Session S20: Free Energy Mapping in Biology and Materials Science II

Computing free-energy landscapes of co-operative structure changes in soft, biological matter

Using computer simulation and self-consistent field theory of coarse-grained models for lipid membranes and diblock copolymers, we study the free-energy landscape of collective phenomena that alter the topology of lipid membranes. These basic processes – pore formation, fusion and fission – often involve time scales of tens of nanometers and milliseconds that are large for atomistic simulation. Frequently, they involve transition states with high curvatures that are difficult to describe by Helfrich-like models. Coarse-grained models can access the relevant time and length scales, allow for a systematic exploration of parameters like the lipid architecture or membrane tension, and they are well suited to study collective phenomena that alter the topology of membranes.

The talk will discuss different computational techniques – Wang-Landau sampling, field-theoretic umbrella sampling, and the string method – to investigate metastable intermediates (like the stalk in the course of membrane fusion) and transition states of pore formation, membrane fusion and fission. Using coarse-grained models, we explore the universal aspects of topology-altering processes in membranes and comment on the extent, to which coarse-grained model capture specific effects of protein-mediated processes.   

From cellulose and lignin to kerogen: molecular simulations of a geological process

The process by which organic matter decomposes deep underground to form petroleum and its underlying kerogen matrix has so far remained a no man’s land to theoreticians, largely because of the geological (M.years) timescale associated with the process. Using a replica exchange accelerated molecular dynamics method initially developed in the context of the micro- to milli-second timescale for protein folding, we simulate the full transformation of cellulose and lignin (the main components of wood) into kerogen under prevailing geological conditions. We observe in sequence (i) the fragmentation of the cellulose crystal and production of water, (ii) the development of an aliphatic macromolecular phase, (iii) its aromatization, and (iv) its aggregation into a stiff porous aromatic carbon upon expulsion of the fluid phase. The composition of the solid residue along the maturation pathway strictly follows what is observed for natural type III kerogens and for artificially matured samples under closed conditions, providing further evidence of a kinetically controlled, irreversible, decomposition process in which the aliphatic (immature) phase is a metastable intermediate.   

RNA Structure Prediction Including Pseudoknots through Direct Enumeration of States

The accurate prediction of RNA secondary structure from primary sequence data has had enormous impact on research from the past forty years. While many algorithms exist to make these predictions, the inclusion of non-nested loops, termed pseudoknots, still poses challenges. We describe how the entropies of pseudoknots of arbitrary complexity can be formulated analytically through a Feynman diagram-like integral formulation. Furthermore, we demonstrate that for sufficiently short RNA sequences (~45 nucleotides) the complete enumeration of possible secondary structures can be accomplished quickly despite the NP-complete nature of the problem. By employing exhaustive enumeration, we are able to exactly compute the entire free energy landscape of potential structures resulting from a primary RNA sequence.   

Two Disease-Causing SNAP-25B Mutations Selectively Impair SNARE C-terminal Assembly

Synaptic exocytosis relies on assembly of three SNARE proteins into a parallel four-helix bundle to drive membrane fusion. SNARE assembly occurs by stepwise zippering of the vesicle-associated SNARE onto a binary SNARE complex on the target plasma membrane. Zippering begins with slow N-terminal association followed by rapid C-terminal zippering, which serves as a power stroke to drive membrane fusion. SNARE mutations have been associated with numerous diseases, especially neurological disorders. It remains unclear how these mutations affect SNARE zippering. Here, we used single-molecule optical tweezers to measure the assembly energy and kinetics of SNARE complexes containing single mutations I67T/N in neuronal SNARE SNAP-25B, which disrupt neurotransmitter release and have been implicated in neurological disorders. We found that both mutations significantly reduced the energy of C-terminal zippering by ~10 kBT, but did not affect N-terminal assembly. Our findings suggest that both mutations impair synaptic exocytosis by destabilizing SNARE assembly. Therefore, our measurements provide insights into the molecular mechanism of the disease caused by SNARE mutations.   

Universal and Efficient Entropy Estimation Using a Compression Algorithm

Characterization of simulated physical systems in equilibrium typically requires calculation of free-energy as a function of some control parameter. The enthalpy of a system is calculable using the apriori choice of interactions (i.e., force field, coupling parameters), yet entropy remains a challenge to quantify. Current free-energy and entropy estimation techniques suffer from being model specific, requiring abundant computation resources and simulation at conditions far from the studied realization. In this talk, I will present a new universal framework to calculate entropy using lossless compression algorithms readily available in every computer [1]. Furthermore, I will demonstrate the scheme’s effectiveness in several model systems and discuss convergence due to various data representations and sampling. The presented scheme is demonstrated to be a practical alternative for entropy calculation in simulated systems, regardless of model specific details, and may also be applied to experimentally recorded data.

[1] R. Avinery, M. Kornreich, R. Beck (2017) arXiv:1709.10164   

Computational high-throughput screening of drug-membrane thermodynamics

The thermodynamic partitioning of small molecules in lipid membranes is of fundamental importance for pharmaceutical applications. In silico, structural resolution over the molecule permeation can be obtained through the potential of mean force, which can be further employed to gain insights into the permeation kinetics. However, the extensive computational resources required by atomistic molecular dynamics simulations and the size of compound space hamper the possibility of utilizing the potential of mean force in computational drug screening. Coarse-grained models efficiently address both issues, as they significantly mitigate the computational expense while capturing the relevant physical properties, and reduce the size of chemical space. In this work, we introduce a high-throughput screening of compound space by means of coarse-grained molecular dynamics simulations. This allows us to identify simple relationships between bulk properties and key features of the potential of mean force. The potential of mean force thereby becomes an easily accessible quantity in drug-screening applications. By connecting the coarse-grained and atomistic compound spaces, we show that our results are representative of the transmembrane behavior of a set of more than 400000 small molecules.   

Insights into Protegrin Antimicrobial Peptides Membrane Translocation by Multistep Molecular Dynamics Simulations

Protegrin-1 (PG-1) is a cationic arginine-rich antimicrobial peptide. It is known that PG-1 induces membrane disruption by forming a pore leading to cell death. However, the insertion mechanism for these highly cationic peptides into hydrophobic membrane environment is still poorly understood. The timescale for pore formation is in the range from minutes to hours, which is beyond the timescale of conventional MD simulations. It has been found that the arginine gaunidinium and lipid phosphate groups form a strong bidentate complex and is crucial for translocation. To investigate the role of the bidentate complex for PG-1 translocation, we applied MD simulations using different approaches to overcome the free energy barrier and timescale limitations. Electroporation was implemented to facilitate the translocation process. Potential of mean force calculations was performed to calculate the free energy of the bidentate complex insertion. Our results suggest that the complex alone is still unfavorable for PG-1 insertion inside hydrophobic environment. Pore formation may be the prerequisite for PG-1 translocation.   

Energy landscapes from single-particle imaging of biological processes in and out of equilibrium

Ideally, a measurement of the free energy landscape of a biomolecule would combine the sampling of a macroscopic ensemble with the microscopic information of molecular simulation. We have developed a graph-theoretic technique which allows us to map the low-dimensional conformational manifold embedded in noisy single-particle cryo-electron microscope images[1,2]. Recently we successfully applied the method to X-ray Free Electron Laser diffraction images to map the process of genome release of the PR772 virus[3]. In all cases, we find continuous structural pathways on the extracted landscape which correspond directly to known biological function. Processes such as viral infection are highly non-equilibrium; in principle, the underlying free energy landscape can be derived from such non-equilibrium measurements, and we demonstrate this possibility in simple models. Single-particle imaging promises unprecedented access to the energy landscapes of biological systems.

[1] Trajectories of the ribosome as a Brownian nanomachine. PNAS (2014).

[2] Conformational Dynamics and Energy Landscapes of Ligand Binding in RyR1. bioRxiv (2017).

[3] Conformational landscape of a virus by single-particle X-ray scattering. Nat. Methods (2017).   

From KB to KB: observing entropy dynamics of complex systems using lossless compression algorithms

Free-energy estimation is key in the characterization of protein structure dynamics and binding prediction for applications such as drug-design. The enthalpy of a simulated protein can be calculated throughout the simulation using an apriori choice of the force field, yet entropy remains a challenge to quantify. Moreover, current entropy estimation techniques, in particular for large protein simulations, suffer from requiring abundant computation resources or the requirement of additional knowledge such as the protein ground-state. Here, I will present our recently developed scheme for universal estimation of entropy using lossless compression algorithm¹. Specifically, we apply our scheme on MD simulations of a protein fluctuating between folded and unfolded states. Our calculated entropy difference between the states successfully yields values comparable to previous estimates. Moreover, by applying our scheme for short windows along the simulation timeline, we demonstrate unmatched knowledge-free detection of the folding events and structure. This demonstrates a novel model-independent approach and opens a new window onto the entropy dynamics of complex systems.
¹ Avinery, Kornreich & Beck (2017) arXiv:1709.10164   

The kinetics of solution-phase Ag nanowire growth mediated by PVP: A theoretical perspective

A broad collection of Ag nanostructures can be synthesized in solution with the aid of polyvinylpyrrolidone (PVP). Among these, the growth of fivefold-twinned nanowires is particularly confounding, as it requires a growth rate 10²–10³ times faster along the nanowire axis than laterally. These structures grow from Mark’s decahedron seeds, which possess re-entrant “notches” at each twin boundary on the {100} side facets. These notches serve as “super-highways” to direct a high atom diffusion flux to the {111} ends, and thus elongate the nanowire. We calculate relevant adatom diffusion energy barriers for a bare Ag nanowire, incorporate these into finite Markov chain calculations to obtain the net growth rates of the nanowire length and diameter, and find that nanowires cannot form from bare Ag because atom accumulates on the nanowire sides, leading a lateral growth. However, by accounting for the solution environment and sampling the free energies around the edges and sides, we find that the region near the edge on the {111} end can become more energetically favored due to the semi-flexibility of PVP, and thus an atom’s transition towards the end becomes faster than the reverse path, leading to high-aspect-ratio Ag nanowires. Our results can explain several aspects of experiments.   

Toward realistic dynamical simulations of advanced materials, including ultrafast phase transitions

We propose several new approaches to realistic dynamical simulations of advanced materials, including ultrafast phase transitions. The first three of these are illustrated with proof-of-principle calculations using simple models. In the first approach, correlation effects are included in a time-dependent quasiparticle equation which is based on the Kadanoff-Baym equations. This approach is appropriate for an ultrafast Mott-Hubbard transition. In the second approach, phenomenological Landau-Ginzburg-like order parameters are coupled to one another and to the vector potential of the laser pulse, so that the phase transition is described by time-dependent Landau-Ginzburg theory. This approach is appropriate for one mechanism which is apparently observed for light-induced superconductivity. In the third approach, an electronic temperature can be obtained in a density-functional simulation which omits electron correlation. In the fourth and most ambitious approach, a density-functional electronic Hamiltonian can be modified by the addition of pair-correlation-based terms which are determined self-consistently.   

An evaluation of the accuracy of dynamic transition matrix calculations of Ising spin systems

In recent calculations of the Ising model density of states, it was found that a temperature schedule derived by monitoring the sampling of states with different magnetizations yielded a direct, simply implemented transition matrix procedure that exceeded the accuracy of techniques that that accumulate elements from multiple slowly annealing Markov chains.(1) This talk examines the influence of various computational parameters on the procedure and presents additional comparisons with existing methods.

(1) Dynamic canonical and microcanonical transition matrix analyses of critical behavior, D. Yevick, Y.H. Lee, Eur. Phys. J. B (2017) 90: 81.