Tihamér Geyer

Adhesive water networks facilitate binding of protein interfaces

Water structure has an essential role in biological assembly. Hydrophobic dewetting has been documented as a general mechanism for the assembly of hydrophobic surfaces; however, the association mechanism of hydrophilic interfaces remains mysterious and cannot be explained by simple continuum water models that ignore the solvent structure. Here we study the association of two hydrophilic proteins using unbiased extensive molecular dynamics simulations that reproducibly recovered the native bound complex. The water in the interfacial gap forms an adhesive hydrogen-bond network between the interfaces stabilizing early intermediates before native contacts are formed. Furthermore, the interfacial gap solvent showed a reduced dielectric shielding up to distances of few nanometres during the diffusive phase. The interfacial gap solvent generates an anisotropic dielectric shielding with a strongly preferred directionality for the electrostatic interactions along the association direction.

An O(N2) approximation for hydrodynamic interactions in Brownian dynamics simulations.

In the Ermak-McCammon algorithm for Brownian dynamics, the hydrodynamic interactions (HIs) between N spherical particles are described by a 3Nx3N diffusion tensor. This tensor has to be factorized at each time step with a runtime of O(N(3)), making the calculation of the correlated random displacements the bottleneck for many-particle simulations. Here we present a faster algorithm for this step, which is based on a truncated expansion of the hydrodynamic multiparticle correlations as two-body contributions. The comparison to the exact algorithm and to the Chebyshev approximation of Fixman verifies that for bead-spring polymers this approximation yields about 95% of the hydrodynamic correlations at an improved runtime scaling of O(N(2)) and a reduced memory footprint. The approximation is independent of the actual form of the hydrodynamic tensor and can be applied to arbitrary particle configurations. This now allows to include HI into large many-particle Brownian dynamics simulations, where until now the runtime scaling of the correlated random motion was prohibitive.

Interfacing Brownian dynamics simulations

Starting from the flux of particles in a Brownian dynamics simulation we derive boundary conditions, which allow us (i) to couple a Brownian dynamics calculation to a reservoir of particles of a given density, i.e., setting up constant density boundary conditions, and (ii) to build an interface between Brownian dynamics and a diffusional treatment of adjacent simulation volumes. With these algorithms it is sometimes possible to dramatically reduce the system size--and therefore the necessary resources--of multiparticle Brownian dynamics calculations. In this paper we give one-dimensional examples which illustrate potential applications and savings.

Coarse-grained Brownian dynamics simulations of protein translocation through nanopores.

A crucial process in biological cells is the translocation of newly synthesized proteins across cell membranes via integral membrane protein pores termed translocons. Recent improved techniques now allow producing artificial membranes with pores of similar dimensions of a few nm as the translocon system. For the translocon system, the protein has to be unfolded, whereas the artificial pores are wide enough so that small proteins can pass through even when folded. To study how proteins permeate through such membrane pores, we used coarse-grained Brownian dynamics simulations where the proteins were modeled as single beads or bead-spring polymers for both folded and unfolded states. The pores were modeled as cylindrical holes through the membrane with various radii and lengths. Diffusion was driven by a concentration gradient created across the porous membrane. Our results for both folded and unfolded configurations show the expected reciprocal relation between the flow rate and the pore length in agreement with an analytical solution derived by Brunn et al. [Q. J. Mech. Appl. Math. 37, 311 (1984)]. Furthermore, we find that the geometric constriction by the narrow pore leads to an accumulation of proteins at the pore entrance, which in turn compensates for the reduced diffusivity of the proteins inside the pore.

Design of a Gated Molecular Proton Channel

The generation of an electrochemical pH gradient across biological membranes using energy from photosynthesis and respiration provides the universal driving force in cells for the production of adenosine triphosphate (ATP), the energy unit of life. Creating such an electrochemical potential requires the transportation of protons against a thermodynamic gradient. In biological proton pumps, chemical energy is used to induce protein conformational changes during each catalytic cycle where one or a few protons are pumped against a proton concentration gradient across the membrane. On the other hand, membrane channels also exist that mediate continuous particle exchange and may be switched between open and closed states. Being able to design nanochannels with similar functions would be of great importance for creating novel molecular devices with a wide range of applications such as molecular motors, fuel cells, rechargeable nanobatteries that provide energy to other nanomachines, and the generation of locally and temporally controlled pH jumps on microfluidic chips.

Bridging the gap: linking molecular simulations and systemic descriptions of cellular compartments.

Metabolic processes in biological cells are commonly either characterized at the level of individual enzymes and metabolites or at the network level. Often these two paradigms are considered as mutually exclusive because concepts from neither side are suited to describe the complete range of scales. Additionally, when modeling metabolic or regulatory cellular systems, often a large fraction of the required kinetic parameters are unknown. This even applies to such simple and extensively studied systems like the photosynthetic apparatus of purple bacteria. Using the chromatophore vesicles of Rhodobacter sphaeroides as a model system, we show that a consistent kinetic model emerges when fitting the dynamics of a molecular stochastic simulation to a set of time dependent experiments even though about two thirds of the kinetic parameters in this system are not known from experiment. Those kinetic parameters that were previously known all came out in the expected range. The simulation model was built from independent protein units composed of elementary reactions processing single metabolites. This pools-and-proteins approach naturally compiles the wealth of available molecular biological data into a systemic model and can easily be extended to describe other systems by adding new protein or nucleic acid types. The automated parameter optimization, performed with an evolutionary algorithm, reveals the sensitivity of the model to the value of each parameter and the relative importances of the experiments used. Such an analysis identifies the crucial system parameters and guides the setup of new experiments that would add most knowledge for a systemic understanding of cellular compartments. The successful combination of the molecular model and the systemic parametrization presented here on the example of the simple machinery for bacterial photosynthesis shows that it is actually possible to combine molecular and systemic modeling. This framework can now straightforwardly be applied to other currently less well characterized but biologically more relevant systems.

Mixing normal and anomalous diffusion

In the densely filled biological cells often subdiffusion is observed, where the average squared displacement increases slower than linear with the length of the observation interval. One reason for such subdiffusive behavior is attractive interactions between the diffusing particles that lead to temporary complex formation. Here, we show that such transient binding is not an average state of the particles but that intervals of free diffusion alternate with slower displacement when bound to neighboring particles. The observed macroscopic behavior is then the weighted average of these two contributions. Interestingly, even at very high concentrations, the unbound fraction still exhibits essentially normal diffusion.

Do we have to explicitly model the ions in Brownian dynamics simulations of proteins

Brownian dynamics (BD) is a very efficient coarse-grained simulation technique which is based on Einsteins explanation of the diffusion of colloidal particles. On these length scales well beyond the solvent granularity, a treatment of the electrostatic interactions on a Debye-Hückel (DH) level with its continuous ion densities is consistent with the implicit solvent of BD. On the other hand, since many years BD is being used as a workhorse simulation technique for the much smaller biological proteins. Here, the assumption of a continuous ion density, and therefore the validity of the DH electrostatics, becomes questionable. We therefore investigated for a few simple cases how far the efficient DH electrostatics with point charges can be used and when the ions should be included explicitly in the BD simulation. We find that for large many-protein scenarios or for binary association rates, the conventional continuum methods work well and that the ions should be included explicitly when detailed association trajectories or protein folding are investigated.

Electron impact double ionization of helium from classical trajectory calculations

With a recently proposed quasiclassical ansatz [Geyer and Rost, J. Phys. B 35 (2002) 1479] it is possible to perform classical trajectory ionization calculations on many electron targets. The autoionization of the target is prevented by a M\o{}ller type backward--forward propagation scheme and allows to consider all interactions between all particles without additional stabilization. The application of the quasiclassical ansatz for helium targets is explained and total and partially differential cross sections for electron impact double ionization are calculated. In the high energy regime the classical description fails to describe the dominant TS1 process, which leads to big deviations, whereas for low energies the total cross section is reproduced well. Differential cross sections calculated at 250 eV await their experimental confirmation.

Coarse-Grained Simulations of Protein Backbone Dynamics. 1. Local Sterics Define the Dihedral Angles.

Here, we present a coarse-grained model targeted for implicit solvent simulations of unfolded or intrinsically disordered proteins. The hierarchical model with its nonspherical building blocks allows one to reproduce the local dynamics of the backbone with simple harmonic bonds and steric collisions between a small number of atoms at the correct off-center positions on the building blocks. Here in part 1, we also describe the implementation of the global shape of the protein chain and the extended local interactions that add a first secondary structure bias, which will subsequently be augmented by additional hydrophobic interactions, hydrogen bonds, and dipole dipole couplings along the backbone. Due to its hierarchical setup, the model has a near-atomistic resolution on the local scale and the overall numerical efficiency of a coarse-grained model such that even long protein chains can be simulated efficiently.