Toward in vivo relevant drug design.

Current early and preclinical drug discovery are rooted in decades-old empirical principles describing structure-free energy and structure-function relationships under equilibrium conditions that frequently break down under in vivo conditions. Improved prediction of efficacy and toxicity depends on a paradigm shift to in vivo-relevant principles describing the true nonequilibrium/nonlinear dynamic (NLD) nature of cellular systems. Here, we outline a holistic, in vivo-relevant first principles theory ('Biodynamics'), in which cellular function/dysfunction, and pharmaco-/toxicodynamic effects are considered as emergent behaviors of multimolecular systems powered by covalent and noncovalent free energy sources. The reduction to practice of Biodynamics theory consists of in silico simulations performed at the atomistic and molecular systems levels, versus empirical models fit to in vitro data under the classical paradigm.

Probing the Dynamic Structure-Function and Structure-Free Energy Relationships of the Coronavirus Main Protease with Biodynamics Theory.

The SARS-CoV-2 main protease (Mpro) is of major interest as an antiviral drug target. Structure-based virtual screening efforts, fueled by a growing list of apo and inhibitor-bound SARS-CoV/CoV-2 Mpro crystal structures, are underway in many laboratories. However, little is known about the dynamic enzyme mechanism, which is needed to inform both assay development and structure-based inhibitor design. Here, we apply biodynamics theory to characterize the structural dynamics of substrate-induced Mpro activation under nonequilibrium conditions. The catalytic cycle is governed by concerted dynamic structural rearrangements of domain 3 and the m-shaped loop (residues 132-147) on which Cys145 (comprising the thiolate nucleophile and half of the oxyanion hole) and Gly143 (comprising the second half of the oxyanion hole) reside. In particular, we observed the following: (1) Domain 3 undergoes dynamic rigid-body rotation about the domain 2-3 linker, alternately visiting two primary conformational states (denoted as M1 pro ↔ M2 pro); (2) The Gly143-containing crest of the m-shaped loop undergoes up and down translations caused by conformational changes within the rising stem of the loop (Lys137-Asn142) in response to domain 3 rotation and dimerization (denoted as M1/down pro ↔ 2·M2/up pro) (noting that the Cys145-containing crest is fixed in the up position). We propose that substrates associate to the M1/down pro state, which promotes the M2/down pro state, dimerization (denoted as 2·M2/up pro-substrate), and catalysis. Here, we explore the state transitions of Mpro under nonequilibrium conditions, the mechanisms by which they are powered, and the implications thereof for efficacious inhibition under in vivo conditions.

Toward in vivo-relevant hERG safety assessment and mitigation strategies based on relationships between non-equilibrium blocker binding, three-dimensional channel-blocker interactions, dynamic occupancy, dynamic exposure, and cellular arrhythmia.

The human ether-a-go-go-related voltage-gated cardiac ion channel (commonly known as hERG) conducts the rapid outward repolarizing potassium current in cardiomyocytes (IKr). Inadvertent blockade of this channel by drug-like molecules represents a key challenge in pharmaceutical R&D due to frequent overlap between the structure-activity relationships of hERG and many primary targets. Building on our previous work, together with recent cryo-EM structures of hERG, we set about to better understand the energetic and structural basis of promiscuous blocker-hERG binding in the context of Biodynamics theory. We propose a two-step blocker binding process consisting of: The initial capture step: diffusion of a single fully solvated blocker copy into a large cavity lined by the intra-cellular cyclic nucleotide binding homology domain (CNBHD). Occupation of this cavity is a necessary but insufficient condition for ion current disruption.The IKr disruption step: translocation of the captured blocker along the channel axis, such that: The head group, consisting of a quasi-rod-shaped moiety, projects into the open pore, accompanied by partial de-solvation of the binding interface.One tail moiety packs along a kink between the S6 helix and proximal C-linker helix adjacent to the intra-cellular entrance of the pore, likewise accompanied by mutual de-solvation of the binding interface (noting that the association barrier is comprised largely of the total head + tail group de-solvation cost).Blockers containing a highly planar moiety that projects into a putative constriction zone within the closed channel become trapped upon closing, as do blockers terminating prior to this region.A single captured blocker copy may conceivably associate and dissociate to/from the pore many times before exiting the CNBHD cavity. Lastly, we highlight possible flaws in the current hERG safety index (SI), and propose an alternate in vivo-relevant strategy factoring in: Benefit/risk.The predicted arrhythmogenic fractional hERG occupancy (based on action potential (AP) simulations of the undiseased human ventricular cardiomyocyte).Alteration of the safety threshold due to underlying disease.Risk of exposure escalation toward the predicted arrhythmic limit due to patient-to-patient pharmacokinetic (PK) variability, drug-drug interactions, overdose, and use for off-label indications in which the hERG safety parameters may differ from their on-label counterparts.

Building New Bridges between In Vitro and In Vivo in Early Drug Discovery: Where Molecular Modeling Meets Systems Biology.

Cellular drug targets exist within networked function-generating systems whose constituent molecular species undergo dynamic interdependent non-equilibrium state transitions in response to specific perturbations (i.e.. inputs). Cellular phenotypic behaviors are manifested through the integrated behaviors of such networks. However, in vitro data are frequently measured and/or interpreted with empirical equilibrium or steady state models (e.g. Hill, Michaelis-Menten, Briggs-Haldane) relevant to isolated target populations. We propose that cells act as analog computers, "solving" sets of coupled "molecular differential equations" (i.e. represented by populations of interacting species)via "integration" of the dynamic state probability distributions among those populations. Disconnects between biochemical and functional/phenotypic assays (cellular/in vivo) may arise with targetcontaining systems that operate far from equilibrium, and/or when coupled contributions (including target-cognate partner binding and drug pharmacokinetics) are neglected in the analysis of biochemical results. The transformation of drug discovery from a trial-and-error endeavor to one based on reliable design criteria depends on improved understanding of the dynamic mechanisms powering cellular function/dysfunction at the systems level. Here, we address the general mechanisms of molecular and cellular function and pharmacological modulation thereof. We outline a first principles theory on the mechanisms by which free energy is stored and transduced into biological function, and by which biological function is modulated by drug-target binding. We propose that cellular function depends on dynamic counter-balanced molecular systems necessitated by the exponential behavior of molecular state transitions under non-equilibrium conditions, including positive versus negative mass action kinetics and solute-induced perturbations to the hydrogen bonds of solvating water versus kT.

Structure-Kinetic Relationships of Passive Membrane Permeation from Multiscale Modeling.

Passive membrane permeation of small molecules is essential to achieve the required absorption, distribution, metabolism, and excretion (ADME) profiles of drug candidates, in particular intestinal absorption and transport across the blood-brain barrier. Computational investigations of this process typically involve either building QSAR models or performing free energy calculations of the permeation event. Although insightful, these methods rarely bridge the gap between computation and experiment in a quantitative manner, and identifying structural insights to apply toward the design of compounds with improved permeability can be difficult. In this work, we combine molecular dynamics simulations capturing the kinetic steps of permeation at the atomistic level with a dynamic mechanistic model describing permeation at the in vitro level, finding a high level of agreement with experimental permeation measurements. Calculation of the kinetic rate constants determining each step in the permeation event allows derivation of structure-kinetic relationships of permeation. We use these relationships to probe the structural determinants of membrane permeation, finding that the desolvation/loss of hydrogen bonding required to leave the membrane partitioned position controls the membrane flip-flop rate, whereas membrane partitioning determines the rate of leaving the membrane.

Contributions of the membrane dipole potential to the function of voltage-gated cation channels and modulation by small molecule potentiators.

The membrane dipole potential (Ψd) constitutes one of three electrical potentials generated by cell membranes. Ψd arises from the unfavorable parallel alignment of phospholipid and water dipoles, and varies in magnitude both longitudinally and laterally across the bilayer according to membrane composition and phospholipid packing density. In this work, we propose that dynamic counter-balancing between Ψd and the transmembrane potential (ΔΨm) governs the conformational state transitions of voltage-gated ion channels. Ψd consists of 1) static outer, and dynamic inner leaflet components (Ψd(extra) and Ψd(intra), respectively); and 2) a transmembrane component (ΔΨd(inner-outer)), ariing from differences in intra- and extracellular leaflet composition. Ψd(intra), which transitions between high and low energy states (Ψd(intra, high) and Ψd(intra, low)) as a function of channel conformation, is transduced by the pore domain. ΔΨd(inner-outer) is transduced by the voltage-sensing (VS) domain in summation with ΔΨm. Potentiation of voltage-gated ion channels is of interest for the treatment of cardiac, neuronal, and other disorders arising from inherited/acquired ion channel dysfunction. Potentiators are widely believed to alter the rates and voltage-dependencies of channel gating transitions by binding to pockets in the membrane-facing and other regions of ion channel targets. Here, we propose that potentiators alter Ψd(intra) and/or Ψd(extra), thereby increasing or decreasing the energy barriers governing channel gating transitions. We used quantum mechanical and molecular dynamics (MD) simulations to predict the overall Ψd-modulating effects of a series of published positive hERG potentiators partitioned into model DOPC bilayers. Our findings suggest a strong correlation between the magnitude of Ψd-lowering and positive hERG potentiation across the series.

Uncoupling the Structure-Activity Relationships of ß2 Adrenergic Receptor Ligands from Membrane Binding.

Ligand binding to membrane proteins may be significantly influenced by the interaction of ligands with the membrane. In particular, the microscopic ligand concentration within the membrane surface solvation layer may exceed that in bulk solvent, resulting in overestimation of the intrinsic protein-ligand binding contribution to the apparent/measured affinity. Using published binding data for a set of small molecules with the ß2 adrenergic receptor, we demonstrate that deconvolution of membrane and protein binding contributions allows for improved structure-activity relationship analysis and structure-based drug design. Molecular dynamics simulations of ligand bound membrane protein complexes were used to validate binding poses, allowing analysis of key interactions and binding site solvation to develop structure-activity relationships of ß2 ligand binding. The resulting relationships are consistent with intrinsic binding affinity (corrected for membrane interaction). The successful structure-based design of ligands targeting membrane proteins may require an assessment of membrane affinity to uncouple protein binding from membrane interactions.

Implications of Dynamic Occupancy, Binding Kinetics, and Channel Gating Kinetics for hERG Blocker Safety Assessment and Mitigation.

Blockade of the hERG potassium channel prolongs the ventricular action potential (AP) and QT interval, and triggers early after depolarizations (EADs) and torsade de pointes (TdP) arrhythmia. Opinions differ as to the causal relationship between hERG blockade and TdP, the relative weighting of other contributing factors, definitive metrics of preclinical proarrhythmicity, and the true safety margin in humans. Here, we have used in silico techniques to characterize the effects of channel gating and binding kinetics on hERG occupancy, and of blockade on the human ventricular AP. Gating effects differ for compounds that are sterically compatible with closed channels (becoming trapped in deactivated channels) versus those that are incompatible with the closed/closing state, and expelled during deactivation. Occupancies of trappable blockers build to equilibrium levels, whereas those of non-trappable blockers build and decay during each AP cycle. Occupancies of ~83% (non-trappable) versus ~63% (trappable) of open/inactive channels caused EADs in our AP simulations. Overall, we conclude that hERG occupancy at therapeutic exposure levels may be tolerated for nontrappable, but not trappable blockers capable of building to the proarrhythmic occupancy level. Furthermore, the widely used Redfern safety index may be biased toward trappable blockers, overestimating the exposure-IC50 separation in nontrappable cases.

Estimation of Solvation Entropy and Enthalpy via Analysis of Water Oxygen-Hydrogen Correlations.

A statistical-mechanical framework for estimation of solvation entropies and enthalpies is proposed, which is based on the analysis of water as a mixture of correlated water oxygens and water hydrogens. Entropic contributions of increasing order are cast in terms of a Mutual Information Expansion that is evaluated to pairwise interactions. In turn, the enthalpy is computed directly from a distance-based hydrogen bonding energy algorithm. The resulting expressions are employed for grid-based analyses of Molecular Dynamics simulations. In this first assessment of the methodology, we obtained global estimates of the excess entropy and enthalpy of water that are in good agreement with experiment and examined the method's ability to enable detailed elucidation of solvation thermodynamic structures, which can provide valuable knowledge toward molecular design.

Structure-kinetic relationship of carbapenem antibacterials permeating through E. coli OmpC porin.

The emergence of Gram-negative "superbugs" exhibiting resistance to known antibacterials poses a major public health concern. Low molecular weight Gram-negative antibacterials are believed to penetrate the outer bacterial membrane (OM) through porin channels. Therefore, intracellular exposure needed to drive antibacterial target occupancy should depend critically on the translocation rates through these proteins and avoidance of efflux pumps. We used electrophysiology to study the structure-translocation kinetics relationships of a set of carbapenem antibacterials through purified porin OmpC reconstituted in phospholipid bilayers. We also studied the relative susceptibility of OmpC+ and OmpC- E. coli to these compounds as an orthogonal test of translocation. Carbapenems exhibit good efficacy in OmpC-expressing E. coli cells compared with other known antibacterials. Ertapenem, which contains an additional acidic group compared to other analogs, exhibits the fastest entry into OmpC (k(on) ≈ 2 × 10(4) M(-1) s(-1)). Zwitterionic compounds with highly polar groups attached to the penem-2 ring, including panipenem, imipenem and doripenem exhibit faster k(on) (>10(4) M(-1) s(-1)), while meropenem and biapenem with fewer exposed polar groups exhibit slower k(on) (∼5 × 10(3) M(-1) s(-1)). Tebipenem pivoxil and razupenem exhibit ∼13-fold slower k(on) (∼1.5 × 10(3) M(-1) s(-1)) than ertapenem. Overall, our results suggest that (a) OmpC serves as an important route of entry of these antibacterials into E. coli cells; and (b) that the structure-kinetic relationships of carbapenem translocation are governed by H-bond acceptor/donor composition (in accordance with our previous findings that the enthalpic cost of transferring water from the constriction zone to bulk solvent increases in the presence of exposed nonpolar groups).

Contributions of water transfer energy to protein-ligand association and dissociation barriers: Watermap analysis of a series of p38α MAP kinase inhibitors.

In our previous work, we proposed that desolvation and resolvation of the binding sites of proteins can serve as the slowest steps during ligand association and dissociation, respectively, and tested this hypothesis on two protein-ligand systems with known binding kinetics behavior. In the present work, we test this hypothesis on another kinetically-determined protein-ligand system-that of p38α and eight Type II BIRB 796 inhibitor analogs. The kon values among the inhibitor analogs are narrowly distributed (104 ≤ kon ≤ 105 M⁻¹ s⁻¹), suggesting a common rate-determining step, whereas the koff values are widely distributed (10⁻¹ ≤ koff ≤ 10⁻6 s⁻¹), suggesting a spectrum of rate-determining steps. We calculated the solvation properties of the DFG-out protein conformation using an explicit solvent molecular dynamics simulation and thermodynamic analysis method implemented in WaterMap to predict the enthalpic and entropic costs of water transfer to and from bulk solvent incurred upon association and dissociation of each inhibitor. The results suggest that the rate-determining step for association consists of the transfer of a common set of enthalpically favorable solvating water molecules from the binding site to bulk solvent. The rate-determining step for inhibitor dissociation consists of the transfer of water from bulk solvent to specific binding site positions that are unfavorably solvated in the apo protein, and evacuated during ligand association. Different sets of unfavorable solvation are evacuated by each ligand, and the observed dissociation barriers are qualitatively consistent with the calculated solvation free energies of those sets.

New hypotheses about the structure-function of proprotein convertase subtilisin/kexin type 9: analysis of the epidermal growth factor-like repeat A docking site using WaterMap.

LDL cholesterol (LDL-C) is cleared from plasma via cellular uptake and internalization processes that are largely mediated by the low-density lipoprotein cholesterol receptor (LDL-R). LDL-R is targeted for lysosomal degradation by association with proprotein convertase subtilisin-kexin type 9 (PCSK9). Gain of function mutations in PCSK9 can result in excessive loss of receptors and dyslipidemia. On the other hand, receptor-sparing phenomena, including loss-of-function mutations or inhibition of PCSK9, can lead to enhanced clearance of plasma lipids. We hypothesize that desolvation and resolvation processes, in many cases, constitute rate-determining steps for protein-ligand association and dissociation, respectively. To test this hypothesis, we analyzed and compared the predicted desolvation properties of wild-type versus gain-of-function mutant Asp374Tyr PCSK9 using WaterMap, a new in silico method for predicting the preferred locations and thermodynamic properties of water solvating proteins ("hydration sites"). We compared these results with binding kinetics data for PCSK9, full-length LDL-R ectodomain, and isolated EGF-A repeat. We propose that the fast k(on) and entropically driven thermodynamics observed for PCSK9-EGF-A binding stem from the functional replacement of water occupying stable PCSK9 hydration sites (i.e., exchange of PCSK9 H-bonds from water to polar EGF-A groups). We further propose that the relatively fast k(off) observed for EGF-A unbinding stems from the limited displacement of solvent occupying unstable hydration sites. Conversely, the slower k(off) observed for EGF-A and LDL-R unbinding from Asp374Tyr PCSK9 stems from the destabilizing effects of this mutation on PCSK9 hydration sites, with a concomitant increase in the persistence of the bound complex.

New insights about HERG blockade obtained from protein modeling, potential energy mapping, and docking studies.

We created a homology model of the homo-tetrameric pore domain of HERG using the crystal structure of the bacterial potassium channel, KvAP, as a template. We docked a set of known blockers with well-characterized effects on channel function into the lumen of the pore between the selectivity filter and extracellular entrance using a novel docking and refinement procedure incorporating Glide and Prime. Key aromatic groups of the blockers are predicted to form multiple simultaneous ring stacking and hydrophobic interactions among the eight aromatic residues lining the pore. Furthermore, each blocker can achieve these interactions via multiple docking configurations. To further interpret the docking results, we mapped hydrophobic and hydrophilic potentials within the lumen of each refined docked complex. Hydrophilic iso-potential contours define a 'propeller-shaped' volume at the selectivity filter entrance. Hydrophobic contours define a hollow 'crown-shaped' volume located above the 'propeller', whose hydrophobic 'rim' extends along the pore axis between Tyr652 and Phe656. Blockers adopt conformations/binding orientations that closely mimic the shapes and properties of these contours. Blocker basic groups are localized in the hydrophilic 'propeller', forming electrostatic interactions with Ser624 rather than a generally accepted pi-cation interaction with Tyr652. Terfenadine, cisapride, sertindole, ibutilide, and clofilium adopt similar docked poses, in which their N-substituents bridge radially across the hollow interior of the 'crown' (analogous to the hub and spokes of a wheel), and project aromatic/hydrophobic portions into the hydrophobic 'rim'. MK-499 docks with its longitudinal axis parallel to the axis of the pore and 'crown', and its hydrophobic groups buried within the hydrophobic 'rim'.

Characterization of HERG potassium channel inhibition using CoMSiA 3D QSAR and homology modeling approaches.

A data set consisting of twenty-two sertindole analogues and ten structurally diverse inhibitors, spanning a wide range in potency, was analyzed using CoMSiA. A homology model of HERG was constructed from the crystal structure of the open MthK potassium channel. A complementary relationship between our CoMSiA and homology models is apparent when the long inhibitor axis is oriented parallel to the longitudinal axis of the pore, with the tail region pointed toward the selectivity filter. The key elements of the pharmacophore, the CoMSiA and the homology model are: (1) The hydrophobic feature optimally consists of an aromatic group that is capable of engaging in pi-stacking with a Phe656 side chain. Optionally, a second aromatic or hydrophobic group present in some inhibitors may contact an additional Phe656 side chain. (2) The basic nitrogen appears to undergo a pi-cation interaction with Tyr652. (3) The pore diameter (12A+), and depth of the selectivity loop relative to the intracellular opening, act as constraints on the conformation-dependent inhibitor dimensions.