Lutz Maibaum

Decoupling of exchange and persistence times in atomistic models of glass formers

With molecular dynamics simulations of a fluid mixture of classical particles interacting with pairwise additive Weeks-Chandler-Andersen potentials, we consider the time series of particle displacements and thereby determine the distributions for local persistence times and local exchange times. These basic characterizations of glassy dynamics are studied over a range of supercooled conditions and were shown to have behaviors, most notably decoupling, similar to those found in kinetically constrained lattice models of structural glasses. Implications are noted.

Lengthscale dependence of dynamic four-point susceptibilities in glass formers

Dynamical four-point susceptibilities measure the extent of spatial correlations in the dynamics of glass forming systems. We show how these susceptibilities depend on the lengthscales that necessarily form part of their definition. The behavior of these susceptibilities is estimated by means of an analysis in terms of renewal processes within the context of dynamic facilitation. The analytic results are confirmed by numerical simulations of an atomistic model glass former, and of two kinetically constrained models. Hence we argue that the scenario predicted by the dynamic facilitation approach is generic.

Macroscopic Phase Separation, Modulated Phases, and Microemulsions: A Unified Picture of Rafts

We simulate a simple phenomenological model describing phase behavior in a multicomponent membrane, a model capable of producing macroscopic phase separation, modulated phases, and microemulsions, all of which have been discussed in terms of raft phenomena. We show that one effect of thermal fluctuations on the mean-field phase diagram is that it permits a direct transition between either one of the coexisting liquid phases to a microemulsion. This implies that one system exhibiting phase separation can be related to a similar system exhibiting the heterogeneities characteristic of a microemulsion. The two systems could differ in their average membrane composition or in the relative compositions of their exoplasmic and cytoplasmic leaves. The model provides a unified description of these raft-associated phenomena.

Building Markov state models with solvent dynamics

BackgroundMarkov state models have been widely used to study conformational changes of biological macromolecules. These models are built from short timescale simulations and then propagated to extract long timescale dynamics. However, the solvent information in molecular simulations are often ignored in current methods, because of the large number of solvent molecules in a system and the indistinguishability of solvent molecules upon their exchange.MethodsWe present a solvent signature that compactly summarizes the solvent distribution in the high-dimensional data, and then define a distance metric between different configurations using this signature. We next incorporate the solvent information into the construction of Markov state models and present a fast geometric clustering algorithm which combines both the solute-based and solvent-based distances.ResultsWe have tested our method on several different molecular dynamical systems, including alanine dipeptide, carbon nanotube, and benzene rings. With the new solvent-based signatures, we are able to identify different solvent distributions near the solute. Furthermore, when the solute has a concave shape, we can also capture the water number inside the solute structure. Finally we have compared the performances of different Markov state models. The experiment results show that our approach improves the existing methods both in the computational running time and the metastability.ConclusionsIn this paper we have initiated an study to build Markov state models for molecular dynamical systems with solvent degrees of freedom. The methods we described should also be broadly applicable to a wide range of biomolecular simulation analyses.

Large-scale simulations of fluctuating biological membranes

We present a simple, and physically motivated, coarse-grained model of a lipid bilayer, suited for micron scale computer simulations. Each approximately 25 nm(2) patch of bilayer is represented by a spherical particle. Mimicking forces of hydrophobic association, multiparticle interactions suppress the exposure of each spheres equator to its implicit solvent surroundings. The requirement of high equatorial density stabilizes two-dimensional structures without necessitating crystalline order, allowing us to match both the elasticity and fluidity of natural lipid membranes. We illustrate the models versatility and realism by characterizing a membranes response to a prodding nanorod.

Local Density Fluctuations Predict Photoisomerization Quantum Yield of Azobenzene-Modified DNA

Azobenzene incorporated into DNA has a photoisomerization quantum yield that depends on the DNA sequence near the azobenzene attachment site. We use Molecular Dynamics computer simulations to elucidate which physical properties of the modified DNA determine the quantum yield. We show for a wide range of DNA sequences that the photoisomerization quantum yield is strongly correlated with the variance of the number of atoms in close proximity to the outer phenyl ring of the azobenzene group. We infer that quantum yield is controlled by the availability of fluctuations that enable the conformational change. We demonstrate that these simulations can be used as a qualitative predictive tool by calculating the quantum yield for several novel DNA sequences, and confirming these predictions using UV-vis spectroscopy. Our results will be useful for the development of a wide range of applications of photoresponsive DNA nanotechnology.

Identifying the Onset of Phase Separation in Quaternary Lipid Bilayer Systems from Coarse-Grained Simulations

Understanding the (de)mixing behavior of multicomponent lipid bilayers is an important step toward unraveling the nature of spatial composition heterogeneities in cellular membranes and their role in biological function. We use coarse-grained molecular dynamics simulations to study the composition phase diagram of a quaternary mixture of phospholipids and cholesterol. This mixture is known to exhibit both uniform and coexisting phases. We compare and combine different statistical measures of membrane structure to identify the onset of phase coexistence in composition space. An important element in our approach is the dependence of composition heterogeneities on the size of the system. While homogeneous phases can be structured and display long correlation lengths, the hallmark behavior of phase coexistence is the scaling of the apparent correlation length with system size. Because the latter cannot be easily varied in simulations, our method instead uses information obtained from observation windows of different sizes to accurately distinguish phase coexistence from structured homogeneous phases. This approach is built on very general physical principles, and will be beneficial to future studies of the phase behavior of multicomponent lipid bilayers.

Seeing the Forest in Lieu of the Trees: Continuum Simulations of Cell Membranes at Large Length Scales.

Biological membranes exhibit long-range spatial structure in both chemical composition and geometric shape, which gives rise to remarkable physical phenomena and important biological functions. Continuum models that describe these effects play an important role in our understanding of membrane biophysics at large length scales. We review the mathematical framework used to describe both composition and shape degrees of freedom, and present best practices to implement such models in a computer simulation. We discuss in detail two applications of continuum models of cell membranes: the formation of microemulsion and modulated phases, and the effect of membrane-mediated interactions on the assembly of membrane proteins.

Free Energy Calculations of Membrane Permeation: Challenges Due to Strong Headgroup–Solute Interactions

Understanding how different classes of molecules move across biological membranes is a prerequisite to predicting a solutes permeation rate, which is a critical factor in the fields of drug design and pharmacology. We use biased molecular dynamics computer simulations to calculate and compare the free energy profiles of translocation of several small molecules across 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) lipid bilayers as a first step toward determining the most efficient method for free energy calculations. We study the translocation of arginine, a sodium ion, alanine, and a single water molecule using the metadynamics, umbrella sampling, and replica exchange umbrella sampling techniques. Within the fixed lengths of our simulations, we find that all methods produce similar results for charge-neutral permeants, but not for polar or positively charged molecules. We identify the long relaxation time scale of electrostatic interactions between lipid headgroups and the solute to be the principal cause of this difference and show that this slow process can lead to an erroneous dependence of computed free energy profiles on the initial system configuration. We demonstrate the use of committor analysis to validate the proper sampling of the presumed transition state, which in our simulations is achieved only in replica exchange calculations. On the basis of these results we provide some useful guidance to perform and evaluate free energy calculations of membrane permeation.

Fluctuation-Induced Interactions between Membrane-Bound Proteins

The spatial organization of membrane-bound proteins is in part determined by interactions that originate from long-range correlations due to the membranes elastic behavior. Even basic geometric mechanisms, such as the suppression of membrane height fluctuations near protein binding sites, can lead to nontrivial interactions between proteins that might result in their aggregation. To study the effect of such membrane-induced interactions, we devise a simple model that captures (a) a nonspecific repulsion between proteins, (b) elastic properties of the membrane, and (c) a local harmonic coupling between proteins and membrane shape. The models dynamics is governed by Langevin equations to faithfully capture entropic effects and the importance of rare fluctuations. We find that the membrane induces an attractive interaction between the proteins, which aggregate to mitigate the entropic cost of suppressing membrane fluctuations. This generic mechanism might help explain the spatial patterns induced by membrane sculpting proteins.