Energy landscape theory, funnels, specificity, and optimal criterion of biomolecular binding

Membrane lateral organization from potential energy disconnectivity graph

Understanding the thermodynamic and kinetic properties of biomolecules requires elucidation of their complex energy landscape. A disconnectivity graph analysis of the energy landscape provides a framework for mapping the multi-dimensional landscape onto a two-dimensional representation while preserving the key features of the energy landscape. Several studies show that the structure or shape of the disconnectity graph is directly associated with the function of protein and nucleic acid molecules. In this review, we discuss how disconnectivity analysis of the potential energy surface can be extended to lipid molecules to glean important information about membrane organization. The shape of the disconnectivity graphs can be used to predict the lateral organization of multi-component lipid bilayer. We hope that this review encourages the use of disconnectivity graphs routinely by membrane biophysicists to predict the lateral organization of lipids.

Evolution shapes interaction patterns for epistasis and specific protein binding in a two-component signaling system

The elegant design of protein sequence/structure/function relationships arises from the interaction patterns between amino acid positions. A central question is how evolutionary forces shape the interaction patterns that encode long-range epistasis and binding specificity. Here, we combined family-wide evolutionary analysis of natural homologous sequences and structure-oriented evolution simulation for two-component signaling (TCS) system. The magnitude-frequency relationship of coupling conservation between positions manifests a power-law-like distribution and the positions with highly coupling conservation are sparse but distributed intensely on the binding surfaces and hydrophobic core. The structure-specific interaction pattern involves further optimization of local frustrations at or near the binding surface to adapt the binding partner. The construction of family-wide conserved interaction patterns and structure-specific ones demonstrates that binding specificity is modulated by both direct intermolecular interactions and long-range epistasis across the binding complex. Evolution sculpts the interaction patterns via sequence variations at both family-wide and structure-specific levels for TCS system.

Energy landscape quantifications of histone H3.3 recognition by chaperone DAXX reveal an uncoupled binding specificity and affinity

Histone variant H3.3 differs from the canonical histone H3.1 by only five amino acids, yet its chaperone death domain-associated protein (DAXX) can specifically recognize H3.3 over H3.1, despite having a large DAXX-interacting surface on the H3.3-H4 heterodimer common to that on the H3.1-H4 complex. This observation gives rise to the question of, from the binding energy point view, how high binding specificity may be achieved with small differences of the overall binding energy for protein-protein interactions in general. Here we investigate the mechanism of coupling of binding specificity and affinity in protein-protein interactions using the DAXX-H3.3-H4 complex as a model. Using a multi-scale method, we found that the hydrophobic interactions between DAXX and the H3.3-specific region contributed to their initial binding process. And the structural flexibility of the interacting partners contributed to the binding affinity after their encounter. By quantifying the free energy landscape, we revealed that the interaction between the specific residues of H3.3 and DAXX decreased the encounter barrier height while the folding of H3.3-H4 and DAXX increased the depth of the free energy basin of the final binding state. The encounter barrier height, which is not coupled to the thermodynamic stability of the final binding state, had a marked effect on the initial binding rate of flexible histones and chaperones. Based on the energy landscape theory, we found that the intrinsic binding energy funnel of this uncoupled recognition process was affected by the structural flexibility and the flexibility modulated the degree of coupling between binding specificity and affinity. Our work offers a biophysical explanation of the specific recognition between the histones and their chaperones, and also extends the use of energy landscape theory for understanding molecular recognitions in general.

Unbiased molecular dynamics simulation of a first-in-class small molecule inhibitor binds to oncostatin M

Small molecule inhibitors (SMIs) targeting oncostatin M (OSM) signaling pathway represent new therapeutics to combat cancer, inflammatory bowel disease (IBD) and CNS disease. Recently, the first-in-class SMI named SMI-10B that target OSM and block its interaction with receptor (OSMR) were reported. However, the binding pocket and interaction mode of the compound on OSM remain poorly understood, which hampering the rational design of SMIs that target OSM. Here, using SMI-10B as a probe, the multiple pockets on OSM for small molecules binding were extensively explored by unbiased molecular dynamics (MD) simulations. Then, the near-native structure of the complex was identified by molecular mechanics generalized Born surface area (MM/GBSA) binding energy funnel. Moreover, the binding stabilities of the protein-ligand complexes in near- and non-native conformations were verified by additional independent MD runs and absolute free energy perturbation (FEP) calculation. In summary, the unique feature of SMI-10B spontaneously binds to OSM characterized here not only provide detailed information for understanding the molecular mechanism of SMI-10B binding to OSM, but also will facilitate the rational design of novel and more potent SMIs to block OSM signaling.

Learning continuous potentials from smFRET

Potential energy landscapes are useful models in describing events such as protein folding and binding. While single-molecule fluorescence resonance energy transfer (smFRET) experiments encode information on continuous potentials for the system probed, including rarely visited barriers between putative potential minima, this information is rarely decoded from the data. This is because existing analysis methods often model smFRET output assuming, from the onset, that the system probed evolves in a discretized state space to be analyzed within a hidden Markov model (HMM) paradigm. By contrast, here, we infer continuous potentials from smFRET data without discretely approximating the state space. We do so by operating within a Bayesian nonparametric paradigm by placing priors on the family of all possible potential curves. As our inference accounts for a number of required experimental features raising computational cost (such as incorporating discrete photon shot noise), the framework leverages a structured-kernel-interpolation Gaussian process prior to help curtail computational cost. We show that our structured-kernel-interpolation priors for potential energy reconstruction from smFRET analysis accurately infers the potential energy landscape from a smFRET binding experiment. We then illustrate advantages of structured-kernel-interpolation priors for potential energy reconstruction from smFRET over standard HMM approaches by providing information, such as barrier heights and friction coefficients, that is otherwise inaccessible to HMMs.

Lack of Correlation between Landscape Geometry and Transition Rates

Biological cells can exist in a variety of distinct phenotypes, determined by the steady-state solutions of genetic networks governing their cell fate. A popular way of representing these states relies on the creation of landscape related to the relative occupation of these states. It is often assumed that this landscape offers direct information regarding the state-to-state transition rates, suggesting that these are related to barrier heights separating landscape minima. Here, we study a toggle triad network exhibiting multistability and directly demonstrate the lack of any direct correlation between properties of the landscape and corresponding transition rates.

Inferring potential landscapes from noisy trajectories of particles within an optical feedback trap

While particle trajectories encode information on their governing potentials, potentials can be challenging to robustly extract from trajectories. Measurement errors may corrupt a particle’s position, and sparse sampling of the potential limits data in higher energy regions such as barriers. We develop a Bayesian method to infer potentials from trajectories corrupted by Markovian measurement noise without assuming prior functional form on the potentials. As an alternative to Gaussian process priors over potentials, we introduce structured kernel interpolation to the Natural Sciences which allows us to extend our analysis to large datasets. Structured-Kernel-Interpolation Priors for Potential Energy Reconstruction (SKIPPER) is validated on 1D and 2D experimental trajectories for particles in a feedback trap.

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A feedback trap was used to generate noisy Langevin microbead trajectories

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The potential energy surface is recovered using a Bayesian formulation

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The formulation uses a structured-kernel-interpolation Gaussian process (SKI-GP) to tractably approximate Gaussian process regression for larger datasets

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Thanks to our adaptation of SKI-GP, we have broadened the use of Gaussian processes for natural science applications

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

Physics of biomolecular recognition and conformational dynamics

Biomolecular recognition usually leads to the formation of binding complexes, often accompanied by large-scale conformational changes. This process is fundamental to biological functions at the molecular and cellular levels. Uncovering the physical mechanisms of biomolecular recognition and quantifying the key biomolecular interactions are vital to understand these functions. The recently developed energy landscape theory has been successful in quantifying recognition processes and revealing the underlying mechanisms. Recent studies have shown that in addition to affinity, specificity is also crucial for biomolecular recognition. The proposed physical concept of intrinsic specificity based on the underlying energy landscape theory provides a practical way to quantify the specificity. Optimization of affinity and specificity can be adopted as a principle to guide the evolution and design of molecular recognition. This approach can also be used in practice for drug discovery using multidimensional screening to identify lead compounds. The energy landscape topography of molecular recognition is important for revealing the underlying flexible binding or binding-folding mechanisms. In this review, we first introduce the energy landscape theory for molecular recognition and then address four critical issues related to biomolecular recognition and conformational dynamics: (1) specificity quantification of molecular recognition; (2) evolution and design in molecular recognition; (3) flexible molecular recognition; (4) chromosome structural dynamics. The results described here and the discussions of the insights gained from the energy landscape topography can provide valuable guidance for further computational and experimental investigations of biomolecular recognition and conformational dynamics.

Nonspecific Binding-Fundamental Concepts and Consequences for Biosensing Applications

Nature achieves differentiation of specific and nonspecific binding in molecular interactions through precise control of biomolecules in space and time. Artificial systems such as biosensors that rely on distinguishing specific molecular binding events in a sea of nonspecific interactions have struggled to overcome this issue. Despite the numerous technological advancements in biosensor technologies, nonspecific binding has remained a critical bottleneck due to the lack of a fundamental understanding of the phenomenon. To date, the identity, cause, and influence of nonspecific binding remain topics of debate within the scientific community. In this review, we discuss the evolution of the concept of nonspecific binding over the past five decades based upon the thermodynamic, intermolecular, and structural perspectives to provide classification frameworks for biomolecular interactions. Further, we introduce various theoretical models that predict the expected behavior of biosensors in physiologically relevant environments to calculate the theoretical detection limit and to optimize sensor performance. We conclude by discussing existing practical approaches to tackle the nonspecific binding challenge in vitro for biosensing platforms and how we can both address and harness nonspecific interactions for in vivo systems.

Rapid Assessment of T-Cell Receptor Specificity of the Immune Repertoire

Accurate assessment of TCR-antigen specificity at the whole immune repertoire level lies at the heart of improved cancer immunotherapy, but predictive models capable of high-throughput assessment of TCR-peptide pairs are lacking. Recent advances in deep sequencing and crystallography have enriched the data available for studying TCR-p-MHC systems. Here, we introduce a pairwise energy model, RACER, for rapid assessment of TCR-peptide affinity at the immune repertoire level. RACER applies supervised machine learning to efficiently and accurately resolve strong TCR-peptide binding pairs from weak ones. The trained parameters further enable a physical interpretation of interacting patterns encoded in each specific TCR-p-MHC system. When applied to simulate thymic selection of an MHC-restricted T-cell repertoire, RACER accurately estimates recognition rates for tumor-associated neoantigens and foreign peptides, thus demonstrating its utility in helping address the large computational challenge of reliably identifying the properties of tumor antigen-specific T-cells at the level of an individual patient's immune repertoire.

ITScore-NL: An Iterative Knowledge-Based Scoring Function for Nucleic Acid-Ligand Interactions

Nucleic acid-ligand complexes underlie numerous cellular processes, such as gene function expression and regulation, in which their three-dimensional structures are important to understand their functions and thus to develop therapeutic interventions. Given the high cost and technical difficulties in experimental methods, computational methods such as molecular docking have been actively used to investigate nucleic acid-ligand interactions in which an accurate scoring function is crucial. However, because of the limited number of experimental nucleic acid-ligand binding data and structures, the scoring function development for nucleic acid-ligand interactions falls far behind that for protein-protein and protein-ligand interactions. Here, based on our statistical mechanics-based iterative approach, we have developed an iterative knowledge-based scoring function for nucleic acid-ligand interactions, named as ITScore-NL, by explicitly including stacking and electrostatic potentials. Our ITScore-NL scoring function was extensively evaluated for its ability in the binding mode and binding affinity predictions on three diverse test sets and compared with state-of-the-art scoring functions. Overall, ITScore-NL obtained significantly better performance than the other 12 scoring functions and predicted near-native poses with rmsd ≤ 1.5 Å for 71.43% of the cases when the top three binding modes were considered and a good correlation of R = 0.64 in binding affinity prediction on the large test set of 77 nucleic acid-ligand complexes. These results suggested the accuracy of ITScore-NL and the necessity of explicitly including stacking and electrostatic potentials.

Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation

Computational studies play an increasingly important role in chemistry and biophysics, mainly thanks to improvements in hardware and algorithms. In drug discovery and development, computational studies can reduce the costs and risks of bringing a new medicine to market. Computational simulations are mainly used to optimize promising new compounds by estimating their binding affinity to proteins. This is challenging due to the complexity of the simulated system. To assess the present and future value of simulation for drug discovery, we review key applications of advanced methods for sampling complex free-energy landscapes at near nonergodicity conditions and for estimating the rate coefficients of very slow processes of pharmacological interest. We outline the statistical mechanics and computational background behind this research, including methods such as steered molecular dynamics and metadynamics. We review recent applications to pharmacology and drug discovery and discuss possible guidelines for the practitioner. Recent trends in machine learning are also briefly discussed. Thanks to the rapid development of methods for characterizing and quantifying rare events, simulation's role in drug discovery is likely to expand, making it a valuable complement to experimental and clinical approaches.

Funneled energy landscape unifies principles of protein binding and evolution

Most proteins have evolved to spontaneously fold into native structure and specifically bind with their partners for the purpose of fulfilling biological functions. According to Darwin, protein sequences evolve through random mutations, and only the fittest survives. The understanding of how the evolutionary selection sculpts the interaction patterns for both biomolecular folding and binding is still challenging. In this study, we incorporated the constraint of functional binding into the selection fitness based on the principle of minimal frustration for the underlying biomolecular interactions. Thermodynamic stability and kinetic accessibility were derived and quantified from a global funneled energy landscape that satisfies the requirements of both the folding into the stable structure and binding with the specific partner. The evolution proceeds via a bowl-like evolution energy landscape in the sequence space with a closed-ring attractor at the bottom. The sequence space is increasingly reduced until this ring attractor is reached. The molecular-interaction patterns responsible for folding and binding are identified from the evolved sequences, respectively. The residual positions participating in the interactions responsible for folding are highly conserved and maintain the hydrophobic core under additional evolutionary constraints of functional binding. The positions responsible for binding constitute a distributed network via coupling conservations that determine the specificity of binding with the partner. This work unifies the principles of protein binding and evolution under minimal frustration and sheds light on the evolutionary design of proteins for functions.

Passive immunotherapies targeting Aβ and tau in Alzheimer's disease

Amyloid-β (Aβ) and tau proteins currently represent the two most promising targets to treat Alzheimer's disease. The most extensively developed method to treat the pathologic forms of these proteins is through the administration of exogenous antibodies, or passive immunotherapy. In this review, we discuss the molecular-level strategies that researchers are using to design an effective therapeutic antibody, given the challenges in treating this disease. These challenges include selectively targeting a protein that has misfolded or is pathological rather than the more abundant, healthy protein, designing strategic constructs for immunizing an animal to raise an antibody that has the appropriate conformational selectivity to achieve this end, and clearing the pathological protein species before prion-like cell-to-cell spread of misfolded protein has irreparably damaged neurons, without invoking damaging inflammatory responses in the brain that naturally arise when the innate immune system is clearing foreign agents. The various solutions to these problems in current clinical trials will be discussed.

Nonequilibrium Thermodynamics in Cell Biology: Extending Equilibrium Formalism to Cover Living Systems

We discuss new developments in the nonequilibrium dynamics and thermodynamics of living systems, giving a few examples to demonstrate the importance of nonequilibrium thermodynamics for understanding biological dynamics and functions. We study single-molecule enzyme dynamics, in which the nonequilibrium thermodynamic and dynamic driving forces of chemical potential and flux are crucial for the emergence of non-Michaelis-Menten kinetics. We explore single-gene expression dynamics, in which nonequilibrium dissipation can suppress fluctuations. We investigate the cell cycle and identify the nutrition supply as the energy input that sustains the stability, speed, and coherence of cell cycle oscillation, from which the different vital phases of the cell cycle emerge. We examine neural decision-making processes and find the trade-offs among speed, accuracy, and thermodynamic costs that are important for neural function. Lastly, we consider the thermodynamic cost for specificity in cellular signaling and adaptation.

Heterogeneous and rate-dependent streptavidin-biotin unbinding revealed by high-speed force spectroscopy and atomistic simulations

Receptor-ligand interactions are essential for biological function and their binding strength is commonly explained in terms of static lock-and-key models based on molecular complementarity. However, detailed information on the full unbinding pathway is often lacking due, in part, to the static nature of atomic structures and ensemble averaging inherent to bulk biophysics approaches. Here we combine molecular dynamics and high-speed force spectroscopy on the streptavidin-biotin complex to determine the binding strength and unbinding pathways over the widest dynamic range. Experiment and simulation show excellent agreement at overlapping velocities and provided evidence of the unbinding mechanisms. During unbinding, biotin crosses multiple energy barriers and visits various intermediate states far from the binding pocket, while streptavidin undergoes transient induced fits, all varying with loading rate. This multistate process slows down the transition to the unbound state and favors rebinding, thus explaining the long lifetime of the complex. We provide an atomistic, dynamic picture of the unbinding process, replacing a simple two-state picture with one that involves many routes to the lock and rate-dependent induced-fit motions for intermediates, which might be relevant for other receptor-ligand bonds.

Superfunneled Energy Landscape of Protein Evolution Unifies the Principles of Protein Evolution, Folding, and Design

Evolution is essential for shaping the biological functions. Darwin proposed the selection as the driving force for evolution upon mutations. While mutations are clear, the quantification of the selection force is still challenging. In this study, we identified and quantified both thermodynamic stability and kinetic accessibility as the selection forces for protein evolution. The protein evolution can be viewed and quantified as a trajectory moving along a superfunneled energy landscape with a line attractor at the bottom. The resulting evolved sequences and structures show strong protein characteristics including the hydrophobic core, high designability, and fast folding. The evolution principle uncovered here is validated on real proteins and sheds light on the protein design.

Quantifying the Intrinsic Conformation Energy Landscape Topography of Proteins with Large-Scale Open-Closed Transition

Large-scale conformational changes of proteins, including the open-closed transitions, are crucial for a variety of protein functions. These open-closed transitions are often associated with ligand binding. However, the understandings of the underlying mechanisms of the conformational changes within proteins during the open-closed transitions are still challenging at present. In this study, we quantified the intrinsic underlying conformational energy landscapes of five different proteins with large-scale open-closed transitions. This is realized by exploring the underlying density of states and the intrinsic conformational energy landscape topography measure Λ. Λ is a dimensionless ratio of conformational energy gap δE versus conformational energy roughness δE and configurational entropy S or size of the intrinsic conformational energy landscape. By quantifying the Λ of intrinsic open-closed conformational (Λ^oc) and intrinsic global folding (Λ^global) energy landscapes, we show that both intrinsic open-closed conformation energy and entropy landscapes are funneled toward the closed state. Furthermore, our results indicate the strong correlations between Λ and thermodynamics (conformational state transition temperature against trapping temperature) as well as between Λ and kinetics (open-closed kinetic time) of these proteins. This shows that the intrinsic conformational landscape topography determines both the conformational thermodynamic stability and kinetic speed of the conformational dynamics. Our investigations provide important insights for understanding the fundamental mechanisms of the protein conformational dynamics in a physical and global way.

RosettaLigandEnsemble: A Small-Molecule Ensemble-Driven Docking Approach

RosettaLigand is a protein-small-molecule (ligand) docking software capable of predicting binding poses and is used for virtual screening of medium-sized ligand libraries. Structurally similar small molecules are generally found to bind in the same pose to one binding pocket, despite some prominent exceptions. To make use of this information, we have developed RosettaLigandEnsemble (RLE). RLE docks a superimposed ensemble of congeneric ligands simultaneously. The program determines a well-scoring overall pose for this superimposed ensemble before independently optimizing individual protein-small-molecule interfaces. In a cross-docking benchmark of 89 protein-small-molecule co-crystal structures across 20 biological systems, we found that RLE improved sampling efficiency in 62 cases, with an average change of 18%. In addition, RLE generated more consistent docking results within a congeneric series and was capable of rescuing the unsuccessful docking of individual ligands, identifying a nativelike top-scoring model in 10 additional cases. The improvement in RLE is driven by a balance between having a sizable common chemical scaffold and meaningful modifications to distal groups. The new ensemble docking algorithm will work well in conjunction with medicinal chemistry structure-activity relationship (SAR) studies to more accurately recapitulate protein-ligand interfaces. We also tested whether optimizing the rank correlation of RLE-binding scores to SAR data in the refinement step helps the high-resolution positioning of the ligand. However, no significant improvement was observed.

SPA-LN: a scoring function of ligand-nucleic acid interactions via optimizing both specificity and affinity

Nucleic acids have been widely recognized as potential targets in drug discovery and aptamer selection. Quantifying the interactions between small molecules and nucleic acids is critical to discover lead compounds and design novel aptamers. Scoring function is normally employed to quantify the interactions in structure-based virtual screening. However, the predictive power of nucleic acid–ligand scoring functions is still a challenge compared to other types of biomolecular recognition. With the rapid growth of experimentally determined nucleic acid–ligand complex structures, in this work, we develop a knowledge-based scoring function of nucleic acid–ligand interactions, namely SPA-LN. SPA-LN is optimized by maximizing both the affinity and specificity of native complex structures. The development strategy is different from those of previous nucleic acid–ligand scoring functions which focus on the affinity only in the optimization. The native conformation is stabilized while non-native conformations are destabilized by our optimization, making the funnel-like binding energy landscape more biased toward the native state. The performance of SPA-LN validates the development strategy and provides a relatively more accurate way to score the nucleic acid–ligand interactions.

Funneled potential and flux landscapes dictate the stabilities of both the states and the flow: Fission yeast cell cycle

Using fission yeast cell cycle as an example, we uncovered that the non-equilibrium network dynamics and global properties are determined by two essential features: the potential landscape and the flux landscape. These two landscapes can be quantified through the decomposition of the dynamics into the detailed balance preserving part and detailed balance breaking non-equilibrium part. While the funneled potential landscape is often crucial for the stability of the single attractor networks, we have uncovered that the funneled flux landscape is crucial for the emergence and maintenance of the stable limit cycle oscillation flow. This provides a new interpretation of the origin for the limit cycle oscillations: There are many cycles and loops existed flowing through the state space and forming the flux landscapes, each cycle with a probability flux going through the loop. The limit cycle emerges when a loop stands out and carries significantly more probability flux than other loops. We explore how robustness ratio (RR) as the gap or steepness versus averaged variations or roughness of the landscape, quantifying the degrees of the funneling of the underlying potential and flux landscapes. We state that these two landscapes complement each other with one crucial for stabilities of states on the cycle and the other crucial for the stability of the flow along the cycle. The flux is directly related to the speed of the cell cycle. This allows us to identify the key factors and structure elements of the networks in determining the stability, speed and robustness of the fission yeast cell cycle oscillations. We see that the non-equilibriumness characterized by the degree of detailed balance breaking from the energy pump quantified by the flux is the cause of the energy dissipation for initiating and sustaining the replications essential for the origin and evolution of life. Regulating the cell cycle speed is crucial for designing the prevention and curing strategy of cancer.

We have uncovered that the non-equilibrium network dynamics and global properties are determined by two essential features: the potential landscape and the flux landscape. We have found that the funneled potential landscape is crucial for the stability of the states on the cell cycle, however, the stabilities of the oscillation states cannot guarantee the stable directional flows. We have uncovered that the funneled flux landscape is important for the emergence and maintenance of the stable limit cycle oscillation flow. This work will allow us to identify the key factors and structure elements of the networks in determining the stability, speed and robustness of the fission yeast cell cycle oscillations. We see that the non-equilibriumness characterized by the degree of detailed balance breaking from the energy pump quantified by the flux is the cause of the energy dissipation for initiating and sustaining the replications essential for the origin and evolution of life. Regulating the cell cycle speed is crucial for designing the prevention and curing strategy of cancer.

Molecular mechanism of multispecific recognition of Calmodulin through conformational changes

Calmodulin (CaM) is found to have the capability to bind multiple targets. Investigations on the association mechanism of CaM to its targets are crucial for understanding protein-protein binding and recognition. Here, we developed a structure-based model to explore the binding process between CaM and skMLCK binding peptide. We found the cooperation between nonnative electrostatic interaction and nonnative hydrophobic interaction plays an important role in nonspecific recognition between CaM and its target. We also found that the conserved hydrophobic anchors of skMLCK and binding patches of CaM are crucial for the transition from high affinity to high specificity. Furthermore, this association process involves simultaneously both local conformational change of CaM and global conformational changes of the skMLCK binding peptide. We found a landscape with a mixture of the atypical "induced fit," the atypical "conformational selection," and "simultaneously binding-folding," depending on the synchronization of folding and binding. Finally, we extend our discussions on multispecific binding between CaM and its targets. These association characteristics proposed for CaM and skMLCK can provide insights into multispecific binding of CaM.

Scoring Functions of Protein-Ligand Interactions

Scoring function of protein-ligand interactions is used to recognize the “native” binding pose of a ligand on the protein and to predict the binding affinity, so that the active small molecules can be discriminated from the non-active ones. Scoring function is widely used in computationally molecular docking and structure-based drug discovery. The development and improvement of scoring functions have broad implications in pharmaceutical industry and academic research. During the past three decades, much progress have been made in methodology and accuracy for scoring functions, and many successful cases have be witnessed in virtual database screening. In this chapter, the authors introduced the basic types of scoring functions and their derivations, the commonly-used evaluation methods and benchmarks, as well as the underlying challenges and current solutions. Finally, the authors discussed the promising directions to improve and develop scoring functions for future molecular docking-based drug discovery.

A Quantitative Model for cAMP Binding to the Binding Domain of MloK1

Ligand-protein binding processes are essential in biological systems. A well-studied system is the binding of cyclic adenosine monophosphate to the cyclic nucleotide binding domain of the bacterial potassium channel MloK1. Strikingly, the measured on-rate for cyclic adenosine monophosphate binding is two orders of magnitude slower than a simple Smoluchowski diffusion model would suggest. To resolve this discrepancy and to characterize the ligand-binding path in structural and energetic terms, we calculated 1100 ligand-binding molecular dynamics trajectories and tested two scenarios: In the first scenario, the ligand transiently binds to the protein surface and then diffuses along the surface into the binding site. In the second scenario, only ligands that reach the protein surface in the vicinity of the binding site proceed into the binding site. Here, a binding funnel, which increasingly confines the translational as well as the rotational degrees of freedom, determines the binding pathways and limits the on-rate. From the simulations, we identified five surface binding states and calculated the rates between these surface binding states, the binding site, and the bulk. We find that the transient binding of the ligands to the surface binding states does not affect the on-rate, such that this effect alone cannot explain the observed low on-rate. Rather, by quantifying the translational and rotational degrees of freedom and by calculating the binding committor, our simulations confirmed the existence of a binding funnel as the main bottleneck. Direct binding via the binding funnel dominates the binding kinetics, and only ∼10% of all ligands proceed via the surface into the binding site. The simulations further predict an on-rate between 15 and 40μs-1(mol/l)-1, which agrees with the measured on-rate.

Energy Landscape Topography Reveals the Underlying Link Between Binding Specificity and Activity of Enzymes

Enzyme activity (often quantified by k_cat/K_m) is the main function of enzyme when it is active against the specific substrate. Higher or lower activities are highly desired for the design of novel enzyme and drug resistance. However, it is difficult to measure the activities of all possible variants and find the “hot-spot” within the limit of experimental time. In this study, we explore the underlying energy landscape of enzyme-substrate interactions and introduce the intrinsic specificity ratio (ISR), which reflects the landscape topography. By studying two concrete systems, we uncover the statistical correlation between the intrinsic specificity and the enzyme activity k_cat/K_m. This physics-based concept and method show that the energy landscape topography is valuable for understanding the relationship between enzyme specificity and activity. In addition, it can reveal the underlying mechanism of enzyme-substrate actions and has potential applications on enzyme design.

Protein Ensembles: How Does Nature Harness Thermodynamic Fluctuations for Life? The Diverse Functional Roles of Conformational Ensembles in the Cell

All soluble proteins populate conformational ensembles that together constitute the native state. Their fluctuations in water are intrinsic thermodynamic phenomena, and the distributions of the states on the energy landscape are determined by statistical thermodynamics; however, they are optimized to perform their biological functions. In this review we briefly describe advances in free energy landscape studies of protein conformational ensembles. Experimental (nuclear magnetic resonance, small-angle X-ray scattering, single-molecule spectroscopy, and cryo-electron microscopy) and computational (replica-exchange molecular dynamics, metadynamics, and Markov state models) approaches have made great progress in recent years. These address the challenging characterization of the highly flexible and heterogeneous protein ensembles. We focus on structural aspects of protein conformational distributions, from collective motions of single- and multi-domain proteins, intrinsically disordered proteins, to multiprotein complexes. Importantly, we highlight recent studies that illustrate functional adjustment of protein conformational ensembles in the crowded cellular environment. We center on the role of the ensemble in recognition of small- and macro-molecules (protein and RNA/DNA) and emphasize emerging concepts of protein dynamics in enzyme catalysis. Overall, protein ensembles link fundamental physicochemical principles and protein behavior and the cellular network and its regulation.

Universal statistical fluctuations in thermodynamics and kinetics of single molecular recognition

We investigated the main universal statistical distributions of single molecular recognition. The distributions of the single molecule binding free energy spectrum or density of states were characterized in the ligand-receptor binding energy landscape. The analytical results are consistent with the microscopic molecular simulations. The free energy distribution of different binding modes or states for a single molecule ligand receptor pair is approximately Gaussian near the mean and exponential at the tail. The equilibrium constant of single molecule binding is log-normal distributed near the mean and power law distributed near the tail. Additionally, we found that the kinetics distribution of single molecule ligand binding can be characterized by log-normal around the mean and power law distribution near the tail. This distribution is caused by exploration of the underlying inhomogeneous free energy landscape. Different ligand-receptor binding complexes have the same universal form of distribution but differ in parameters.

Multiscale method for modeling binding phenomena involving large objects: application to kinesin motor domains motion along microtubules

Many biological phenomena involve the binding of proteins to a large object. Because the electrostatic forces that guide binding act over large distances, truncating the size of the system to facilitate computational modeling frequently yields inaccurate results. Our multiscale approach implements a computational focusing method that permits computation of large systems without truncating the electrostatic potential and achieves the high resolution required for modeling macromolecular interactions, all while keeping the computational time reasonable. We tested our approach on the motility of various kinesin motor domains. We found that electrostatics help guide kinesins as they walk: N-kinesins towards the plus-end, and C-kinesins towards the minus-end of microtubules. Our methodology enables computation in similar, large systems including protein binding to DNA, viruses, and membranes.

Sequence diversity and ligand-induced structural rearrangements of viper hyaluronidase

The study focuses on ligand-induced structural changes of viper hyaluronidase and also provides insight into structure-based drug design for eukaryotic hyaluronidases, which could be future drug targets in cancer treatment, and venom spreading.

Landscape of kinetically trapped binary assemblies

For two-component assemblies, an inherent structure diagram (ISD) is the relationship between set inter-subunit energies and the types of kinetic traps (inherent structures) one may obtain from those energies. It has recently been shown that two-component ISDs are apportioned into regions or plateaux within which inherent structures display uniform features (e.g., stoichometries and morphologies). Interestingly, structures from one of the plateaux were also found to be robust outcomes of one type of non-equilibrium growth, which indicates the usefulness of the two-component ISD in predicting outcomes of some types of far-from-equilibrium growth. However, little is known as to how the ISD is apportioned into distinct plateaux. Also, while each plateau displays classes of structures that are morphologically distinct, little is known about the source of these distinct morphologies. This article outlines an analytic treatment of the two-component ISD and shows that the manner in which any ISD is apportioned arises from a single unitless order parameter. Additionally, the analytical framework allows for the characterization of local properties of the trapped structures within each ISD plateau. This work may prove to be useful in the design of novel classes of robust nonequilibrium assemblies.

Bifurcation analysis and potential landscapes of the p53-Mdm2 module regulated by the co-activator programmed cell death 5

The dynamics of p53 play important roles in the regulation of cell fate decisions in response to various stresses, and programmed cell death 5 (PDCD5) functions as a co-activator of p53 that modulates p53 dynamics. In the present paper, we investigated how p53 dynamics are modulated by PDCD5 during the deoxyribose nucleic acid damage response using methods of bifurcation analysis and potential landscape. Our results revealed that p53 activities display rich dynamics under different PDCD5 levels, including monostability, bistability with two stable steady states, oscillations, and the coexistence of a stable steady state (or two states) and an oscillatory state. The physical properties of the p53 oscillations were further demonstrated by the potential landscape in which the potential force attracts the system state to the limit cycle attractor, and the curl flux force drives coherent oscillation along the cyclic trajectory. We also investigated the efficiency with which PDCD5 induced p53 oscillations. We show that Hopf bifurcation can be induced by increasing the PDCD5 efficiency and that the system dynamics exhibited clear transition features in both barrier height and energy dissipation when the efficiency was close to the bifurcation point.

Optimizing the affinity and specificity of ligand binding with the inclusion of solvation effect

Solvation effect is an important factor for protein-ligand binding in aqueous water. Previous scoring function of protein-ligand interactions rarely incorporates the solvation model into the quantification of protein-ligand interactions, mainly due to the immense computational cost, especially in the structure-based virtual screening, and nontransferable application of independently optimized atomic solvation parameters. In order to overcome these barriers, we effectively combine knowledge-based atom-pair potentials and the atomic solvation energy of charge-independent implicit solvent model in the optimization of binding affinity and specificity. The resulting scoring functions with optimized atomic solvation parameters is named as specificity and affinity with solvation effect (SPA-SE). The performance of SPA-SE is evaluated and compared to 20 other scoring functions, as well as SPA. The comparative results show that SPA-SE outperforms all other scoring functions in binding affinity prediction and "native" pose identification. Our optimization validates that solvation effect is an important regulator to the stability and specificity of protein-ligand binding. The development strategy of SPA-SE sets an example for other scoring function to account for the solvation effect in biomolecular recognitions.

The universal statistical distributions of the affinity, equilibrium constants, kinetics and specificity in biomolecular recognition

We uncovered the universal statistical laws for the biomolecular recognition/binding process. We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor. The results of the analytical studies are confirmed by the microscopic flexible docking simulations. The distribution of binding affinity is Gaussian around the mean and becomes exponential near the tail. The equilibrium constants of the binding follow a log-normal distribution around the mean and a power law distribution in the tail. The intrinsic specificity for biomolecular recognition measures the degree of discrimination of native versus non-native binding and the optimization of which becomes the maximization of the ratio of the free energy gap between the native state and the average of non-native states versus the roughness measured by the variance of the free energy landscape around its mean. The intrinsic specificity obeys a Gaussian distribution near the mean and an exponential distribution near the tail. Furthermore, the kinetics of binding follows a log-normal distribution near the mean and a power law distribution at the tail. Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors. The elucidation of distributions of the kinetics and free energy has guiding roles in studying biomolecular recognition and function through small-molecule evolution and chemical genetics.

Uncovering the principles and underlying mechanisms of biomolecular recognition and molecular binding process is crucial for understanding the function and evolution, yet challenging. We meet the challenge by quantifying the statistical natures of the relevant physical variables of biomolecular recognition using the analytical model combined with microscopic flexible docking simulation methods. We uncovered the universal statistical laws obeyed by the affinity, equilibrium constant, intrinsic specificity and kinetics for biomolecular recognition. The general statistical laws based on energy landscape theory can serve as a conceptual framework for molecular recognition in biological repertoires. They can be applied to molecular selection, in vitro evolution process, high throughput screening and virtual screening for drug discovery. The statistical laws in combinations with experiments provide quantitative signatures of a specific ligand binding to a specific receptor, these resultant laws as a guideline will contribute to drug design against a specific target. Our developed statistical methodology is general and applicable for all other biomolecular recognitions.

Residues remote from the binding pocket control the antagonist selectivity towards the corticotropin-releasing factor receptor-1

The corticotropin releasing factors receptor-1 and receptor-2 (CRF1R and CRF2R) are therapeutic targets for treating neurological diseases. Antagonists targeting CRF1R have been developed for the potential treatment of anxiety disorders and alcohol addiction. It has been found that antagonists targeting CRF1R always show high selectivity, although CRF1R and CRF2R share a very high rate of sequence identity. This has inspired us to study the origin of the selectivity of the antagonists. We have therefore built a homology model for CRF2R and carried out unbiased molecular dynamics and well-tempered metadynamics simulations for systems with the antagonist CP-376395 in CRF1R or CRF2R to address this issue. We found that the side chain of Tyr(6.63) forms a hydrogen bond with the residue remote from the binding pocket, which allows Tyr(6.63) to adopt different conformations in the two receptors and results in the presence or absence of a bottleneck controlling the antagonist binding to or dissociation from the receptors. The rotameric switch of the side chain of Tyr356(6.63) allows the breaking down of the bottleneck and is a perquisite for the dissociation of CP-376395 from CRF1R.

Computational discovery and experimental verification of tyrosine kinase inhibitor pazopanib for the reversal of memory and cognitive deficits in rat model neurodegeneration

Pazopanib, a tyrosine kinase inhibitor marketed for cancer treatment, abrogates the course of neurodegeneration.

Cognition and memory impairment are hallmarks of the pathological cascade of various neurodegenerative disorders. Herein, we developed a novel computational strategy with two-dimensional virtual screening for not only affinity but also specificity. We integrated the two-dimensional virtual screening with ligand screening for 3D shape, electrostatic similarity and local binding site similarity to find existing drugs that may reduce the signs of cognitive deficits. For the first time, we found that pazopanib, a tyrosine kinase inhibitor marketed for cancer treatment, inhibits acetylcholinesterase (AchE) activities at sub-micromolar concentration. We evaluated and compared the effects of intragastrically-administered pazopanib with donepezil, a marketed AchE inhibitor, in cognitive and behavioral assays including the novel object recognition test, Y maze and Morris water maze test. Surprisingly, we found that pazopanib can restore memory loss and cognitive dysfunction to a similar extent as donepezil in a dosage of 15 mg kg^–1, only one fifth of the equivalent clinical dosage for cancer treatment. Furthermore, we demonstrated that pazopanib dramatically enhances the hippocampal Ach levels and increases the expression of the synaptic marker SYP. These findings suggest that pazopanib may become a viable treatment option for memory and cognitive deficits with a good safety profile in humans.

Energy landscape of all-atom protein-protein interactions revealed by multiscale enhanced sampling

Protein-protein interactions are regulated by a subtle balance of complicated atomic interactions and solvation at the interface. To understand such an elusive phenomenon, it is necessary to thoroughly survey the large configurational space from the stable complex structure to the dissociated states using the all-atom model in explicit solvent and to delineate the energy landscape of protein-protein interactions. In this study, we carried out a multiscale enhanced sampling (MSES) simulation of the formation of a barnase-barstar complex, which is a protein complex characterized by an extraordinary tight and fast binding, to determine the energy landscape of atomistic protein-protein interactions. The MSES adopts a multicopy and multiscale scheme to enable for the enhanced sampling of the all-atom model of large proteins including explicit solvent. During the 100-ns MSES simulation of the barnase-barstar system, we observed the association-dissociation processes of the atomistic protein complex in solution several times, which contained not only the native complex structure but also fully non-native configurations. The sampled distributions suggest that a large variety of non-native states went downhill to the stable complex structure, like a fast folding on a funnel-like potential. This funnel landscape is attributed to dominant configurations in the early stage of the association process characterized by near-native orientations, which will accelerate the native inter-molecular interactions. These configurations are guided mostly by the shape complementarity between barnase and barstar, and lead to the fast formation of the final complex structure along the downhill energy landscape.

Dynamic nature of the protein-protein interactions is an important element of cellular processes such as metabolic reactions and signal transduction, but its atomistic details are still unclear. Computational survey using molecular dynamics simulation is a straightforward method to elucidate these atomistic protein-protein interaction processes. However, a sufficient configurational sampling of the large system containing the atomistic protein complex model and explicit solvent remains a great challenge due to the long timescale involved. Here, we demonstrate that the multiscale enhanced sampling (MSES) successfully captured the atomistic details of the association/dissociation processes of a barnase-barstar complex covering the sampled space from the native complex structure to fully non-native configurations. The landscape derived from the simulation indicates that the association process is funnel-like downhill, analogously to the funnel landscape of fast-folding proteins. The funnel was found to be originated from near-native orientations guided by the shape complementarity between barnase and barstar, accelerating the formation of native inter-molecular interactions to complete the final complex structure.

Specificity and affinity quantification of flexible recognition from underlying energy landscape topography

Flexibility in biomolecular recognition is essential and critical for many cellular activities. Flexible recognition often leads to moderate affinity but high specificity, in contradiction with the conventional wisdom that high affinity and high specificity are coupled. Furthermore, quantitative understanding of the role of flexibility in biomolecular recognition is still challenging. Here, we meet the challenge by quantifying the intrinsic biomolecular recognition energy landscapes with and without flexibility through the underlying density of states. We quantified the thermodynamic intrinsic specificity by the topography of the intrinsic binding energy landscape and the kinetic specificity by association rate. We found that the thermodynamic and kinetic specificity are strongly correlated. Furthermore, we found that flexibility decreases binding affinity on one hand, but increases binding specificity on the other hand, and the decreasing or increasing proportion of affinity and specificity are strongly correlated with the degree of flexibility. This shows more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Our work provides a theoretical foundation and quantitative explanation of the previous qualitative studies on the relationship among flexibility, affinity and specificity. In addition, we found that the folding energy landscapes are more funneled with binding, indicating that binding helps folding during the recognition. Finally, we demonstrated that the whole binding-folding energy landscapes can be integrated by the rigid binding and isolated folding energy landscapes under weak flexibility. Our results provide a novel way to quantify the affinity and specificity in flexible biomolecular recognition.

Flexibility in biomolecular recognition is crucial for the function. Flexibility often leads to moderate binding affinity but high binding specificity, challenging the conventional wisdom that high specificity is guaranteed by high affinity. Currently, understanding of the relationship between affinity and specificity in flexible biomolecular recognition is still obscure, even in a qualitative way. By exploring the intrinsic biomolecular recognition energy landscapes, we provided a novel way to quantify the thermodynamic intrinsic specificity by energy landscape topography and kinetic specificity by association rate. We show quantitatively that flexibility decreases binding affinity while increases binding specificity, and the relative changes in affinity and specificity are strongly correlated with the degree of flexibility. Our results show that more (less) flexibility leads to weaker (stronger) coupling between affinity and specificity. Importantly, we demonstrated that flexibility modulates affinity and specificity through the underlying energy landscape. Our study establishes the quantitative relationship among flexibility, affinity and specificity, bridging the gap between theory and experiments.

Exploring multi-dimensional coordinate-dependent diffusion dynamics on the energy landscape of protein conformation change

We explore the multi-dimensional diffusion dynamics of protein conformational change. We found in general that the diffusion is anisotropic and inhomogeneous. The directional and positional dependence of diffusion have significant impacts on the protein conformational kinetics: the dominant kinetic path of conformational change is shifted from the naively expected steepest decent gradient paths. The kinetic transition state is shifted away from the transition state. The effective kinetic free energy barrier height, determining the kinetic rate of the conformational change, is shifted away from the one estimated from the thermodynamic free energy barrier. The shift of the transition state in position and value will modify the phi value analysis for identification of hot residues and interactions responsible for conformational dynamics. Ongoing and future experiments can test the predictions of the model.

DrugScorePPI knowledge-based potentials used as scoring and objective function in protein-protein docking

The distance-dependent knowledge-based DrugScore^PPI potentials, previously developed for in silico alanine scanning and hot spot prediction on given structures of protein-protein complexes, are evaluated as a scoring and objective function for the structure prediction of protein-protein complexes. When applied for ranking “unbound perturbation” (“unbound docking”) decoys generated by Baker and coworkers a 4-fold (1.5-fold) enrichment of acceptable docking solutions in the top ranks compared to a random selection is found. When applied as an objective function in FRODOCK for bound protein-protein docking on 97 complexes of the ZDOCK benchmark 3.0, DrugScore^PPI/FRODOCK finds up to 10% (15%) more high accuracy solutions in the top 1 (top 10) predictions than the original FRODOCK implementation. When used as an objective function for global unbound protein-protein docking, fair docking success rates are obtained, which improve by ∼2-fold to 18% (58%) for an at least acceptable solution in the top 10 (top 100) predictions when performing knowledge-driven unbound docking. This suggests that DrugScore^PPI balances well several different types of interactions important for protein-protein recognition. The results are discussed in view of the influence of crystal packing and the type of protein-protein complex docked. Finally, a simple criterion is provided with which to estimate a priori if unbound docking with DrugScore^PPI/FRODOCK will be successful.