Pavel I. Zhuravlev

Molecular noise of capping protein binding induces macroscopic instability in filopodial dynamics

Capping proteins are among the most important regulatory proteins involved in controlling complicated stochastic dynamics of filopodia, which are dynamic finger-like protrusions used by eukaryotic motile cells to probe their environment and help guide cell motility. They attach to the barbed end of a filament and prevent polymerization, leading to effective filament retraction due to retrograde flow. When we simulated filopodial growth in the presence of capping proteins, qualitatively different dynamics emerged, compared with actin-only system. We discovered that molecular noise due to capping protein binding and unbinding leads to macroscopic filopodial length fluctuations, compared with minuscule fluctuations in the actin-only system. Thus, our work shows that molecular noise of signaling proteins may induce micrometer-scale growth–retraction cycles in filopodia. When capped, some filaments eventually retract all the way down to the filopodial base and disappear. This process endows filopodium with a finite lifetime. Additionally, the filopodia transiently grow several times longer than in actin-only system, since less actin transport is required because of bundle thinning. We have also developed an accurate mean-field model that provides qualitative explanations of our numerical simulation results. Our results are broadly consistent with experiments, in terms of predicting filopodial growth retraction cycles and the average filopodial lifetimes.

Deconstructing the Native State: Energy Landscapes, Function, and Dynamics of Globular Proteins

Proteins are highly complex molecules with features exquisitely selected by nature to carry out essential biological functions. Physical chemistry and polymer physics provide us with the tools needed to make sense of this complexity. Upon translation, many proteins fold to a thermodynamically stable form known as the native state. The native state is not static, but consists of a hierarchy of conformations, that are continuously explored through dynamics. In this review we provide a brief introduction to some of the core concepts required in the discussion of the protein native dynamics using energy landscapes ideas. We first discuss recent works which have challenged the structure-function paradigm by demonstrating function in disordered proteins. Next we examine the hierarchical organization in the energy landscapes using atomistic molecular dynamics simulations and principal component analysis. In particular, the role of direct and water-mediated contacts in sculpting the landscape is elaborated. Another approach to studying the native state ensemble is based on choosing high-resolution order parameters for computing one- or two-dimensional free energy surfaces. We demonstrate that 2D free energy surfaces provide rich thermodynamic and kinetic information about the native state ensemble. Brownian dynamics simulations on such a surface indicate that protein conformational dynamics is weakly activated. Finally, we briefly discuss implicit and coarse-grained protein models and emphasize the solvent role in determining native state structure and dynamics.

Functional versus folding landscapes: the same yet different

Protein functional landscapes are characterized by a modest number of states compared with the folding landscapes, allowing brute force sampling of these states for smaller proteins using computer simulations. On the other hand, because the functional landscape topographies are complicated, the native state dynamics are often difficult to interpret. Nevertheless, a number of experimental and computational techniques have recently emerged that are designed to reveal the essential features of the native landscape, such as the hierarchical organization of conformational substates. These studies also shed light on the mechanisms of protein function, for example, explaining how chemical energy is transduced in molecular motors. Overall, interpreting experimental results in the light of the functional landscape paradigm considerably enhances the understanding of complex biomolecular processes.

Computing free energy of a large-scale allosteric transition in adenylate kinase using all atom explicit solvent simulations.

During allosteric motions proteins navigate rugged energy landscapes. Hence, mapping of these multidimensional landscapes into lower dimensional manifolds is important for gaining deeper insights into allosteric dynamics. Using a recently developed computational technique, we calculated the free energy difference between the open and closed states of adenylate kinase, an allosteric protein which was extensively studied previously using both experimental and theoretical approaches. Two independent simulations indicate reasonable convergence of the computed free energy profiles. The numerical value of the open/closed free energy difference is only 1-2 k(B)T, much smaller than some of the prior estimates. We also found that the conformations structurally close to the open form still retain many LID-NMP contacts, suggesting that the conformational basin of the closed form is larger than expected. The latter suggestion may explain the discrepancy in relative populations of open and closed forms of unligated adenylate kinase, observed in NMR and FRET experiments.

Theory of active transport in filopodia and stereocilia

The biological processes in elongated organelles of living cells are often regulated by molecular motor transport. We determined spatial distributions of motors in such organelles, corresponding to a basic scenario when motors only walk along the substrate, bind, unbind, and diffuse. We developed a mean-field model, which quantitatively reproduces elaborate stochastic simulation results as well as provides a physical interpretation of experimentally observed distributions of Myosin IIIa in stereocilia and filopodia. The mean-field model showed that the jamming of the walking motors is conspicuous, and therefore damps the active motor flux. However, when the motor distributions are coupled to the delivery of actin monomers toward the tip, even the concentration bump of G actin that they create before they jam is enough to speed up the diffusion to allow for severalfold longer filopodia. We found that the concentration profile of G actin along the filopodium is rather nontrivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this nonmonotonous shape is expected to occur under a broad set of conditions. We also find that the stationary motor distribution is universal for the given set of model parameters regardless of the organelle length, which follows from the form of the kinetic equations and the boundary conditions.

Design of Active Transport Must Be Highly Intricate: A Possible Role of Myosin and Ena/VASP for G-Actin Transport in Filopodia

Recent modeling of filopodia--the actin-based cell organelles employed for sensing and motility--reveals that one of the key limiting factors of filopodial length is diffusional transport of G-actin monomers to the polymerizing barbed ends. We have explored the possibility of active transport of G-actin by myosin motors, which would be an expected biological response to overcome the limitation of a diffusion-based process. We found that in a straightforward implementation of active transport the increase in length was unimpressive, < or = 30%, due to sequestering of G-actin by freely diffusing motors. However, artificially removing motor sequestration reactions led to approximately threefold increases in filopodial length, with the transport being mainly limited by the motors failing to detach from the filaments near the tip, clogging the cooperative conveyer belt dynamics. Making motors sterically transparent led to a qualitative change of the dynamics to a different regime of steady growth without a stationary length. Having identified sequestration and clogging as ubiquitous constraints to motor-driven transport, we devised and tested a speculative means to sidestep these limitations in filopodia by employing cross-linking and putative scaffolding roles of Ena/VASP proteins. We conclude that a naïve design of molecular-motor-based active transport would almost always be inefficient--an intricately organized kinetic scheme, with finely tuned rate constants, is required to achieve high-flux transport.

High Resolution Approach to the Native State Ensemble Kinetics and Thermodynamics

Many biologically interesting functions such as allosteric switching or protein-ligand binding are determined by the kinetics and mechanisms of transitions between various conformational substates of the native basin of globular proteins. To advance our understanding of these processes, we constructed a two-dimensional free energy surface (FES) of the native basin of a small globular protein, Trp-cage. The corresponding order parameters were defined using two native substructures of Trp-cage. These calculations were based on extensive explicit water all-atom molecular dynamics simulations. Using the obtained two-dimensional FES, we studied the transition kinetics between two Trp-cage conformations, finding that switching process shows a borderline behavior between diffusive and weakly-activated dynamics. The transition is well-characterized kinetically as a biexponential process. We also introduced a new one-dimensional reaction coordinate for the conformational transition, finding reasonable qualitative agreement with the two-dimensional kinetics results. We investigated the distribution of all the 38 native nuclear magnetic resonance structures on the obtained FES, analyzing interactions that stabilize specific low-energy conformations. Finally, we constructed a FES for the same system but with simple dielectric model of water instead of explicit water, finding that the results were surprisingly similar in a small region centered on the native conformations. The dissimilarities between the explicit and implicit model on the larger-scale point to the important role of water in mediating interactions between amino acid residues.

Protein fluxes along the filopodium as a framework for understanding the growth-retraction dynamics: the interplay between diffusion and active transport.

We present a picture of filopodial growth and retraction from physics perspective, where we emphasize the significance of the role played by protein fluxes due to spatially extended nature of the filopodium. We review a series of works, which used stochastic simulations and mean field analytical modeling to find the concentration profile of G-actin inside a filopodium, which, in turn, determines the stationary filopodial length. In addition to extensively reviewing the prior works, we also report some new results on the role of active transport in regulating the length of filopodia. We model a filopodium where delivery of actin monomers towards the tip can occur both through passive diffusion and active transport by myosin motors. We found that the concentration profile of G-actin along the filopodium is rather non-trivial, containing a narrow minimum near the base followed by a broad maximum. For efficient enough actin transport, this non-monotonous shape is expected to occur under a broad set of conditions. We also raise the issue of slow approach to the stationary length and the possibility of multiple steady state solutions.

Rigorous Calculation of Free Energy Difference Between Open and Closed States of Adenylate Kinase from Explicit Solvent Molecular Dynamics

Biological functions of proteins are closely connected to their dynamics in the native state. These dynamics are governed by the proteins native energy landscape. Therefore, constructing detailed maps of these landscapes is essential for studying protein function and dynamics, especially, in more interesting cases of allosteric proteins, molecular motors or enzymatic catalysis. One fundamental approach to creating energy landscape maps is to start from measuring free energy differences between a pair of protein conformations, for instance, two allosteric states. Doing it in a computer simulation with explicit solvent is a challenging problem, but recently we have developed a general method for this purpose. Given two conformations of a polymer chain, our procedure can calculate the free energy difference in a computationally efficient way. The essence of the method is in a proper “reaction coordinate” that drives the system from one conformation to the other one, and in a special confinement potential which limits the phase space needed to be explored without affecting the free energy difference. We have used the method on a small protein Trp-cage as a proof of concept. Also we have calculated free energy difference between the open and closed states of adenylate kinase with no ligand. Although, this is a thoroughly studied enzyme both experimentally and in silico, the efforts to calculate free energy difference between the two allosteric states have not yet achieved a final result.