Diffusion and association processes in biological systems: theory, computation and experiment

Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics

A novel approach to simulate simple protein-ligand systems at large time and length scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes, is limited to isotropic ligands in a single conformational state, and lacks multiparticle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parameterize the model, it is capable of modeling protein-protein interactions over large time and length scales, and it can be extended to handle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two protein-protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules. To enable reproducibility, we have published our code in the MSM/RD software package.

Modeling Effects of Surface Properties and Probe Density for Nanoscale Biosensor Design: A Case Study of DNA Hybridization near Surfaces

Electrochemical biosensors have extremely robust applications while offering ease of preparation, miniaturization, and tunability. By adjusting the arrangement and properties of immobilized probes on the sensor surface to optimize target-probe association, one can design highly sensitive and efficient sensors. In electrochemical nucleic acid biosensors, a self-assembled monolayer (SAM) is widely used as a tunable surface with inserted DNA or RNA probes to detect target sequences. The effects of inhomogeneous probe distribution across surfaces are difficult to study experimentally due to inadequate resolution. Regions of high probe density may inhibit hybridization with targets, and the magnitude of the effect may vary depending on the hybridization mechanism on a given surface. Another fundamental question concerns diffusion and hybridization of DNA taking place on surfaces and whether it speeds up or hinders molecular recognition. We used all-atom Brownian dynamics simulations to help answer these questions by simulating the hybridization process of single-stranded DNA (ssDNA) targets with a ssDNA probe on polar, nonpolar, and anionic SAMs at three different probe surface densities. Moreover, we simulated three tightly packed probe clusters by modeling clusters with different interprobe spacing on two different surfaces. Our results indicate that hybridization efficiency depends strongly on finding a balance that allows attractive forces to steer target DNA toward probes without anchoring it to the surface. Furthermore, we found that the hybridization rate becomes severely hindered when interprobe spacing is less than or equal to the target DNA length, proving the need for a careful design to both enhance target-probe association and avoid steric hindrance. We developed a general kinetic model to predict hybridization times and found that it works accurately for typical probe densities. These findings elucidate basic features of nanoscale biosensors, which can aid in rational design efforts and help explain trends in experimental hybridization rates at different probe densities.

Combining Virtual Reality Visualization with Ensemble Molecular Dynamics to Study Complex Protein Conformational Changes

Molecular dynamics (MD) simulations are increasingly used to elucidate relationships between protein structure, dynamics, and their biological function. Currently, it is extremely challenging to perform MD simulations of large-scale structural rearrangements in proteins that occur on millisecond timescales or beyond, as this requires very significant computational resources, or the use of cumbersome "collective variable" enhanced sampling protocols. Here, we describe a framework that combines ensemble MD simulations and virtual reality visualization (eMD-VR) to enable users to interactively generate realistic descriptions of large amplitude, millisecond timescale protein conformational changes in proteins. Detailed tests demonstrate that eMD-VR substantially decreases the computational cost of folding simulations of a WW domain, without the need to define collective variables a priori. We further show that eMD-VR generated pathways can be combined with Markov state models to describe the thermodynamics and kinetics of large-scale loop motions in the enzyme cyclophilin A. Our results suggest eMD-VR is a powerful tool for exploring protein energy landscapes in bioengineering efforts.

MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

Molecular simulations of cellular processes

It is, nowadays, possible to simulate biological processes in conditions that mimic the different cellular compartments. Several groups have performed these calculations using molecular models that vary in performance and accuracy. In many cases, the atomistic degrees of freedom have been eliminated, sacrificing both structural complexity and chemical specificity to be able to explore slow processes. In this review, we will discuss the insights gained from computer simulations on macromolecule diffusion, nuclear body formation, and processes involving the genetic material inside cell-mimicking spaces. We will also discuss the challenges to generate new models suitable for the simulations of biological processes on a cell scale and for cell-cycle-long times, including non-equilibrium events such as the co-translational folding, misfolding, and aggregation of proteins. A prominent role will be played by the wise choice of the structural simplifications and, simultaneously, of a relatively complex energetic description. These challenging tasks will rely on the integration of experimental and computational methods, achieved through the application of efficient algorithms. Graphical abstract.

Decoupling diffusion from the bimolecular photoinduced electron transfer reaction: a combined ultrafast spectroscopic and kinetic analysis

We have studied the bimolecular photoinduced electron transfer (PET) reaction between benzophenone (Bp) and DABCO using femtosecond broadband transient absorption spectroscopy in different compositions of acetonitrile/1-butanol binary solvent mixtures.

The conformational feasibility for the formation of reaching dimer in ASV and HIV integrase: a molecular dynamics study

Retroviral integrases are reported to form alternate dimer assemblies like the core-core dimer and reaching dimer. The core-core dimer is stabilized predominantly by an extensive interface between two catalytic core domains. The reaching dimer is stabilized by N-terminal domains that reach to form intermolecular interfaces with the other subunit's core and C-terminal domains (CTD), as well as CTD-CTD interactions. In this study, molecular dynamics (MD), Brownian dynamics (BD) simulations, and free energy analyses, were performed to elucidate determinants for the stability of the reaching dimer forms of full-length Avian Sarcoma Virus (ASV) and Human Immunodeficiency Virus (HIV) IN, and to examine the role of the C-tails (the last ~16-18 residues at the C-termini) in their structural dynamics. The dynamics of an HIV reaching dimer derived from small angle X-ray scattering and protein crosslinking data, was compared with the dynamics of a core-core dimer model derived from combining the crystal structures of two-domain fragments. The results showed that the core domains in the ASV reaching dimer express free dynamics, whereas those in the HIV reaching dimer are highly stable. BD simulations suggest a higher rate of association for the HIV core-core dimer than the reaching dimer. The predicted stability of these dimers was therefore ranked in the following order: ASV reaching dimer < HIV reaching dimer < composite core-core dimer. Analyses of MD trajectories have suggested residues that are critical for intermolecular contacts in each reaching dimer. Tests of these predictions and insights gained from these analyses could reveal a potential pathway for the association and dissociation of full-length IN multimers.

Modeling and simulation of protein-surface interactions: achievements and challenges

Understanding protein-inorganic surface interactions is central to the rational design of new tools in biomaterial sciences, nanobiotechnology and nanomedicine. Although a significant amount of experimental research on protein adsorption onto solid substrates has been reported, many aspects of the recognition and interaction mechanisms of biomolecules and inorganic surfaces are still unclear. Theoretical modeling and simulations provide complementary approaches for experimental studies, and they have been applied for exploring protein-surface binding mechanisms, the determinants of binding specificity towards different surfaces, as well as the thermodynamics and kinetics of adsorption. Although the general computational approaches employed to study the dynamics of proteins and materials are similar, the models and force-fields (FFs) used for describing the physical properties and interactions of material surfaces and biological molecules differ. In particular, FF and water models designed for use in biomolecular simulations are often not directly transferable to surface simulations and vice versa. The adsorption events span a wide range of time- and length-scales that vary from nanoseconds to days, and from nanometers to micrometers, respectively, rendering the use of multi-scale approaches unavoidable. Further, changes in the atomic structure of material surfaces that can lead to surface reconstruction, and in the structure of proteins that can result in complete denaturation of the adsorbed molecules, can create many intermediate structural and energetic states that complicate sampling. In this review, we address the challenges posed to theoretical and computational methods in achieving accurate descriptions of the physical, chemical and mechanical properties of protein-surface systems. In this context, we discuss the applicability of different modeling and simulation techniques ranging from quantum mechanics through all-atom molecular mechanics to coarse-grained approaches. We examine uses of different sampling methods, as well as free energy calculations. Furthermore, we review computational studies of protein-surface interactions and discuss the successes and limitations of current approaches.

Effects of confinement on models of intracellular macromolecular dynamics

The motions of particles in a viscous fluid confined within a spherical cell have been simulated using Brownian and Stokesian dynamics simulations. High volume fractions mimicking the crowded interior of biological cells were used. Importantly, although confinement yields an overall slowdown in motion, the qualitative effects of motion in the interior of the cell can be effectively modeled as if the system were an infinite periodic system. However, we observe layering of particles at the cell wall due to steric interactions in the confined space. Motions of nearby particles are also strongly correlated at the cell wall, and these correlations increase when hydrodynamic interactions are modeled. Further, particles near the cell wall have a tendency to remain near the cell wall. A consequence of these effects is that the mean contact time between particles is longer at the cell wall than in the interior of the cell. These findings identify a specific way that confinement affects the interactions between particles and points to a previously unidentified mechanism that may play a role in signal transduction and other processes near the membrane of biological cells.

Assessing the potential of atomistic molecular dynamics simulations to probe reversible protein-protein recognition and binding

Protein-protein recognition and binding are governed by diffusion, noncovalent forces and conformational flexibility, entangled in a way that only molecular dynamics simulations can dissect at high resolution. Here we exploited ubiquitin's noncovalent dimerization equilibrium to assess the potential of atomistic simulations to reproduce reversible protein-protein binding, by running submicrosecond simulations of systems with multiple copies of the protein at millimolar concentrations. The simulations essentially fail because they lead to aggregates, yet they reproduce some specificity in the binding interfaces as observed in known covalent and noncovalent ubiquitin dimers. Following similar observations in literature we hint at electrostatics and water descriptions as the main liable force field elements, and propose that their optimization should consider observables relevant to multi-protein systems and unfolded proteins. Within limitations, analysis of binding events suggests salient features of protein-protein recognition and binding, to be retested with improved force fields. Among them, that specific configurations of relative direction and orientation seem to trigger fast binding of two molecules, even over 50 Å distances; that conformational selection can take place within surface-to-surface distances of 10 to 40 Å i.e. well before actual intermolecular contact; and that establishment of contacts between molecules further locks their conformations and relative orientations.

webSDA: a web server to simulate macromolecular diffusional association

Macromolecular interactions play a crucial role in biological systems. Simulation of diffusional association (SDA) is a software for carrying out Brownian dynamics simulations that can be used to study the interactions between two or more biological macromolecules. webSDA allows users to run Brownian dynamics simulations with SDA to study bimolecular association and encounter complex formation, to compute association rate constants, and to investigate macromolecular crowding using atomically detailed macromolecular structures. webSDA facilitates and automates the use of the SDA software, and offers user-friendly visualization of results. webSDA currently has three modules: 'SDA docking' to generate structures of the diffusional encounter complexes of two macromolecules, 'SDA association' to calculate bimolecular diffusional association rate constants, and 'SDA multiple molecules' to simulate the diffusive motion of hundreds of macromolecules. webSDA is freely available to all users and there is no login requirement. webSDA is available at http://mcm.h-its.org/webSDA/.

Diffusion-limited attachment of large spherical particles to flexible membrane-immobilized receptors

Relatively large (~100 nm) spherical particles, e.g., virions, vesicles, or metal nanoparticles, often interact with short (<10 nm) flexible receptors immobilized in a lipid membrane or on other biologically relevant surfaces. The attachment kinetics of such particles may be limited globally by their diffusion toward a membrane or locally by diffusion around receptors. The detachment kinetics, also, can be limited by diffusion. Focusing on local diffusion limitations and using suitable approximations, we present expressions for the corresponding rate constants and identify their dependence on particle size and receptor length. We also illustrate features likely to be observed in such kinetics for particles (e.g., vesicles) with a substantial size distribution. The results obtained are generic and can be used to interpret a variety of situations. For example, we estimate upper values of virion attachment rate constants and clarify the likely effect of vesicle size distribution on previously observed non-exponential kinetics of vesicle detachment.

LipidWrapper: an algorithm for generating large-scale membrane models of arbitrary geometry

As ever larger and more complex biological systems are modeled in silico, approximating physiological lipid bilayers with simple planar models becomes increasingly unrealistic. In order to build accurate large-scale models of subcellular environments, models of lipid membranes with carefully considered, biologically relevant curvature will be essential. In the current work, we present a multi-scale utility called LipidWrapper capable of creating curved membrane models with geometries derived from various sources, both experimental and theoretical. To demonstrate its utility, we use LipidWrapper to examine an important mechanism of influenza virulence. A copy of the program can be downloaded free of charge under the terms of the open-source FreeBSD License from http://nbcr.ucsd.edu/lipidwrapper. LipidWrapper has been tested on all major computer operating systems.

FOUNDATIONS FOR MODELING THE DYNAMICS OF GENE REGULATORY NETWORKS: A MULTILEVEL-PERSPECTIVE REVIEW

A promising alternative for unraveling the principles under which the dynamic interactions among genes lead to cellular phenotypes relies on mathematical and computational models at different levels of abstraction, from the molecular level of protein-DNA interactions to the system level of functional relationships among genes. This review article presents, under a bottom–up perspective, a hierarchy of approaches to modeling gene regulatory network dynamics, from microscopic descriptions at the single-molecule level in the spatial context of an individual cell to macroscopic models providing phenomenological descriptions at the population-average level. The reviewed modeling approaches include Molecular Dynamics, Particle-Based Brownian Dynamics, the Master Equation approach, Ordinary Differential Equations, and the Boolean logic abstraction. Each of these frameworks is motivated by a particular biological context and the nature of the insight being pursued. The setting of gene network dynamic models from such frameworks involves assumptions and mathematical artifacts often ignored by the non-specialist. This article aims at providing an entry point for biologists new to the field and computer scientists not acquainted with some recent biophysically-inspired models of gene regulation. The connections promoting intuition between different abstraction levels and the role that approximations play in the modeling process are highlighted throughout the paper.

The scoring of poses in protein-protein docking: current capabilities and future directions

BACKGROUND

Protein-protein docking, which aims to predict the structure of a protein-protein complex from its unbound components, remains an unresolved challenge in structural bioinformatics. An important step is the ranking of docked poses using a scoring function, for which many methods have been developed. There is a need to explore the differences and commonalities of these methods with each other, as well as with functions developed in the fields of molecular dynamics and homology modelling.

RESULTS

We present an evaluation of 115 scoring functions on an unbound docking decoy benchmark covering 118 complexes for which a near-native solution can be found, yielding top 10 success rates of up to 58%. Hierarchical clustering is performed, so as to group together functions which identify near-natives in similar subsets of complexes. Three set theoretic approaches are used to identify pairs of scoring functions capable of correctly scoring different complexes. This shows that functions in different clusters capture different aspects of binding and are likely to work together synergistically.

CONCLUSIONS

All functions designed specifically for docking perform well, indicating that functions are transferable between sampling methods. We also identify promising methods from the field of homology modelling. Further, differential success rates by docking difficulty and solution quality suggest a need for flexibility-dependent scoring. Investigating pairs of scoring functions, the set theoretic measures identify known scoring strategies as well as a number of novel approaches, indicating promising augmentations of traditional scoring methods. Such augmentation and parameter combination strategies are discussed in the context of the learning-to-rank paradigm.

ReaDDy--a software for particle-based reaction-diffusion dynamics in crowded cellular environments

We introduce the software package ReaDDy for simulation of detailed spatiotemporal mechanisms of dynamical processes in the cell, based on reaction-diffusion dynamics with particle resolution. In contrast to other particle-based reaction kinetics programs, ReaDDy supports particle interaction potentials. This permits effects such as space exclusion, molecular crowding and aggregation to be modeled. The biomolecules simulated can be represented as a sphere, or as a more complex geometry such as a domain structure or polymer chain. ReaDDy bridges the gap between small-scale but highly detailed molecular dynamics or Brownian dynamics simulations and large-scale but little-detailed reaction kinetics simulations. ReaDDy has a modular design that enables the exchange of the computing core by efficient platform-specific implementations or dynamical models that are different from Brownian dynamics.

Investigating the motion of diblock copolymer assemblies in ionic liquids by in situ electron microscopy

The movement of individual block copolymer micelles in free-standing films of ionic liquids is investigated by transmission electron microscopy with the aim of providing an easily accessible high-resolution imaging tool for the in situ observation of particle movement in a liquid environment. A proof of concept and first studies on the behavior of individual particles in the fluid are demonstrated.

Krylov subspace methods for computing hydrodynamic interactions in brownian dynamics simulations

Hydrodynamic interactions play an important role in the dynamics of macromolecules. The most common way to take into account hydrodynamic effects in molecular simulations is in the context of a brownian dynamics simulation. However, the calculation of correlated brownian noise vectors in these simulations is computationally very demanding and alternative methods are desirable. This paper studies methods based on Krylov subspaces for computing brownian noise vectors. These methods are related to Chebyshev polynomial approximations, but do not require eigenvalue estimates. We show that only low accuracy is required in the brownian noise vectors to accurately compute values of dynamic and static properties of polymer and monodisperse suspension models. With this level of accuracy, the computational time of Krylov subspace methods scales very nearly as O(N(2)) for the number of particles N up to 10 000, which was the limit tested. The performance of the Krylov subspace methods, especially the "block" version, is slightly better than that of the Chebyshev method, even without taking into account the additional cost of eigenvalue estimates required by the latter. Furthermore, at N = 10,000, the Krylov subspace method is 13 times faster than the exact Cholesky method. Thus, Krylov subspace methods are recommended for performing large-scale brownian dynamics simulations with hydrodynamic interactions.

Atomic detail brownian dynamics simulations of concentrated protein solutions with a mean field treatment of hydrodynamic interactions

High macromolecular concentrations are a distinguishing feature of living organisms. Understanding how the high concentration of solutes affects the dynamic properties of biological macromolecules is fundamental for the comprehension of biological processes in living systems. In this paper, we describe the implementation of mean field models of translational and rotational hydrodynamic interactions into an atomically detailed many-protein brownian dynamics simulation method. Concentrated solutions (30-40% volume fraction) of myoglobin, hemoglobin A, and sickle cell hemoglobin S were simulated, and static structure factors, oligomer formation, and translational and rotational self-diffusion coefficients were computed. Good agreement of computed properties with available experimental data was obtained. The results show the importance of both solvent mediated interactions and weak protein-protein interactions for accurately describing the dynamics and the association properties of concentrated protein solutions. Specifically, they show a qualitative difference in the translational and rotational dynamics of the systems studied. Although the translational diffusion coefficient is controlled by macromolecular shape and hydrodynamic interactions, the rotational diffusion coefficient is affected by macromolecular shape, direct intermolecular interactions, and both translational and rotational hydrodynamic interactions.

On docking, scoring and assessing protein-DNA complexes in a rigid-body framework

We consider the identification of interacting protein-nucleic acid partners using the rigid body docking method FTdock, which is systematic and exhaustive in the exploration of docking conformations. The accuracy of rigid body docking methods is tested using known protein-DNA complexes for which the docked and undocked structures are both available. Additional tests with large decoy sets probe the efficacy of two published statistically derived scoring functions that contain a huge number of parameters. In contrast, we demonstrate that state-of-the-art machine learning techniques can enormously reduce the number of parameters required, thereby identifying the relevant docking features using a miniscule fraction of the number of parameters in the prior works. The present machine learning study considers a 300 dimensional vector (dependent on only 15 parameters), termed the Chemical Context Profile (CCP), where each dimension reflects a specific type of protein amino acid-nucleic acid base interaction. The CCP is designed to capture the chemical complementarities of the interface and is well suited for machine learning techniques. Our objective function is the Chemical Context Discrepancy (CCD), which is defined as the angle between the native system's CCP vector and the decoy's vector and which serves as a substitute for the more commonly used root mean squared deviation (RMSD). We demonstrate that the CCP provides a useful scoring function when certain dimensions are properly weighted. Finally, we explore how the amino acids on a protein's surface can help guide DNA binding, first through long-range interactions, followed by direct contacts, according to specific preferences for either the major or minor grooves of the DNA.

Gating and Intermolecular Interactions in Ligand-Protein Association: Coarse-Grained Modeling of HIV-1 Protease

Most biological processes are initiated or mediated by the association of ligands and proteins. This work studies multistep, ligand-protein association processes by Brownian dynamics simulations with coarse-grained models for HIV-1 protease (HIVp) and its neutral ligands. We report the average association times when the ligand concentration is 100 μM. The influence of crowding on the simulated binding time was also studied. HIVp has flexible loops that serve as a gate during the ligand binding processes. It is believed that the flaps are partially closed most of the time in its free state. To accelerate our simulations, we fixed a part of the HIVp and reparameterized our coarse-grained model, using atomistic molecular dynamics simulations, to reproduce the "gating" motions of HIVp. HIVp-ligand interactions changed the gating behavior of HIVp and helped ligands diffuse on HIVp surface to accelerate binding. The structural adjustment of the ligand toward its final stable state was the limiting step in the binding processes, which is highly system dependent. The intermolecular attraction between the ligands and crowder proteins contributes the most to the crowding effects. The results highlight broader implications in recognition pathways under more complex environment that considers molecular dynamics and conformational changes. This work brings insights into ligand-protein associations and is helpful in the design of targeted ligands.