Anatoly Malevanets

Mesoscopic model for solvent dynamics

Complex fluids such as polymers in solution or multispecies reacting systems in fluid flows often can be studied only by employing a simplified description of the solvent motions. A stochastic model utilizing a synchronous, discrete-time dynamics with continuous velocities and local multiparticle collisions is developed for this purpose. An H theorem is established for the model and the hydrodynamic equations and transport coefficients are derived. The results of simulations are presented which verify the properties of the model and demonstrate its utility as a hydrodynamics medium for the study of complex fluids.

Solute molecular dynamics in a mesoscale solvent

A hybrid molecular dynamics (MD) algorithm which combines a full MD description of solute–solute and solute–solvent interactions with a mesoscale treatment of solvent-solvent interactions is developed. The solvent dynamics is modeled on a mesoscale level by coarse graining the system into cells and updating the velocities of the solvent molecules by multiparticle collisions within each cell. The solvent dynamics is such that the correct hydrodynamic equations are obtained in the macroscopic limit and a Boltzmann distribution of velocities is established in equilibrium. Discrete-time versions of the hydrodynamic equations and Green–Kubo autocorrelation functions are derived. Between the discrete-time solvent–solvent collisions the system evolves by the classical equations of motion. The hybrid MD scheme is illustrated by an application to the Brownian motion of a nanocolloidal particle in the mesoscale solvent and concentrated nanocolloidal suspensions.

Mechanism and energy landscape of domain swapping in the B1 domain of protein G.

Three-dimensional domain swapping has emerged as a ubiquitous process for homo-oligomer formation in many unrelated proteins, but the molecular mechanism of this process is still poorly understood. Here we present a mechanism for the swapping reaction in the B1 domain of the immunoglobulin G binding protein from group G of Streptococcus (GB1). This is a particularly attractive system for investigating the swapping process, as the swapped dimer formed by the quadruple mutant (L5V/F30V/Y33F/A34F) of GB1 was recently shown to exist in equilibrium with a monomer-like conformation over time scales of minutes. According to our mechanism, swapping in GB1 starts from the C-terminus of the polypeptide chain and progresses by exchanging an increasing portion of the chains until a stable conformational state is reached. This exchange process does not involve unfolding. Rather, the conformational changes of individual monomers and their association are tightly coupled to minimize solvent exposure and maximize the total number of native contacts at all times, thereby closely approximating the minimum energy path of the reaction. Using detailed atomic descriptions, we compute the complete free-energy profiles of the exchange reaction for the GB1 quadruple mutant that forms swapped dimers and for the wild-type protein, which is monomeric. In both GB1 forms, intermediates sample a surprisingly wide range of nearly isoenergetic association modes and hinge conformations, indicating that the exchange reaction is a non-specific process akin to encounter complex formation where the amino acid sequence plays a marginal role. The main role of the mutations in the swapping process is to destabilize the GB1 monomer state, while stabilizing the swapped dimer conformation, with non-native intersubunit interactions, fostered by mutant side chains, contributing significantly to this stabilization. Our findings are rationalized in terms of a generic swapping mechanism that involves the association of activated molecular species, and it is argued that a similar mechanism may apply to swapping in other protein systems.

Variation of droplet acidity during evaporation

Variation of acidity and associated chemical changes of macromolecules in evaporating droplets is of central importance in electrosprayed aerosols. We study changes in acidity during evolution of a droplet that is composed of solvent and a charge binding macromolecule. We analyze the acidity of the droplet using analytical theory and stochastic modeling. We derive a universal relation for the minimum pH of a droplet in the presence of a protein and the results are confirmed by the stochastic modeling of ubiquitin and lysozyme at varying values of pH. We establish that in acidic droplets, once the number of solvated charges reaches the macroion charge, the further droplet evaporation, counter-intuitively, reduces the number of charges on the macromolecule and increases the droplet pH.

Disintegration mechanisms of charged nanodroplets: novel systems for applying methods of activated processes

We review recent advances in the understanding of ejection mechanisms of solvated ions and charged macromolecules from highly charged nanodroplets. While the physical basis for the instability leading to droplet fragmentation is relatively well understood, a description of molecular mechanism of the fragmentation in complex systems is still missing. Development of a comprehensive model for the droplet fragmentation is further complicated by chemical modifications of the charged macromolecules (macroions) in a changing droplet environment. We highlight several different molecular simulation techniques used to study fragmentation of charged droplets with different solutes. Ejection of simple ions is analysed using theory of activated processes and transfer reaction coordinate (TRC). The TRC was shown to adequately represent complex rearrangement of solvent molecules in the course of evaporation. The critical value of the square of the charge to volume ratio for spontaneous ejection of simple solvated ions from aqueous droplets is found to be very close to that predicted by Rayleighs model. On the contrary, the presence of macromolecules adds a level of complexity into the system where the charge-induced instabilities cannot be described by a conventional theory such as Rayleigh or ion-evaporation mechanism. Additional charge–charge interactions between charged sites on a macromolecule dramatically change the macroion ejection mechanism. Molecular dynamics simulations reveal a number of distinct scenarios: contiguous extrusion, drying-out, star-like formation of solvent surrounding a macroion and pearl formation along the macromolecular chain.

Interplay of buried histidine protonation and protein stability in prion misfolding

Misofolding of mammalian prion proteins (PrP) is believed to be the cause of a group of rare and fatal neurodegenerative diseases. Despite intense scrutiny however, the mechanism of the misfolding reaction remains unclear. We perform nuclear Magnetic Resonance and thermodynamic stability measurements on the C-terminal domains (residues 90–231) of two PrP variants exhibiting different pH-induced susceptibilities to aggregation: the susceptible hamster prion (GHaPrP) and its less susceptible rabbit homolog (RaPrP). The pKa of histidines in these domains are determined from titration experiments, and proton-exchange rates are measured at pH 5 and pH 7. A single buried highly conserved histidine, H187/H186 in GHaPrP/RaPrP, exhibited a markedly down shifted pKa ~5 for both proteins. However, noticeably larger pH-induced shifts in exchange rates occur for GHaPrP versus RaPrP. Analysis of the data indicates that protonation of the buried histidine destabilizes both PrP variants, but produces a more drastic effect in the less stable GHaPrP. This interpretation is supported by urea denaturation experiments performed on both PrP variants at neutral and low pH, and correlates with the difference in disease susceptibility of the two species, as expected from the documented linkage between destabilization of the folded state and formation of misfolded and aggregated species.

Advances in Modeling the Stability of Noncovalent Complexes in Charged Droplets with Applications in Electrospray Ionization-MS Experiments

Electrospray ionization mass spectrometry is used extensively to measure the equilibrium constant of noncovalent complexes. In this Perspective, we attempt to present an accessible introduction to computational methodologies that can be applied to determine the stability of weak noncovalent complexes in their journey from bulk solution into the gaseous state. We demonstrate the usage of the methods on two typical examples of noncovalent complexes drawn from a broad class of nucleic acids and transient protein complexes found in aqueous droplets. We conclude that this new emerging direction in the use of simulations can lead to estimates of equilibrium constant corrections due to complex dissociation in the carrier droplet and finding of agents that may stabilize the protein interfaces.

Differential flow instability in the Ginzburg-Landau and Swift-Hohenberg approximations

Abstract The effects of a differential flow of the components of a reaction-diffusion system which is close to its stability boundary are described within the long wavelength approximation. In the vicinity of the Hopf bifurcation the systems evolution is governed by a complex Ginzburg-Landau equation modified by a purely imaginary convective term. If the system is near the zero real eigenvalue bifurcation, the governing equation is a modified Swift-Hohenberg equation. In both cases the homogeneous, stable reference steady state may be destabilized by the differential flow. In the Ginzburg-Landau equation, the destabilization occurs as long as the flow velocity exceeds some critical value v cr , which tends to zero as the system approaches the Hopf bifurcation. In the modified Swift-Hohenberg equation, the flow has either a destabilizing or stabilizing effect, depending on the sign of one of the system parameters. Destabilization occurs when the flow velocity exceeds some threshold; however in this case, the threshold remains finite even at the bifurcation point. In both Ginzburg-Landau and Swift-Hohenberg equations the differential flow instability produces traveling plane waves. The stability analysis shows that once a periodic plane wave is established, its spatial period remains unchanged over a finite range of the flow velocity and changes in discrete steps — the phenomenon of ‘wavenumber locking’. ‘Wavenumber locking’ is verified in numerical experiments with the Ginzburg-Landau equation. Near Hopf bifurcation, the Benjamin-Feir instability may occur. In this case irregular traveling waves are found, but a regular component of the wave pattern survives. Depending on a parameter, the differential flow either promotes or deters the Benjamin-Feir instability. As a result, the increasing flow may swithc the periodic wave pattern into a irregular state or, conversely, may stabilize the previously induced irregular pattern and produce periodic waves.

Role of a reaction coordinate in free energy calculations

Abstract The free energy calculation method emerges as a viable technique for ‘in-silico’ calorimetry. Efficient sampling techniques and the good choice of a reaction path connecting the reactant and the product state enable accurate computations of the free energy differences. We argue that in many cases the thermodynamic integration technique has the lowest variance when the transformation between the reactant and the product state proceeds along the natural path of the studied chemical reaction. We provide examples of free energy calculations for the fragmentation of the charged clusters and the swapping reaction of oligomer formation in proteins that follow a tentative reaction mechanism.

Landau–Ginzburg theory for ‘star’-shaped droplets

ABSTRACT Molecular simulations have shown that when a nano-drop comprising a single spherical central ion and a dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology. A linear continuum model of the ‘star’-shapes comprised electrostatic and surface energy is not sufficient to describe these shapes. We employ combined molecular dynamics, continuum electrostatics and macroscopic modelling in order to construct a unified free energy functional that describes the observed star-shaped droplets. We demonstrate that the Landau free energy coupled to the third-order Steinhardt invariant mimics the shapes of droplets detected in molecular simulations. Using the maximum likelihood technique we build a universal free energy functional that describes droplets for a range of Rayleigh fissility parameter. The analysis of the macroscopic free energy demonstrates the origin of the finite amplitude perturbations just above the Rayleigh limit. We argue that the presence of the finite amplitude perturbations precludes the use of the small parameter perturbation method for the analysis of the shapes above the Rayleigh limit of the corresponding spherical shape. GRAPHICAL ABSTRACT