phase. These pathways will serve as reference \nreactions for our subsequent EVB calculations in water. We delineated each reaction pathway into \ntwo primary steps: a proton transfer between a cysteine and a histidine residue, and a concerted \nmechanism involving a proton transfer coupled with a nucleophilic attack (PT-NA), which can \noccur directly or with solvent assistance (see Figure 3). https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Figure 3: Reaction mechanisms for (a) nirmatrelvir and (b) its alkyne-substituted derivative. We examine \na solvent-assisted concerted proton transfer-nucleophilic attack step for nitrile group of nirmatrelvir, while \nfor the alkyne group we examine a direct mechanism. SH\nN\nNH\nN\nH\nO\nR\nS\nCys145\nN\nNH\nHis41\nH\n-\n+\nCys145\nHis41\nN\nH\nO\nS\nR\nCys145\nN\nH\nO\nN\nS\nHN\nNH\nH O H\n-\nR\n+\nHis41\nCys145\nSH\nN\nNH\nCys145\nHis41\nN\nH\nO\nHN\nS\nR\nCys145\na\nb a N\nH\nO\nN\nS\nHN\nNH\nH O H\n-\nR\n+\nHis41\nCys145\nSH\nN\nNH\nCys145\nHis41\nN\nH\nO\nHN\nS\nR\nCys145\na\nb SH\nN\nNH\nN\nH\nO\nR\nS\nCys145\nN\nNH\nHis41\nH\n-\n+\nCys145\nHis41\nN\nH\nO\nS\nR\nCys145\nN\nH\nO\nN\nS\nHN\nNH\nH O H\n-\nR\n+\nHis41\nCys145\nSH\nN\nNH\nCys145\nHis41\nN\nH\nO\nHN\nS\nR\nCys145\na\nb NH SH\nN\nNH\nN\nH\nO\nR\nS\nCys145\nN\nNH\nHis41\nH\n-\n+\nCys145\nHis41\nN\nH\nO\nS\nR\nCys145\nHis41\nCys145\nb b b Figure 3: Reaction mechanisms for (a) nirmatrelvir and (b) its alkyne-substituted derivative. We examine \na solvent-assisted concerted proton transfer-nucleophilic attack step for nitrile group of nirmatrelvir, while \nfor the alkyne group we examine a direct mechanism. Figure 3: Reaction mechanisms for (a) nirmatrelvir and (b) its alkyne-substituted derivative. We examine \na solvent-assisted concerted proton transfer-nucleophilic attack step for nitrile group of nirmatrelvir, while \nfor the alkyne group we examine a direct mechanism. The calibration of the EVB simulations was informed by these mechanistic explorations, as \ndetailed in Figure S3. Our attempt to identify the transition state for a water-assisted mechanism \nfor the alkyne group proved unsuccessful. Ab Initio Calculations However, we do not expect the absence of this pathway \nto significantly affect the energy barrier. This is based on the assumption that the non-polar nature \nof the alkyne group most likely hinders the introduction of water, unlike the polar nitrile group, \nwhich showed a lower energy barrier with a water-assisted mechanism compared to a direct \nmechanism (vide infra). We also investigated alternate possible mechanism involving the role of \nAsp187 in stabilizing the transition state. This mechanism, however, was found to be insufficiently \nendothermic to validate the proposed Cys145-His41-Asp187 catalytic triad hypothesis.45 As a result of these findings, we focused on a direct PT-NA mechanism for the alkyne group. In \ncontrast, for the nitrile group, attention was directed towards a mechanism facilitated by water, as \ndepicted in Figure 3. Alternative mechanisms, including those involving Asp187 and the potential \ncatalytic triad, are illustrated in Figure S4 for further reference. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 EVB Calculations As detailed above, the ab initio calibrated EVB Hamiltonian for the reaction in solution provides \nthe basis for modeling the corresponding enzymatic reactions. The calibrated EVB parameters as \nwell as a summary of the reaction routes that were explored by EVB simulation are given in the \nSupporting Information. Each step was evaluated in a reverse order, starting from the available \ncorresponding structures for the covalent form of the ligand, and we specifically focus on direct \nPT-NA mechanism for the considered warhead. In Figure 4, we present the EVB free energy \nprofile in protein as well as the reference reaction in water for nirmatrelvir, whereas that for the \nalkyne derivative are depicted in Figure 5. The PT-NA step emerged as the kinetic bottleneck for \nboth inhibitors, presenting a reaction barrier (Δ𝐺‡) of 17.5 kcal/mol, which corresponds to an \ninactivation rate constant (𝑘!+&%'), of the order of 1 s\"). This finding is in agreement with a Δ𝐺‡ \npredicted by another QM/MM approach, which posits a 16.3 kcal/mol barrier (𝑘!+&%' ≈10 s\")) \nfor the nitrile group, with a lower exothermicity. 46 Nirmatrelvir\nPT\nΔG‡=20.4\nΔG‡=17.5\nΔG0=-0.1\nΔG0=-1.6\nProton Transfer-\nNucleophilic Attack\nWater\nProtein\n-5\n0\n5\n10\n15\n20\n25\nReaction Coordinate\nEnergy (kcal/mol) Proton Transfer-\nNucleophilic Attack Reaction Coordinate Reaction Coordinate Figure 4: EVB profile for the reaction mechanism of nirmatrelvir, showing that the active site reduces the \nbarrier of the same reaction in water by about 3 kcal/mol and essentially no exothermicity. Figure 4: EVB profile for the reaction mechanism of nirmatrelvir, showing that the active site reduces the \nbarrier of the same reaction in water by about 3 kcal/mol and essentially no exothermicity. Similarly, for the alkyne group, the PT-NA step is the rate-limiting step, presenting an energy \nbarrier of 20.8 kcal/mol and a correspondingly slow inactivation (𝑘!+&%' ≈0.01 𝑠\")). This reaction Similarly, for the alkyne group, the PT-NA step is the rate-limiting step, presenting an energy \nbarrier of 20.8 kcal/mol and a correspondingly slow inactivation (𝑘!+&%' ≈0.01 𝑠\")). This reaction https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 step is notably exothermic and irreversible, with a substantial reaction free energy (Δ𝐺4) of -40 \nkcal/mol. For the overall reaction, the activation energy Δ𝐺‡ for the alkyne group is quantified at \n22.7 kcal/mol, and the reaction results in Δ𝐺4 of -35 kcal/mol. EVB Calculations Figure 5: EVB profile for the reaction mechanism of the nirmatrelvir alkyne derivative, which has a \nhigher barrier in protein and significant exothermicity, approximately 35 kcal/mol in both water and \nprotein. Alkyne Derivative\nPT1\nΔG‡=29.6\nΔG‡=22.7\nΔG0=-35\nProton Transfer-\nNucleophilic Attack\nWater\nProtein\n-40\n-30\n-20\n-10\n0\n10\n20\n30\nReaction Coordinate\nEnergy (kcal/mol) Alkyne Derivative\nPT1\nΔG‡=29.6\nΔG‡=22.7\nΔG0=-35\nProton Transfer-\nNucleophilic Attack\nWater\nProtein\n-40\n-30\n-20\n-10\n0\n10\n20\n30\nReaction Coordinate\nEnergy (kcal/mol) Reaction Coordinate Reaction Coordinate Figure 5: EVB profile for the reaction mechanism of the nirmatrelvir alkyne derivative, which has a \nhigher barrier in protein and significant exothermicity, approximately 35 kcal/mol in both water and \nprotein. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Kinetics Simulation of Inhibitor Selectivity At this point, we must deal with the task of connecting the estimated and observed kinetics. We \napproach this task using a similar kinetics simulation approach to the strategy we developed \npreviously in the study of the irreversible inhibition of tyrosine kinases.35 In general, we can expect \nthat IC50 and 𝐾( are connected in the situation of reversible inhibitor binding. However, here we \nhave two different reactions: one with an extremely exothermic and irreversible reaction, and \nanother that has smaller exothermicity and is reversible. As a result, it is ideal to use the calculated \nreaction free-energy profiles and kinetic simulations to replicate the experimental observable, \nwhich is the time-dependent IC50(t). This should be done in addition to comparing the value of \n𝑘677 = 𝑘!+&%'/𝐾(, as implied by the binding energies and reaction rates. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 We used a simple competitive inhibition scheme to generate the trend of the experimentally \nobserved kinetics. The inhibition assay was simulated, subjecting the enzyme to pre-incubation \nwith the inhibitor for a certain amount of time, and then calculating the initial velocity of product \nformation upon adding the substrate to the assay. We used the same initial conditions as the assay \nused by Zhang and co-workers20 ([𝑆]4 = 20 µM and [𝐸]4 = 0.5 µM). In addition, the initial \nconditions for the alkyne derivative were taken as [𝑆]4 = 20 µM and [𝐸]4 = 0.5 µM. Additional \nsimulation details and assay-dependent parameters are listed in the Supplementary Information. Table 1 lists the calculated kinetic and thermodynamic parameter along with simulated and \nexperimental IC50 values. Our analysis yielded binding affinities of ∆𝐺*!+, = -7.5 kcal/mol for \nnirmatrelvir and ∆𝐺*!+, = −9.7 kcal/mol for its alkyne derivative from our PDLD/S-LRA/β \ncalculations (additional information on the binding energy calculations can be found in the SI). Table 1: Summary of calculated energetics and simulated IC50 values, compared with \nexperimental IC50 values.20 Energies are in kcal/mol while IC50 values are in µM. Compound \nEVB \nPDLD \nSimulated IC50 \nExperimental IC50 \n \n∆𝐺‡ \n∆𝐺\" \nΔ𝐺#$%& \n30s \n15min \n3h \n0h \n15min \n3h \nNirmatrelvir \n17.5 \n-1.6 \n-7.5 \n22 \n1.0 \n0.5 \n0.34 ± 0.11 \n0.56 ± 0.32 \n0.76 ± 0.27 \nAlkyne-Deriv. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Kinetics Simulation of Inhibitor Selectivity 22.7 \n-35 \n-9.7 \n22 \n0.9 \n0.3 \n15.72 ± 7.29 \n0.30 ± 0.12 \n0.063 ± 0.015 Table 1: Summary of calculated energetics and simulated IC50 values, compared with \nexperimental IC50 values.20 Energies are in kcal/mol while IC50 values are in µM. Table 1: Summary of calculated energetics and simulated IC50 values, compared with \nexperimental IC50 values.20 Energies are in kcal/mol while IC50 values are in µM. p\ng\nµ\nCompound \nEVB \nPDLD \nSimulated IC50 \nExperimental IC50 \n \n∆𝐺‡ \n∆𝐺\" \nΔ𝐺#$%& \n30s \n15min \n3h \n0h \n15min \n3h \nNirmatrelvir \n17.5 \n-1.6 \n-7.5 \n22 \n1.0 \n0.5 \n0.34 ± 0.11 \n0.56 ± 0.32 \n0.76 ± 0.27 \nAlkyne-Deriv. 22.7 \n-35 \n-9.7 \n22 \n0.9 \n0.3 \n15.72 ± 7.29 \n0.30 ± 0.12 \n0.063 ± 0.015 The simulated time-dependent IC50 curves are shown in Figure 6. The IC50(t) of both nirmatrelvir \nand its alkyne derivative is predicted to be 250 nM after 3 hours of pre-incubation. However, the \nalkyne derivative initially has a much larger IC50 (10 𝜇M) without any preincubation. The \nexperimental value of 𝑘899 for the alkyne inhibitor20 is 5.3 × 10: M\")s\") while the calculated \n𝑘899 value based on our EVB and binding affinity calculations is 2.3 × 10; M\")s\"). The deviation \nbetween the experimental and predicted IC50 likely originates from a discrepancy in the binding \naffinity, which may be in part due to the experimental relative error. It is also possible that \nPDLD/S-LRA/β is underestimating the binding energy of the inhibitors. Measurements of 𝐾( of \nthese inhibitors at higher precision would help to clarify the issue. https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 Figure 6: Simulated incubation assay of Mpro under different preincubation times with the inhibitors, \nnirmatrelvir (a) and its alkyne derivative (b). The IC50 is obtained as the inhibitor concentration for which \nthe velocity of product formation is cut by 50% (dashed line). The irreversibility of the reaction with the \nalkyne warhead is apparent by strong dependence of the IC50 on pre-incubation time. Kinetics Simulation of Inhibitor Selectivity 0h\n30s\n15m\n3h\n1\n10\n100\n1000\n104\n105\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n[I] (nM)\nv0([I]) (Norm.)\nNirmatrelvir\n(a)\n0h\n30s\n15m\n3h\n1\n10\n100\n1000\n104\n105\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n[I] (nM)\nv0([I]) (Norm.)\nAlkyne\nDerivative\n(b) 0h\n30s\n15m\n3h\n1\n10\n100\n1000\n104\n105\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n[I] (nM)\nv0([I]) (Norm.)\nNirmatrelvir\n(a) 0h\n30s\n15m\n3h\n1\n10\n100\n1000\n104\n105\n0.0\n0.2\n0.4\n0.6\n0.8\n1.0\n[I] (nM)\nv0([I]) (Norm.)\nAlkyne\nDerivative\n(b) Figure 6: Simulated incubation assay of Mpro under different preincubation times with the inhibitors, \nnirmatrelvir (a) and its alkyne derivative (b). The IC50 is obtained as the inhibitor concentration for which \nthe velocity of product formation is cut by 50% (dashed line). The irreversibility of the reaction with the \nalkyne warhead is apparent by strong dependence of the IC50 on pre-incubation time. Data Availability Optimized and transition state ab initio structures used for the EVB reference reactions are \navailable at https://github.com/Mojgan-Asadi/mpro-ab-initio. Conclusions The main protease (Mpro) of the coronavirus, a cysteine protease featuring a Cys145-His41 \ncatalytic dyad, is essential for viral replication and the subsequent infection in humans. The present \nstudy builds on the existing body of work on SARS-CoV-2 Mpro inhibitors, highlighting covalent \ninhibition as a particularly promising strategy in the development of antiviral drugs. Specifically, \nthe inhibitors nirmatrelvir and its analogs can act on Mpro either reversibly or irreversibly to \nobstruct the virus's lifecycle. Our investigation delved into the thermodynamics of inhibition by two distinct inhibitors, each \ncharacterized by different reactive groups i.e., one bearing a nitrile group and the other an alkyne \ngroup. By employing both EVB and PDLD/S-LRA/β simulations, we were able to delineate the https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 https://doi.org/10.26434/chemrxiv-2024-c3vxj Content not peer-reviewed by ChemRxiv. License: CC BY 4.0 binding energetics associated with both covalent and non-covalent interactions of these \ncompounds. The insights from our kinetic modeling, detailed in Table 1, align with experimental \ndata and notably reveal the superior efficacy of the alkyne-modified inhibitor over a duration of \nthree hours. Nonetheless, to reconcile certain qualitative deviations observed at shorter intervals, \nfurther experiments with reduced relative errors are necessary. A point of ongoing inquiry is the \nprecise binding affinities of nirmatrelvir and its derivatives. The study notes that the binding \naffinity is subject to significant variation depending on the tautomeric form of HIS163; however, \nno other histidine residue has been found to exert a comparable influence. In conclusion, while there remains room for refinement in our results, it is important to \nacknowledge the contribution of our work in simulating the time-dependent potency of covalent \ninhibitors. This approach, as exemplified in the context of Mpro inhibitors, promises to be a valuable \ntool in the identification and subsequent pharmaceutical assessment of potential lead compounds. In conclusion, while there remains room for refinement in our results, it is important to \nacknowledge the contribution of our work in simulating the time-dependent potency of covalent \ninhibitors. This approach, as exemplified in the context of Mpro inhibitors, promises to be a valuable \ntool in the identification and subsequent pharmaceutical assessment of potential lead compounds. 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