Prediction of Optimal Folding Routes of Proteins That Satisfy the Principle of Lowest Entropy Loss: Dynamic Contact Maps and Optimal Control

An optimization model is introduced in which proteins try to evade high energy regions of the folding landscape, and prefer low entropy loss routes during folding. We make use of the framework of optimal control whose convenient solution provides practical and useful insight into the sequence of events during folding. We assume that the native state is available. As the protein folds, it makes different set of contacts at different folding steps. The dynamic contact map is constructed from these contacts. The topology of the dynamic contact map changes during the course of folding and this information is utilized in the dynamic optimization model. The solution is obtained using the optimal control theory. We show that the optimal solution can be cast into the form of a Gaussian Network that governs the optimal folding dynamics. Simulation results on three examples (CI2, Sso7d and Villin) show that folding starts by the formation of local clusters. Non-local clusters generally require the formation of several local clusters. Non-local clusters form cooperatively and not sequentially. We also observe that the optimal controller prefers “zipping” or small loop closure steps during folding. The folding routes predicted by the proposed method bear strong resemblance to the results in the literature

Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations

Understanding and control of structures and rates involved in protein-ligand binding are es- sential for drug design. Unfortunately, atomistic molecular dynamics (MD) simulations cannot di- rectly sample the excessively long residence and rearrangement times of tightly binding complexes. Here we exploit the recently developed multi-ensemble Markov model framework to compute full protein-peptide kinetics of the oncoprotein fragment 25−109Mdm2 and the nano-molar inhibitor peptide PMI. Using this system, we report, for the first time, direct estimates of kinetics beyond the seconds timescales using simulations of an all-atom MD model, with high accuracy and pre- cision. These results only require explicit simulations on the sub-milliseconds timescale and are tested against existing mutagenesis data and our own experimental measurements of the dissoci- ation and association rates. The full kinetic model reveals an overall downhill but rugged binding funnel with multiple pathways. The overall strong binding arises from a variety of conformations with different hydrophobic contact surfaces that interconvert on the milliseconds timescale.Funding is acknowledged by European Commission (ERC StG “pcCells” to F.N.), Deutsche Forschungsgemeinschaft (SFB 1114/C3, SFB 740/D7, and TRR 186/A12 to F.N. and SFB 1114/A4 to F.N. and T.W.). J.C. is a Wellcome Trust Senior Research Fellow (WT 095195MA). J.S. is a Marie Sklodowska-Curie Internationally outgoing fellow. M.D.C. is supported by a Biotechnology and Biological Sciences Research Council (BBSRC) studentship

Modeling of B cell Synapse Formation by Monte Carlo Simulation Shows That Directed Transport of Receptor Molecules Is a Potential Formation Mechanism

The formation of the protein segregation structure known as the “immunological synapse” in the contact region between B cells and antigen presenting cells appears to precede antigen (Ag) uptake by B cells. The mature B cell synapse consists of a central cluster of B cell receptor/Antigen (BCR/Ag) complexes surrounded by a ring of LFA-1/ICAM-1 complexes. In this study, we used an in silico model to investigate whether cytoskeletally driven transport of molecules toward the center of the contact zone is a potential mechanism of immunological synapse formation in B cells. We modeled directed transport by the cytoskeleton in an effective manner, by biasing the diffusion of molecules toward the center of the contact zone. Our results clearly show that biased diffusion of BCR/Ag complexes on the B cell surface is sufficient to produce patterns similar to experimentally observed immunological synapses. This is true even in the presence of significant membrane deformation as a result of receptor–ligand binding, which in previous work we showed had a detrimental effect on synapse formation at high antigen affinity values. Comparison of our model’s results to those of experiments shows that our model produces synapses for realistic length, time, and affinity scales. Our results also show that strong biased diffusion of free molecules has a negative effect on synapse formation by excluding BCR/Ag complexes from the center of the contact zone. However, synapses may still form provided the bias in diffusion of free molecules is an order-of-magnitude weaker than that of BCR/Ag complexes. We also show how diffusion trajectories obtained from single-molecule tracking experiments can generate insight into the mechanism of synapse formation

Combining Optimal Control Theory and Molecular Dynamics for Protein Folding

A new method to develop low-energy folding routes for proteins is presented. The novel aspect of the proposed approach is the synergistic use of optimal control theory with Molecular Dynamics (MD). In the first step of the method, optimal control theory is employed to compute the force field and the optimal folding trajectory for the atoms of a Coarse-Grained (CG) protein model. The solution of this CG optimization provides an harmonic approximation of the true potential energy surface around the native state. In the next step CG optimization guides the MD simulation by specifying the optimal target positions for the atoms. In turn, MD simulation provides an all-atom conformation whose positions match closely the reference target positions determined by CG optimization. This is accomplished by Targeted Molecular Dynamics (TMD) which uses a bias potential or harmonic restraint in addition to the usual MD potential. Folding is a dynamical process and as such residues make different contacts during the course of folding. Therefore CG optimization has to be reinitialized and repeated over time to accomodate these important changes. At each sampled folding time, the active contacts among the residues are recalculated based on the all-atom conformation obtained from MD. Using the new set of contacts, the CG potential is updated and the CG optimal trajectory for the atoms is recomputed. This is followed by MD. Implementation of this repetitive CG optimization - MD simulation cycle generates the folding trajectory. Simulations on a model protein Villin demonstrate the utility of the method. Since the method is founded on the general tools of optimal control theory and MD without any restrictions, it is widely applicable to other systems. It can be easily implemented with available MD software packages

Effects of Intracellular Calcium and Actin Cytoskeleton on TCR Mobility Measured by Fluorescence Recovery

Background: The activation of T lymphocytes by specific antigen is accompanied by the formation of a specialized signaling region termed the immunological synapse, characterized by the clustering and segregation of surface molecules and, in particular, by T cell receptor (TCR) clustering. Methodology/Principal Findings: To better understand TCR motion during cellular activation, we used confocal microscopy and photo-bleaching recovery techniques to investigate the lateral mobility of TCR on the surface of human T lymphocytes under various pharmacological treatments. Using drugs that cause an increase in intracellular calcium, we observed a decrease in TCR mobility that was dependent on a functional actin cytoskeleton. In parallel experiments measurement of filamentous actin by FACS analysis showed that raising intracellular calcium also causes increased polymerization of the actin cytoskeleton. These in vitro results were analyzed using a mathematical model that revealed effective binding parameters between TCR and the actin cytoskeleton. Conclusion/Significance: We propose, based on our results, that increase in intracellular calcium levels leads to actin polymerization and increases TCR/cytoskeleton interactions that reduce the overall mobility of the TCR. In a physiological setting, this may contribute to TCR re-positioning at the immunological synapse

Molecular Dynamics Simulation of Phosphorylated KID Post-Translational Modification

BACKGROUND:Kinase-inducible domain (KID) as transcriptional activator can stimulate target gene expression in signal transduction by associating with KID interacting domain (KIX). NMR spectra suggest that apo-KID is an unstructured protein. After post-translational modification by phosphorylation, KID undergoes a transition from disordered to well folded protein upon binding to KIX. However, the mechanism of folding coupled to binding is poorly understood. METHODOLOGY:To get an insight into the mechanism, we have performed ten trajectories of explicit-solvent molecular dynamics (MD) for both bound and apo phosphorylated KID (pKID). Ten MD simulations are sufficient to capture the average properties in the protein folding and unfolding. CONCLUSIONS:Room-temperature MD simulations suggest that pKID becomes more rigid and stable upon the KIX-binding. Kinetic analysis of high-temperature MD simulations shows that bound pKID and apo-pKID unfold via a three-state and a two-state process, respectively. Both kinetics and free energy landscape analyses indicate that bound pKID folds in the order of KIX access, initiation of pKID tertiary folding, folding of helix alpha(B), folding of helix alpha(A), completion of pKID tertiary folding, and finalization of pKID-KIX binding. Our data show that the folding pathways of apo-pKID are different from the bound state: the foldings of helices alpha(A) and alpha(B) are swapped. Here we also show that Asn139, Asp140 and Leu141 with large Phi-values are key residues in the folding of bound pKID. Our results are in good agreement with NMR experimental observations and provide significant insight into the general mechanisms of binding induced protein folding and other conformational adjustment in post-translational modification

Membrane-mediated interactions

Interactions mediated by the cell membrane between inclusions, such as membrane proteins or antimicrobial peptides, play important roles in their biological activity. They also constitute a fascinating challenge for physicists, since they test the boundaries of our understanding of self-assembled lipid membranes, which are remarkable examples of two-dimensional complex fluids. Inclusions can couple to various degrees of freedom of the membrane, resulting in different types of interactions. In this chapter, we review the membrane-mediated interactions that arise from direct constraints imposed by inclusions on the shape of the membrane. These effects are generic and do not depend on specific chemical interactions. Hence, they can be studied using coarse-grained soft matter descriptions. We deal with long-range membrane-mediated interactions due to the constraints imposed by inclusions on membrane curvature and on its fluctuations. We also discuss the shorter-range interactions that arise from the constraints on membrane thickness imposed by inclusions presenting a hydrophobic mismatch with the membrane.Comment: 38 pages, 10 figures, pre-submission version. In: Bassereau P., Sens P. (eds) Physics of Biological Membranes. Springer, Cha

Soft Matrices Suppress Cooperative Behaviors among Receptor-Ligand Bonds in Cell Adhesion

The fact that biological tissues are stable over prolonged periods of time while individual receptor-ligand bonds only have limited lifetime underscores the critical importance of cooperative behaviors of multiple molecular bonds, in particular the competition between the rate of rupture of closed bonds (death rate) and the rate of rebinding of open bonds (birth rate) in a bond cluster. We have recently shown that soft matrices can greatly increase the death rate in a bond cluster by inducing severe stress concentration near the adhesion edges. In the present paper, we report a more striking effect that, irrespective of stress concentration, soft matrices also suppress the birth rate in a bond cluster by increasing the local separation distance between open bonds. This is shown by theoretical analysis as well as Monte Carlo simulations based on a stochastic-elasticity model in which stochastic descriptions of molecular bonds and elastic descriptions of interfacial force/separation are unified in a single modeling framework. Our findings not only are important for understanding the role of elastic matrices in cell adhesion, but also have general implications on adhesion between soft materials

Insights in 17β-HSD1 Enzyme Kinetics and Ligand Binding by Dynamic Motion Investigation

BACKGROUND: Bisubstrate enzymes, such as 17beta-hydroxysteroid dehydrogenase type 1 (17beta-HSD1), exist in solution as an ensemble of conformations. 17beta-HSD1 catalyzes the last step of the biosynthesis of estradiol and, thus, it is a potentially attractive target for breast cancer treatment. METHODOLOGY/PRINCIPAL FINDINGS: To elucidate the conformational transitions of its catalytic cycle, a structural analysis of all available crystal structures was performed and representative conformations were assigned to each step of the putative kinetic mechanism. To cover most of the conformational space, all-atom molecular dynamic simulations were performed using the four crystallographic structures best describing apoform, opened, occluded and closed state of 17beta-HSD1 as starting structures. With three of them, binary and ternary complexes were built with NADPH and NADPH-estrone, respectively, while two were investigated as apoform. Free energy calculations were performed in order to judge more accurately which of the MD complexes describes a specific kinetic step. CONCLUSIONS/SIGNIFICANCE: Remarkably, the analysis of the eight long range trajectories resulting from this multi-trajectory/-complex approach revealed an essential role played by the backbone and side chain motions, especially of the betaF alphaG'-loop, in cofactor and substrate binding. Thus, a selected-fit mechanism is suggested for 17beta-HSD1, where ligand-binding induced concerted motions of the FG-segment and the C-terminal part guide the enzyme along its preferred catalytic pathway. Overall, we could assign different enzyme conformations to the five steps of the random bi-bi kinetic cycle of 17beta-HSD1 and we could postulate a preferred pathway for it. This study lays the basis for more-targeted biochemical studies on 17beta-HSD1, as well as for the design of specific inhibitors of this enzyme. Moreover, it provides a useful guideline for other enzymes, also characterized by a rigid core and a flexible region directing their catalysis

Fluctuations in active membranes

Active contributions to fluctuations are a direct consequence of metabolic energy consumption in living cells. Such metabolic processes continuously create active forces, which deform the membrane to control motility, proliferation as well as homeostasis. Membrane fluctuations contain therefore valuable information on the nature of active forces, but classical analysis of membrane fluctuations has been primarily centered on purely thermal driving. This chapter provides an overview of relevant experimental and theoretical approaches to measure, analyze and model active membrane fluctuations. In the focus of the discussion remains the intrinsic problem that the sole fluctuation analysis may not be sufficient to separate active from thermal contributions, since the presence of activity may modify membrane mechanical properties themselves. By combining independent measurements of spontaneous fluctuations and mechanical response, it is possible to directly quantify time and energy-scales of the active contributions, allowing for a refinement of current theoretical descriptions of active membranes.Comment: 38 pages, 9 figures, book chapte