Bridging Microscopic and Macroscopic Mechanisms of p53-MDM2 Binding with Kinetic Network Models

Ligand Gaussian Accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional molecular dynamics (cMD), due to limited simulation time scales. Based on our previously developed ligand Gaussian accelerated molecular dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3″, in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding, and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as the model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 μs simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 were in agreement with the available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligands and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

Protein Retrieval via Integrative Molecular Ensembles (PRIME) through Extended Similarity Indices

Molecular dynamics (MD) simulations are ideally suited to describe conformational ensembles of biomolecules such as proteins and nucleic acids. Microsecond-long simulations are now routine, facilitated by the emergence of graphical processing units. Clustering, which groups objects based on structural similarity, is typically used to process ensembles, leading to different states, their populations, and the identification of representative structures. A popular pipeline combines hierarchical clustering for clustering and selecting the cluster centroid as representative of the cluster. Here, we propose to improve on this approach, by developing a module-Protein Retrieval via Integrative Molecular Ensembles (PRIME), that consists of tools to improve the prediction of the representative in the most populated cluster using extended continuous similarity. PRIME is integrated with our Molecular Dynamics Analysis with N-ary Clustering Ensembles (MDANCE) package and can be used as a postprocessing tool for arbitrary clustering algorithms, compatible with several MD suites. PRIME predictions produced structures that when aligned to the experimental structure were better superposed (lower RMSD). A further benefit of PRIME is its linear scaling─rather than the traditional O(N2) traditionally associated with comparisons of elements in a set.

Impact of Nonnative Interactions on the Binding Kinetics of Intrinsically Disordered p53 with MDM2: Insights from All-Atom Simulation and Markov State Model Analysis

Intrinsically disordered proteins (IDPs) lack a well-defined tertiary structure but are essential players in various biological processes. Their ability to undergo a disorder-to-order transition upon binding to their partners, known as the folding-upon-binding process, is crucial for their function. One classical example is the intrinsically disordered transactivation domain (TAD) of the tumor suppressor protein p53, which quickly forms a structured α-helix after binding to its partner MDM2, with clinical significance for cancer treatment. However, the contribution of nonnative interactions between the IDP and its partner to the rapid binding kinetics, as well as their interplay with native interactions, is not well understood at the atomic level. Here, we used molecular dynamics simulation and Markov state model (MSM) analysis to study the folding-upon-binding mechanism between p53-TAD and MDM2. Our results suggest that the system progresses from the nascent encounter complex to the well-structured encounter complex and finally reaches the native complex, following an induced-fit mechanism. We found that nonnative hydrophobic and hydrogen bond interactions, combined with native interactions, effectively stabilize the nascent and well-structured encounter complexes. Among the nonnative interactions, Leu25p53-Leu54MDM2 and Leu25p53-Phe55MDM2 are particularly noteworthy, as their interaction strength is close to the optimum. Evidently, strengthening or weakening these interactions could both adversely affect the binding kinetics. Overall, our findings suggest that nonnative interactions are evolutionarily optimized to accelerate the binding kinetics of IDPs in conjunction with native interactions.

Ligand Gaussian accelerated Molecular Dynamics 3 (LiGaMD3): Improved Calculations of Binding Thermodynamics and Kinetics of Both Small Molecules and Flexible Peptides

Binding thermodynamics and kinetics play critical roles in drug design. However, it has proven challenging to efficiently predict ligand binding thermodynamics and kinetics of small molecules and flexible peptides using conventional Molecular Dynamics (cMD), due to limited simulation timescales. Based on our previously developed Ligand Gaussian accelerated Molecular Dynamics (LiGaMD) method, we present a new approach, termed "LiGaMD3", in which we introduce triple boosts into three individual energy terms that play important roles in small-molecule/peptide dissociation, rebinding and system conformational changes to improve the sampling efficiency of small-molecule/peptide interactions with target proteins. To validate the performance of LiGaMD3, MDM2 bound by a small molecule (Nutlin 3) and two highly flexible peptides (PMI and P53) were chosen as model systems. LiGaMD3 could efficiently capture repetitive small-molecule/peptide dissociation and binding events within 2 microsecond simulations. The predicted binding kinetic constant rates and free energies from LiGaMD3 agreed with available experimental values and previous simulation results. Therefore, LiGaMD3 provides a more general and efficient approach to capture dissociation and binding of both small-molecule ligand and flexible peptides, allowing for accurate prediction of their binding thermodynamics and kinetics.

Revolutionizing Peptide-Based Drug Discovery: Advances in the Post-AlphaFold Era

Peptide-based drugs offer high specificity, potency, and selectivity. However, their inherent flexibility and differences in conformational preferences between their free and bound states create unique challenges that have hindered progress in effective drug discovery pipelines. The emergence of AlphaFold (AF) and Artificial Intelligence (AI) presents new opportunities for enhancing peptide-based drug discovery. We explore recent advancements that facilitate a successful peptide drug discovery pipeline, considering peptides' attractive therapeutic properties and strategies to enhance their stability and bioavailability. AF enables efficient and accurate prediction of peptide-protein structures, addressing a critical requirement in computational drug discovery pipelines. In the post-AF era, we are witnessing rapid progress with the potential to revolutionize peptide-based drug discovery such as the ability to rank peptide binders or classify them as binders/non-binders and the ability to design novel peptide sequences. However, AI-based methods are struggling due to the lack of well-curated datasets, for example to accommodate modified amino acids or unconventional cyclization. Thus, physics-based methods, such as docking or molecular dynamics simulations, continue to hold a complementary role in peptide drug discovery pipelines. Moreover, MD-based tools offer valuable insights into binding mechanisms, as well as the thermodynamic and kinetic properties of complexes. As we navigate this evolving landscape, a synergistic integration of AI and physics-based methods holds the promise of reshaping the landscape of peptide-based drug discovery.

Markov State Model of Solvent Features Reveals Water Dynamics in Protein-Peptide Binding

In this work, we investigate the role of solvent in the binding reaction of the p53 transactivation domain (TAD) peptide to its receptor MDM2. Previously, our group generated 831 μs of explicit-solvent aggregate molecular simulation trajectory data for the MDM2-p53 peptide binding reaction using large-scale distributed computing and subsequently built a Markov State Model (MSM) of the binding reaction (Zhou et al. 2017). Here, we perform a tICA analysis and construct an MSM with similar hyperparameters while using only solvent-based structural features. We find a remarkably similar landscape but accelerated implied timescales for the slowest motions. The solvent shells contributing most to the first tICA eigenvector are those centered on Lys24 and Thr18 of the p53 TAD peptide in the range of 3-6 Å. Important solvent shells were visualized to reveal solvation and desolvation transitions along the peptide-protein binding trajectories. Our results provide a solvent-centric view of the hydrophobic effect in action for a realistic peptide-protein binding scenario.

A Kinetic Transition Network Model Reveals the Diversity of Protein Dimer Formation Mechanisms

Protein homodimers have been classified as three-state or two-state dimers depending on whether a folded monomer forms before association, but the details of the folding-binding mechanisms are poorly understood. Kinetic transition networks of conformational states have provided insight into the folding mechanisms of monomeric proteins, but extending such a network to two protein chains is challenging as all the relative positions and orientations of the chains need to be included, greatly increasing the number of degrees of freedom. Here, we present a simplification of the problem by grouping all states of the two chains into two layers: a dissociated and an associated layer. We combined our two-layer approach with the Wako-Saito-Muñoz-Eaton method and used Transition Path Theory to investigate the dimer formation kinetics of eight homodimers. The analysis reveals a remarkable diversity of dimer formation mechanisms. Induced folding, conformational selection, and rigid docking are often simultaneously at work, and their contribution depends on the protein concentration. Pre-folded structural elements are always present at the moment of association, and asymmetric binding mechanisms are common. Our two-layer network approach can be combined with various methods that generate discrete states, yielding new insights into the kinetics and pathways of flexible binding processes.

Folding@home: Achievements from over 20 years of citizen science herald the exascale era

Simulations of biomolecules have enormous potential to inform our understanding of biology but require extremely demanding calculations. For over 20 years, the Folding@home distributed computing project has pioneered a massively parallel approach to biomolecular simulation, harnessing the resources of citizen scientists across the globe. Here, we summarize the scientific and technical advances this perspective has enabled. As the project's name implies, the early years of Folding@home focused on driving advances in our understanding of protein folding by developing statistical methods for capturing long-timescale processes and facilitating insight into complex dynamical processes. Success laid a foundation for broadening the scope of Folding@home to address other functionally relevant conformational changes, such as receptor signaling, enzyme dynamics, and ligand binding. Continued algorithmic advances, hardware developments such as graphics processing unit (GPU)-based computing, and the growing scale of Folding@home have enabled the project to focus on new areas where massively parallel sampling can be impactful. While previous work sought to expand toward larger proteins with slower conformational changes, new work focuses on large-scale comparative studies of different protein sequences and chemical compounds to better understand biology and inform the development of small-molecule drugs. Progress on these fronts enabled the community to pivot quickly in response to the COVID-19 pandemic, expanding to become the world's first exascale computer and deploying this massive resource to provide insight into the inner workings of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) virus and aid the development of new antivirals. This success provides a glimpse of what is to come as exascale supercomputers come online and as Folding@home continues its work.

Binding-and-Folding Recognition of an Intrinsically Disordered Protein Using Online Learning Molecular Dynamics

Intrinsically disordered proteins participate in many biological processes by folding upon binding to other proteins. However, coupled folding and binding processes are not well understood from an atomistic point of view. One of the main questions is whether folding occurs prior to or after binding. Here we use a novel, unbiased, high-throughput adaptive sampling approach to reconstruct the binding and folding between the disordered transactivation domain of c-Myb and the KIX domain of the CREB-binding protein. The reconstructed long-term dynamical process highlights the binding of a short stretch of amino acids on c-Myb as a folded α-helix. Leucine residues, especially Leu298-Leu302, establish initial native contacts that prime the binding and folding of the rest of the peptide, with a mixture of conformational selection on the N-terminal region with an induced fit of the C-terminal.

Predicting Biomolecular Binding Kinetics: A Review

Biomolecular binding kinetics including the association (k_on) and dissociation (k_off) rates are critical parameters for therapeutic design of small-molecule drugs, peptides, and antibodies. Notably, the drug molecule residence time or dissociation rate has been shown to correlate with their efficacies better than binding affinities. A wide range of modeling approaches including quantitative structure-kinetic relationship models, Molecular Dynamics simulations, enhanced sampling, and Machine Learning has been developed to explore biomolecular binding and dissociation mechanisms and predict binding kinetic rates. Here, we review recent advances in computational modeling of biomolecular binding kinetics, with an outlook for future improvements.

Computational approaches for the design of modulators targeting protein-protein interactions

BACKGROUND

Protein-protein interactions (PPIs) are intriguing targets for designing novel small-molecule inhibitors. The role of PPIs in various infectious and neurodegenerative disorders makes them potential therapeutic targets . Despite being portrayed as undruggable targets, due to their flat surfaces, disorderedness, and lack of grooves. Recent progresses in computational biology have led researchers to reconsider PPIs in drug discovery.

AREAS COVERED

In this review, we introduce in-silico methods used to identify PPI interfaces and present an in-depth overview of various computational methodologies that are successfully applied to annotate the PPIs. We also discuss several successful case studies that use computational tools to understand PPIs modulation and their key roles in various physiological processes.

EXPERT OPINION

Computational methods face challenges due to the inherent flexibility of proteins, which makes them expensive, and result in the use of rigid models. This problem becomes more significant in PPIs due to their flexible and flat interfaces. Computational methods like molecular dynamics (MD) simulation and machine learning can integrate the chemical structure data into biochemical and can be used for target identification and modulation. These computational methodologies have been crucial in understanding the structure of PPIs, designing PPI modulators, discovering new drug targets, and predicting treatment outcomes.

Competition in drug binding and … the race to equilibrium

Binding kinetics has become a popular topic in pharmacology due to its potential contribution to the selectivity and duration of drug action. Yet, the overall kinetic aspects of complex binding mechanisms are still merely described in terms of elaborate algebraic equations. Interestingly, it has been recommended some 10 years ago to examine such mechanisms in terms of binding fluxes instead of the conventional rate constants. Alike the velocity of product formation in enzymology, those fluxes refer to the velocity by which one target species converts into another one. Novel binding flux-based approaches are utilized to get a better visual insight into the "competition" between two drugs/ligands for a single target as well as between induced fit- and conformational selection pathways for a single ligand within a thermodynamic cycle. The present data were obtained by differential equation-based simulations. Early on, the ligand-binding steps "race" to equilibrium (i.e., when their forward and reverse fluxes are equal) at their individual pace. The overall/global equilibrium is only reached later on. For the competition association assays, this parting might produce a transient "overshoot" of one of the bound target species. A similar overshoot may also show up within a thermodynamic cycle and, at first glance, suggest that the induced fit pathway dominates. Yet, present findings show that under certain circumstances, it could rather be the other way round. Novel binding flux-based approaches offer visually attractive insights into crucial aspects of "complex" binding mechanisms under non-equilibrium conditions.

Towards rational computational peptide design

Peptides are prevalent in biology, mediating as many as 40% of protein-protein interactions, and involved in other cellular functions such as transport and signaling. Their ability to bind with high specificity make them promising therapeutical agents with intermediate properties between small molecules and large biologics. Beyond their biological role, peptides can be programmed to self-assembly, and they are already being used for functions as diverse as oligonuclotide delivery, tissue regeneration or as drugs. However, the transient nature of their interactions has limited the number of structures and knowledge of binding affinities available-and their flexible nature has limited the success of computational pipelines that predict the structures and affinities of these molecules. Fortunately, recent advances in experimental and computational pipelines are creating new opportunities for this field. We are starting to see promising predictions of complex structures, thermodynamic and kinetic properties. We believe in the following years this will lead to robust rational peptide design pipelines with success similar to those applied for small molecule drug discovery.

A litmus test for classifying recognition mechanisms of transiently binding proteins

Partner recognition in protein binding is critical for all biological functions, and yet, delineating its mechanism is challenging, especially when recognition happens within microseconds. We present a theoretical and experimental framework based on straight-forward nuclear magnetic resonance relaxation dispersion measurements to investigate protein binding mechanisms on sub-millisecond timescales, which are beyond the reach of standard rapid-mixing experiments. This framework predicts that conformational selection prevails on ubiquitin’s paradigmatic interaction with an SH3 (Src-homology 3) domain. By contrast, the SH3 domain recognizes ubiquitin in a two-state binding process. Subsequent molecular dynamics simulations and Markov state modeling reveal that the ubiquitin conformation selected for binding exhibits a characteristically extended C-terminus. Our framework is robust and expandable for implementation in other binding scenarios with the potential to show that conformational selection might be the design principle of the hubs in protein interaction networks.

The authors provide a litmus test for the recognition mechanism of transiently binding proteins based on nuclear magnetic resonance and find a conformational selection binding mechanism through concentration-dependent kinetics of ubiquitin and SH3.

Markov State Study of Electrostatic Channeling within the Tricarboxylic Acid Cycle Supercomplex

The high efficiency of cascade reactions in supramolecular enzyme nanoassemblies, known as metabolons, has attracted substantial attention in various fields ranging from fundamental biochemistry and molecular biology to recent applications in biofuel cells, biosensors, and chemical synthesis. One reason for the high efficiency of metabolons is the structures formed by sequential enzymes that allow the direct transport of intermediates between consecutive active sites. The supercomplex of malate dehydrogenase (MDH) and citrate synthase (CS) is an ideal example of the controlled transport of intermediates via electrostatic channeling. Here, using a combination of molecular dynamics (MD) simulations and a Markov state model (MSM), we examined the transport process of the intermediate oxaloacetate (OAA) from MDH to CS. The MSM enables the identification of the dominant transport pathways of OAA from MDH to CS. Analysis of all pathways using a hub score approach reveals a small set of residues that control OAA transport. This set includes an arginine residue previously identified experimentally. MSM analysis of a mutated complex, where the identified arginine is replaced by alanine, led to a 2-fold decrease in transfer efficiency, also consistent with experimental results. This work provides a molecular-level understanding of the electrostatic channeling mechanism and will enable the further design of catalytic nanostructures utilizing electrostatic channeling.

Estimation of binding rates and affinities from multiensemble Markov models and ligand decoupling

Accurate and efficient simulation of the thermodynamics and kinetics of protein-ligand interactions is crucial for computational drug discovery. Multiensemble Markov Model (MEMM) estimators can provide estimates of both binding rates and affinities from collections of short trajectories but have not been systematically explored for situations when a ligand is decoupled through scaling of non-bonded interactions. In this work, we compare the performance of two MEMM approaches for estimating ligand binding affinities and rates: (1) the transition-based reweighting analysis method (TRAM) and (2) a Maximum Caliber (MaxCal) based method. As a test system, we construct a small host-guest system where the ligand is a single uncharged Lennard-Jones (LJ) particle, and the receptor is an 11-particle icosahedral pocket made from the same atom type. To realistically mimic a protein-ligand binding system, the LJ ϵ parameter was tuned, and the system was placed in a periodic box with 860 TIP3P water molecules. A benchmark was performed using over 80 µs of unbiased simulation, and an 18-state Markov state model was used to estimate reference binding affinities and rates. We then tested the performance of TRAM and MaxCal when challenged with limited data. Both TRAM and MaxCal approaches perform better than conventional Markov state models, with TRAM showing better convergence and accuracy. We find that subsampling of trajectories to remove time correlation improves the accuracy of both TRAM and MaxCal and that in most cases, only a single biased ensemble to enhance sampled transitions is required to make accurate estimates.

Unprotected peptide macrocyclization and stapling via a fluorine-thiol displacement reaction

We report the discovery of a facile peptide macrocyclization and stapling strategy based on a fluorine thiol displacement reaction (FTDR), which renders a class of peptide analogues with enhanced stability, affinity, cellular uptake, and inhibition of cancer cells. This approach enabled selective modification of the orthogonal fluoroacetamide side chains in unprotected peptides in the presence of intrinsic cysteines. The identified benzenedimethanethiol linker greatly promoted the alpha helicity of a variety of peptide substrates, as corroborated by molecular dynamics simulations. The cellular uptake of benzenedimethanethiol stapled peptides appeared to be universally enhanced compared to the classic ring-closing metathesis (RCM) stapled peptides. Pilot mechanism studies suggested that the uptake of FTDR-stapled peptides may involve multiple endocytosis pathways in a distinct pattern in comparison to peptides stapled by RCM. Consistent with the improved cell permeability, the FTDR-stapled lead Axin and p53 peptide analogues demonstrated enhanced inhibition of cancer cells over the RCM-stapled analogues and the unstapled peptides.

Strategies capable of stapling unprotected peptides in a straightforward, chemoselective, and clean manner, as well as promoting cellular uptake are of great interest. Here the authors report a peptide macrocyclization and stapling strategy which satisfies those criteria, based on a fluorine thiol displacement reaction.

Potential of rescue and reactivation of tumor suppressor p53 for cancer therapy

The tumor suppressor protein p53, a transcription product of the anti-oncogene TP53, is a critical factor in preventing cellular cancerization and killing cancer cells by inducing apoptosis. As a result, p53 is often referred to as the "guardian of the genome." Almost half of cancers possess genetic mutations in the TP53 gene, and most of these mutations result in the malfunction of p53, which promotes aggregation. In some cases, the product of the TP53 mutant allele shows higher aggregation propensity; the mutant co-aggregates with the normal (functional) p53 protein, thus losing cellular activity of the p53 guardian. Cancer might also progress because of the proteolytic degradation of p53 by activated E3 ubiquitination enzymes, MDM2 and MDM4. The inhibition of the specific interaction between MDM2 (MDM4) and p53 also results in increased p53 activity in cancer cells. Although the molecular targets of the drugs are different, two drug discovery strategies with a common goal, "rescuing p53 protein," have recently emerged. To conduct this approach, various biophysical methods of protein characterization were employed. In this review, we focus on these two independent strategies based on the unique biophysical features of the p53 protein.

Progress in deep Markov state modeling: Coarse graining and experimental data restraints

Recent advances in deep learning frameworks have established valuable tools for analyzing the long-timescale behavior of complex systems, such as proteins. In particular, the inclusion of physical constraints, e.g., time-reversibility, was a crucial step to make the methods applicable to biophysical systems. Furthermore, we advance the method by incorporating experimental observables into the model estimation showing that biases in simulation data can be compensated for. We further develop a new neural network layer in order to build a hierarchical model allowing for different levels of details to be studied. Finally, we propose an attention mechanism, which highlights important residues for the classification into different states. We demonstrate the new methodology on an ultralong molecular dynamics simulation of the Villin headpiece miniprotein.

The prediction of protein-ligand unbinding for modern drug discovery

INTRODUCTION

Drug-target thermodynamic and kinetic information have perennially important roles in drug design. The prediction of protein-ligand unbinding, which can provide important kinetic information, in experiments continues to face great challenges. Uncovering protein-ligand unbinding through molecular dynamics simulations has become efficient and inexpensive with the progress and enhancement of computing power and sampling methods.

AREAS COVERED

In this review, various sampling methods for protein-ligand unbinding and their basic principles are firstly briefly introduced. Then, their applications in predicting aspects of protein-ligand unbinding, including unbinding pathways, dissociation rate constants, residence time and binding affinity, are discussed.

EXPERT OPINION

Although various sampling methods have been successfully applied in numerous systems, they still have shortcomings and deficiencies. Most enhanced sampling methods require researchers to possess a wealth of prior knowledge of collective variables or reaction coordinates. In addition, most systems studied at present are relatively simple, and the study of complex systems in real drug research remains greatly challenging. Through the combination of machine learning and enhanced sampling methods, prediction accuracy can be further improved, and some problems encountered in complex systems also may be solved.

Induced fit versus conformational selection: From rate constants to fluxes… and back to rate constants

Induced fit- (IF) and conformational selection (CS) binding mechanisms have long been regarded to be mutually exclusive. Yet, they are now increasingly considered to produce the final ligand-target complex alongside within a thermodynamic cycle. This viewpoint benefited from the introduction of binding fluxes as a tool for analyzing the overall behavior of such cycle. This study aims to provide more vivid and applicable insights into this emerging field. In this respect, combining differential equation- based simulations and hitherto little explored alternative modes of calculation provide concordant information about the intricate workings of such cycle. In line with previous reports, we observe that the relative contribution of IF increases with the ligand concentration at equilibrium. Yet the baseline contribution may vary from one case to another and simulations as well as calculations show that this parameter is essentially regulated by the dissociation rate of both pathways. Closer attention should be paid to how the contributions of IF and CS compare at physiologically relevant drug/ligand concentrations. To this end, a simple equation discloses how changing a limited set of "microscopic" rate constants can extend the concentration range at which CS contributes most effectively. Finally, it could also be beneficial to extend the utilization of flux- based approaches to more physiologically relevant time scales and alternative binding models.

The diversity of molecular interactions involving intrinsically disordered proteins: A molecular modeling perspective

Intrinsically Disordered Proteins and Regions (IDPs/IDRs) are key components of a multitude of biological processes. Conformational malleability enables IDPs/IDRs to perform very specialized functions that cannot be accomplished by globular proteins. The functional role for most of these proteins is related to the recognition of other biomolecules to regulate biological processes or as a part of signaling pathways. Depending on the extent of disorder, the number of interacting sites and the type of partner, very different architectures for the resulting assemblies are possible. More recently, molecular condensates with liquid-like properties composed of multiple copies of IDPs and nucleic acids have been proven to regulate key processes in eukaryotic cells. The structural and kinetic details of disordered biomolecular complexes are difficult to unveil experimentally due to their inherent conformational heterogeneity. Computational approaches, alone or in combination with experimental data, have emerged as unavoidable tools to understand the functional mechanisms of this elusive type of assemblies. The level of description used, all-atom or coarse-grained, strongly depends on the size of the molecular systems and on the timescale of the investigated mechanism. In this mini-review, we describe the most relevant architectures found for molecular interactions involving IDPs/IDRs and the computational strategies applied for their investigation.

Solution-State Preorganization of Cyclic β-Hairpin Ligands Determines Binding Mechanism and Affinities for MDM2

Understanding mechanisms of protein folding and binding is crucial to designing their molecular function. Molecular dynamics (MD) simulations and Markov state model (MSM) approaches provide a powerful way to understand complex conformational change that occurs over long time scales. Such dynamics are important for the design of therapeutic peptidomimetic ligands, whose affinity and binding mechanism are dictated by a combination of folding and binding. To examine the role of preorganization in peptide binding to protein targets, we performed massively parallel explicit-solvent MD simulations of cyclic β-hairpin ligands designed to mimic the p53 transactivation domain and competitively bind mouse double minute 2 homologue (MDM2). Disrupting the MDM2-p53 interaction is a therapeutic strategy to prevent degradation of the p53 tumor suppressor in cancer cells. MSM analysis of over 3 ms of aggregate trajectory data enabled us to build a detailed mechanistic model of coupled folding and binding of four cyclic peptides which we compare to experimental binding affinities and rates. The results show a striking relationship between the relative preorganization of each ligand in solution and its affinity for MDM2. Specifically, changes in peptide conformational populations predicted by the MSMs suggest that entropy loss upon binding is the main factor influencing affinity. The MSMs also enable detailed examination of non-native interactions which lead to misfolded states and comparison of structural ensembles with experimental NMR measurements. In contrast to an MSM study of p53 transactivation domain (TAD) binding to MDM2, MSMs of cyclic β-hairpin binding show a conformational selection mechanism. Finally, we make progress toward predicting accurate off rates of cyclic peptides using multiensemble Markov models (MEMMs) constructed from unbiased and biased simulated trajectories.

Computational Modeling as a Tool to Investigate PPI: From Drug Design to Tissue Engineering

Protein-protein interactions (PPIs) mediate a large number of important regulatory pathways. Their modulation represents an important strategy for discovering novel therapeutic agents. However, the features of PPI binding surfaces make the use of structure-based drug discovery methods very challenging. Among the diverse approaches used in the literature to tackle the problem, linear peptides have demonstrated to be a suitable methodology to discover PPI disruptors. Unfortunately, the poor pharmacokinetic properties of linear peptides prevent their direct use as drugs. However, they can be used as models to design enzyme resistant analogs including, cyclic peptides, peptide surrogates or peptidomimetics. Small molecules have a narrower set of targets they can bind to, but the screening technology based on virtual docking is robust and well tested, adding to the computational tools used to disrupt PPI. We review computational approaches used to understand and modulate PPI and highlight applications in a few case studies involved in physiological processes such as cell growth, apoptosis and intercellular communication.

Effect of Stapling on the Thermodynamics of mdm2-p53 Binding

Protein-protein interaction (PPI) is one of the key regulatory features driving biomolecular processes and hence is targeted for designing therapeutics against diseases. Small peptides are a new and emerging class of therapeutics owing to their high specificity and low toxicity. For achieving efficient targeting of the PPI, amino acid side chains are often stapled together, resulting in the rigidification of these peptides. Exploring the scope of these peptides demands a comprehensive understanding of their working principle. In this work, two stapled p53 peptides have been considered to delineate their binding mechanism with mdm2 using computational approaches. The addition of stapling agent protects the secondary structure of the peptides even in the case of thermal and chemical denaturation. Although the introduction of a stapling agent increases the hydrophobicity of the peptide, the enthalpic stabilization decreases. This is overcome by the lowering of the entropic penalty, and the overall binding affinity improves. The mechanistic insights into the benefit of peptide stapling can be adopted for further improvement of peptide therapeutics.

Coupling Monte Carlo, Variational Implicit Solvation, and Binary Level-Set for Simulations of Biomolecular Binding

We develop a hybrid approach that combines the Monte Carlo (MC) method, a variational implicit-solvent model (VISM), and a binary level-set method for the simulation of biomolecular binding in an aqueous solvent. The solvation free energy for the biomolecular complex is estimated by minimizing the VISM free-energy functional of all possible solute-solvent interfaces that are used as dielectric boundaries. This functional consists of the solute volumetric, solute-solvent interfacial, solute-solvent van der Waals interaction, and electrostatic free energy. A technique of shifting the dielectric boundary is used to accurately predict the electrostatic part of the solvation free energy. Minimizing such a functional in each MC move is made possible by our new and fast binary level-set method. This method is based on the approximation of surface area by the convolution of an indicator function with a compactly supported kernel and is implemented by simple flips of numerical grid cells locally around the solute-solvent interface. We apply our approach to the p53-MDM2 system for which the two molecules are approximated by rigid bodies. Our efficient approach captures some of the poses before the final bound state. All-atom molecular dynamics simulations with most of such poses quickly reach the final bound state. Our work is a new step toward realistic simulations of biomolecular interactions. With further improvement of coarse graining and MC sampling, and combined with other models, our hybrid approach can be used to study the free-energy landscape and kinetic pathways of ligand binding to proteins.

Recent advances in atomic molecular dynamics simulation of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) play important roles in cellular functions. The inherent structural heterogeneity of IDPs makes the high-resolution experimental characterization of IDPs extremely difficult. Molecular dynamics (MD) simulation could provide the atomic-level description of the structural and dynamic properties of IDPs. This perspective reviews the recent progress in atomic MD simulation studies of IDPs, including the development of force fields and sampling methods, as well as applications in IDP-involved protein-protein interactions. The employment of large-scale simulations and advanced sampling techniques allows more accurate estimation of the thermodynamics and kinetics of IDP-mediated protein interactions, and the holistic landscape of the binding process of IDPs is emerging.

An integrated view of p53 dynamics, function, and reactivation

The tumor suppressor p53 plays a vital role in responding to cell stressors such as DNA damage, hypoxia, and tumor formation by inducing cell-cycle arrest, senescence, or apoptosis. Expression level alterations and mutational frequency implicates p53 in most human cancers. In this review, we show how both computational and experimental methods have been used to provide an integrated view of p53 dynamics, function, and reactivation potential. We argue that p53 serves as an exceptional case study for developing methods in modeling intrinsically disordered proteins. We describe how these methods can be leveraged to improve p53 reactivation molecule design and other novel therapeutic modalities, such as PROteolysis TARgeting Chimeras (PROTACs).

Markov State Models to Elucidate Ligand Binding Mechanism

Molecular dynamics simulations can now routinely access the microsecond timescale, making feasible direct sampling of ligand association events. While Markov State Model (MSM) approaches offer a useful framework for analyzing such trajectory data to gain insight into binding mechanisms, accurate modeling of ligand association pathways and kinetics must be done carefully. We describe methods and good practices for constructing MSMs of ligand binding from unbiased trajectory data and discuss how to use time-lagged independent component analysis (tICA) to build informative models, using as an example recent simulation work to model the binding of phenylalanine to the regulatory ACT domain dimer of phenylalanine hydroxylase. We describe a variety of methods for estimating association rates from MSMs and discuss how to distinguish between conformational selection and induced-fit mechanisms using MSMs. In addition, we review some examples of MSMs constructed to elucidate the mechanisms by which p53 transactivation domain (TAD) and related peptides bind the oncoprotein MDM2.

A disordered encounter complex is central to the yeast Abp1p SH3 domain binding pathway

Protein-protein interactions are involved in a wide range of cellular processes. These interactions often involve intrinsically disordered proteins (IDPs) and protein binding domains. However, the details of IDP binding pathways are hard to characterize using experimental approaches, which can rarely capture intermediate states present at low populations. SH3 domains are common protein interaction domains that typically bind proline-rich disordered segments and are involved in cell signaling, regulation, and assembly. We hypothesized, given the flexibility of SH3 binding peptides, that their binding pathways include multiple steps important for function. Molecular dynamics simulations were used to characterize the steps of binding between the yeast Abp1p SH3 domain (AbpSH3) and a proline-rich IDP, ArkA. Before binding, the N-terminal segment 1 of ArkA is pre-structured and adopts a polyproline II helix, while segment 2 of ArkA (C-terminal) adopts a 310 helix, but is far less structured than segment 1. As segment 2 interacts with AbpSH3, it becomes more structured, but retains flexibility even in the fully engaged state. Binding simulations reveal that ArkA enters a flexible encounter complex before forming the fully engaged bound complex. In the encounter complex, transient nonspecific hydrophobic and long-range electrostatic contacts form between ArkA and the binding surface of SH3. The encounter complex ensemble includes conformations with segment 1 in both the forward and reverse orientation, suggesting that segment 2 may play a role in stabilizing the correct binding orientation. While the encounter complex forms quickly, the slow step of binding is the transition from the disordered encounter ensemble to the fully engaged state. In this transition, ArkA makes specific contacts with AbpSH3 and buries more hydrophobic surface. Simulating the binding between ApbSH3 and ArkA provides insight into the role of encounter complex intermediates and nonnative hydrophobic interactions for other SH3 domains and IDPs in general.

Characterization of partially ordered states in the intrinsically disordered N-terminal domain of p53 using millisecond molecular dynamics simulations

The exploration of intrinsically disordered proteins in isolation is a crucial step to understand their complex dynamical behavior. In particular, the emergence of partially ordered states has not been explored in depth. The experimental characterization of such partially ordered states remains elusive due to their transient nature. Molecular dynamics mitigates this limitation thanks to its capability to explore biologically relevant timescales while retaining atomistic resolution. Here, millisecond unbiased molecular dynamics simulations were performed in the exemplar N-terminal region of p53. In combination with state-of-the-art Markov state models, simulations revealed the existence of several partially ordered states accounting for [Formula: see text] 40% of the equilibrium population. Some of the most relevant states feature helical conformations similar to the bound structure of p53 to Mdm2, as well as novel [Formula: see text]-sheet elements. This highlights the potential complexity underlying the energy surface of intrinsically disordered proteins.

Computational Investigation on the p53-MDM2 Interaction Using the Potential of Mean Force Study

Murine double minute 2 (MDM2) proteins are found to be overproduced by many human tumors in order to inhibit the functioning of p53 molecules, a tumor suppressor protein. Thus, reactivating p53 functioning in cancer cells by disrupting p53-MDM2 interactions may offer a significant approach in cancer treatment. However, the structural characterization of the p53-MDM2 complex at the atomistic level and the mechanism of binding/unbinding of the p53-MDM2 complex still remain unclear. Therefore, we demonstrate here the probable binding (unbinding) pathway of transactivation domain 1 of p53 during the formation (dissociation) of the p53-MDM2 complex in terms of free energy as a function of reaction coordinate from the potential of mean force (PMF) study using two different force fields: ff99SB and ff99SB-ILDN. From the PMF plot, we noticed the PMF to have a minimum value at a p53-MDM2 separation of 12 Å, with a dissociation energy of 30 kcal mol^-1. We also analyzed the conformational dynamics and stability of p53 as a function of its distance of separation from MDM2. The secondary structure content (helix and turns) in p53 was found to vary with its distance of separation from MDM2. The p53-MDM2 complex structure with lowest potential energy was isolated from the ensemble at the reaction coordinate corresponding to the minimum PMF value and subjected to molecular dynamics simulation to identify the interface surface area, interacting residues at the interface, and the stability of the complex. The simulation results highlight the importance of hydrogen bonds and the salt bridge between Lys94 of MDM2 and Glu17 of p53 in the stability of the p53-MDM2 complex. We also carried out the binding free energy calculations and the per residue energy decomposition analyses of the interface residues of the p53-MDM2 complex. We found that the binding affinity between MDM2 and p53 is indeed high [ΔG _bind = -7.29 kcal mol^-1 from molecular mechanics/Poisson-Boltzmann surface area (MM/PBSA) and ΔG _bind = -53.29 kcal mol^-1 from molecular mechanics/generalized borne surface area]. The total binding energy obtained using the MM/PBSA method was noticed to be closer to the experimental values (-6.4 to -9.0 kcal mol^-1). The p53-MDM2 complex binding profile was observed to follow the same trend even in the duplicate simulation run and also in the simulation carried out with different force fields. We found that Lys51, Leu54, Tyr100, and Tyr104 from MDM2 and the residues Phe19, Trp23, and Leu26 from p53 provide the highest energy contributions for the p53-MDM2 interaction. Our findings highlight the prominent structural and binding characteristics of the p53-MDM2 complex that may be useful in designing potential inhibitors to disrupt the p53-MDM2 interactions.

The Maximum Caliber Variational Principle for Nonequilibria

Ever since Clausius in 1865 and Boltzmann in 1877, the concepts of entropy and of its maximization have been the foundations for predicting how material equilibria derive from microscopic properties. But, despite much work, there has been no equally satisfactory general variational principle for nonequilibrium situations. However, in 1980, a new avenue was opened by E.T. Jaynes and by Shore and Johnson. We review here maximum caliber, which is a maximum-entropy-like principle that can infer distributions of flows over pathways, given dynamical constraints. This approach is providing new insights, particularly into few-particle complex systems, such as gene circuits, protein conformational reaction coordinates, network traffic, bird flocking, cell motility, and neuronal firing.

Calmodulin-Calcineurin Interaction beyond the Calmodulin-Binding Region Contributes to Calcineurin Activation

Calcineurin (CaN) is a calcium-dependent phosphatase involved in numerous signaling pathways. Its activation is in part driven by the binding of calmodulin (CaM) to a CaM recognition region (CaMBR) within CaN's regulatory domain (RD). However, secondary interactions between CaM and the CaN RD may be necessary to fully activate CaN. Specifically, it is established that the CaN RD folds upon CaM binding and a region C-terminal to CaMBR, the "distal helix", assumes an α-helix fold and contributes to activation [Dunlap, T. B., et al. (2013) Biochemistry 52, 8643-8651]. We hypothesized in that previous study that this distal helix can bind CaM in a region distinct from the canonical CaMBR. To test this hypothesis, we utilized molecular simulations, including replica-exchange molecular dynamics, protein-protein docking, and computational mutagenesis, to determine potential distal helix-binding sites on CaM's surface. We isolated a potential binding site on CaM (site D) that facilitates moderate-affinity interprotein interactions and predicted that mutation of site D residues K30 and G40 on CaM would weaken CaN distal helix binding. We experimentally confirmed that two variants (K30E and G40D) indicate weaker binding of a phosphate substrate p-nitrophenyl phosphate to the CaN catalytic site by a phosphatase assay. This weakened substrate affinity is consistent with competitive binding of the CaN autoinhibition domain to the catalytic site, which we suggest is due to the weakened distal helix-CaM interactions. This study therefore suggests a novel mechanism for CaM regulation of CaN that may extend to other CaM targets.

Variational selection of features for molecular kinetics

The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long time-scale kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of 12 fast-folding protein simulations and show that our procedure leads to more efficient model selection.

On the removal of initial state bias from simulation data

Classical atomistic simulations of biomolecules play an increasingly important role in molecular life science. The structure of current computing architectures favors methods that run multiple trajectories at once without requiring extensive communication between them. Many advanced sampling strategies in the field fit this mold. These approaches often rely on an adaptive logic and create ensembles of comparatively short trajectories whose starting points are not distributed according to the correct Boltzmann weights. This type of bias is notoriously difficult to remove, and Markov state models (MSMs) are one of the few strategies available for recovering the correct kinetics and thermodynamics from these ensembles of trajectories. In this contribution, we analyze the performance of MSMs in the thermodynamic reweighting task for a hierarchical set of systems. We show that MSMs can be rigorous tools to recover the correct equilibrium distribution for systems of sufficiently low dimensionality. This is conditional upon not tampering with local flux imbalances found in the data. For a real-world application, we find that a pure likelihood-based inference of the transition matrix produces the best results. The removal of the bias is incomplete, however, and for this system, all tested MSMs are outperformed by an alternative albeit less general approach rooted in the ideas of statistical resampling. We conclude by formulating some recommendations for how to address the reweighting issue in practice.

Exposing the Nucleation Site in α-Helix Folding: A Joint Experimental and Simulation Study

One of the fundamental events in protein folding is α-helix formation, which involves sequential development of a series of helical hydrogen bonds between the backbone C═O group of residues i and the -NH group of residues i + 4. While we now know a great deal about α-helix folding dynamics, a key question that remains to be answered is where the productive helical nucleation event occurs. Statistically, a helical nucleus (or the first helical hydrogen-bond) can form anywhere within the peptide sequence in question; however, the one that leads to productive folding may only form at a preferred location. This consideration is based on the fact that the α-helical structure is inherently asymmetric, due to the specific alignment of the helical hydrogen bonds. While this hypothesis is plausible, validating it is challenging because there is not an experimental observable that can be used to directly pinpoint the location of the productive nucleation process. Therefore, in this study we combine several techniques, including peptide cross-linking, laser-induced temperature-jump infrared spectroscopy, and molecular dynamics simulations, to tackle this challenge. Taken together, our experimental and simulation results support an α-helix folding mechanism wherein the productive nucleus is formed at the N-terminus, which propagates toward the C-terminal end of the peptide to yield the folded structure. In addition, our results show that incorporation of a cross-linker can lead to formation of differently folded conformations, underscoring the need for all-atom simulations to quantitatively assess the proposed cross-linking design.

Choice of Adaptive Sampling Strategy Impacts State Discovery, Transition Probabilities, and the Apparent Mechanism of Conformational Changes

Interest in atomically detailed simulations has grown significantly with recent advances in computational hardware and Markov state modeling (MSM) methods, yet outstanding questions remain that hinder their widespread adoption. Namely, how do alternative sampling strategies explore conformational space and how might this influence predictions generated from the data? Here, we seek to answer these questions for four commonly used sampling methods: (1) a single long simulation, (2) many short simulations run in parallel, (3) adaptive sampling, and (4) our recently developed goal-oriented sampling algorithm, FAST. We first develop a theoretical framework for analytically calculating the probability of discovering select states on simple landscapes, where we uncover the drastic effects of varying the number and length of simulations. We then use kinetic Monte Carlo simulations on a variety of physically inspired landscapes to characterize the probability of discovering particular states and transition pathways for each of the four methods. Consistently, we find that FAST simulations discover each target state with the highest probability, while traversing realistic pathways. Furthermore, we uncover the potential pathology that short parallel simulations sometimes predict an incorrect transition pathway by crossing large energy barriers that long simulations would typically circumnavigate. We refer to this pathology as "pathway tunneling". To protect against this phenomenon when using adaptive-sampling and FAST simulations, we introduce the FAST-string method. This method enhances sampling along the highest-flux transition paths to refine an MSMs transition probabilities and discriminate between competing pathways. Additionally, we compare the performance of a variety of MSM estimators in describing accurate thermodynamics and kinetics. For adaptive sampling, we recommend simply normalizing the transition counts out of each state after adding small pseudocounts to avoid creating sources or sinks. Lastly, we evaluate whether our insights from simple landscapes hold for all-atom molecular dynamics simulations of the folding of the λ-repressor protein. Remarkably, we find that FAST-contacts predicts the same folding pathway as a set of long simulations but with orders of magnitude less simulation time.

Simulation of spontaneous G protein activation reveals a new intermediate driving GDP unbinding

Activation of heterotrimeric G proteins is a key step in many signaling cascades. However, a complete mechanism for this process, which requires allosteric communication between binding sites that are ~30 Å apart, remains elusive. We construct an atomically detailed model of G protein activation by combining three powerful computational methods: metadynamics, Markov state models (MSMs), and CARDS analysis of correlated motions. We uncover a mechanism that is consistent with a wide variety of structural and biochemical data. Surprisingly, the rate-limiting step for GDP release correlates with tilting rather than translation of the GPCR-binding helix 5. β-Strands 1 - 3 and helix 1 emerge as hubs in the allosteric network that links conformational changes in the GPCR-binding site to disordering of the distal nucleotide-binding site and consequent GDP release. Our approach and insights provide foundations for understanding disease-implicated G protein mutants, illuminating slow events in allosteric networks, and examining unbinding processes with slow off-rates.

Free Energy Landscape of the Complete Transport Cycle in a Key Bacterial Transporter

PepT_So is a proton-coupled bacterial symporter, from the major facilitator superfamily (MFS), which transports di-/tripeptide molecules. The recently obtained crystal structure of PepT_So provides an unprecedented opportunity to gain an understanding of functional insights of the substrate transport mechanism. Binding of the proton and peptide molecule induces conformational changes into occluded (OC) and outward-facing (OF) states, which we are able to characterize using molecular dynamics (MD) simulations. The structural knowledge of the OC and OF state is important to fully understand the major energy barrier associated with the transport cycle. In order to gain functional insight into the interstate dynamics, we performed extensive all atom MD simulations. The Markov state model was constructed to identify the free energy barriers between the states, and kinetic information on intermediate pathways was obtained using the transition pathway theory (TPT). TPT shows that the OF state is obtained by the movement of TM1 and TM7 at the extracellular side approximately 12-16 Å away from each other, and the inward movement of TM4 and TM10 at the intracellular halves to 3-4 Å characterizes the OC state. Helix distance distributions obtained from MD simulations were compared with experimental double electron-electron resonance spectroscopy and were found to be in excellent agreement with previous studies. We also predicted the optimal positions for placement of methane thiosulfonate spin label probes to capture the slowest protein dynamics. Our finding sheds light on the conformational cycle of this key membrane transporter and the functional relationships between the multiple intermediate states.

Complete Coupled Binding-Folding Pathway of the Intrinsically Disordered Transcription Factor Protein Brinker Revealed by Molecular Dynamics Simulations and Markov State Modeling

Intrinsically disordered proteins (IDPs) make up a large class of proteins that lack stable structures in solution, existing instead as dynamic conformational ensembles. To perform their biological functions, many IDPs bind to other proteins or nucleic acids. Although IDPs are unstructured in solution, when they interact with binding partners, they fold into defined three-dimensional structures via coupled binding-folding processes. Because they frequently underlie IDP function, the mechanisms of this coupled binding-folding process are of great interest. However, given the flexibility inherent to IDPs and the sparse populations of intermediate states, it is difficult to reveal binding-folding pathways at atomic resolution using experimental methods. Computer simulations are another tool for studying these pathways at high resolution. Accordingly, we have applied 40 μs of unbiased molecular dynamics simulations and Markov state modeling to map the complete binding-folding pathway of a model IDP, the 59-residue C-terminal portion of the DNA binding domain of Drosophila melanogaster transcription factor Brinker (BrkDBD). Our modeling indicates that BrkDBD binds to its cognate DNA and folds in ∼50 μs by an induced fit mechanism, acquiring most of its stable secondary and tertiary structure only after it reaches the final binding site on the DNA. The protein follows numerous pathways en route to its bound and folded conformation, occasionally becoming stuck in kinetic traps. Each binding-folding pathway involves weakly bound, increasingly folded intermediate states located at different sites on the DNA surface. These findings agree with experimental data and provide additional insight into the BrkDBD folding mechanism and kinetics.

Perspective: Maximum caliber is a general variational principle for dynamical systems

We review here Maximum Caliber (Max Cal), a general variational principle for inferring distributions of paths in dynamical processes and networks. Max Cal is to dynamical trajectories what the principle of maximum entropy is to equilibrium states or stationary populations. In Max Cal, you maximize a path entropy over all possible pathways, subject to dynamical constraints, in order to predict relative path weights. Many well-known relationships of non-equilibrium statistical physics-such as the Green-Kubo fluctuation-dissipation relations, Onsager's reciprocal relations, and Prigogine's minimum entropy production-are limited to near-equilibrium processes. Max Cal is more general. While it can readily derive these results under those limits, Max Cal is also applicable far from equilibrium. We give examples of Max Cal as a method of inference about trajectory distributions from limited data, finding reaction coordinates in bio-molecular simulations, and modeling the complex dynamics of non-thermal systems such as gene regulatory networks or the collective firing of neurons. We also survey its basis in principle and some limitations.