Gary A. Huber

Electrodiffusion: A continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluchowski equation (SE), the Poisson equation (PE), and the Poisson-Nernst-Planck equation (PNPE) in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

Browndye: A Software Package for Brownian Dynamics.

A new software package, Browndye, is presented for simulating the diffusional encounter of two large biological molecules. It can be used to estimate second-order rate constants and encounter probabilities, and to explore reaction trajectories. Browndye builds upon previous knowledge and algorithms from software packages such as UHBD, SDA, and Macrodox, while implementing algorithms that scale to larger systems.

Channeling by Proximity: The Catalytic Advantages of Active Site Colocalization Using Brownian Dynamics.

Nature often colocalizes successive steps in a metabolic pathway. Such organization is predicted to increase the effective concentration of pathway intermediates near their recipient active sites and to enhance catalytic efficiency. Here, the pathway of a two-step reaction is modeled using a simple spherical approximation for the enzymes and substrate particles. Brownian dynamics are used to simulate the trajectory of a substrate particle as it diffuses between the active site zones of two different enzyme spheres. The results approximate distances for the most effective reaction pathways, indicating that the most effective reaction pathway is one in which the active sites are closely aligned. However, when the active sites are too close, the ability of the substrate to react with the first enzyme was hindered, suggesting that even the most efficient orientations can be improved for a system that is allowed to rotate or change orientation to optimize the likelihood of reaction at both sites.

Electrostatically Biased Binding of Kinesin to Microtubules

An electrostatic field rotates, slides, and guides the kinesin head to bind the microtubule at a site a short distance ahead, thus determining the direction of movement of the motor.

Dynamics and calcium association to the N-terminal regulatory domain of human cardiac troponin C: a multiscale computational study.

Troponin C (TnC) is an important regulatory molecule in cardiomyocytes. Calcium binding to site II in TnC initiates a series of molecular events that result in muscle contraction. The most direct change upon Ca2+ binding is an opening motion of the molecule that exposes a hydrophobic patch on the surface allowing for Troponin I to bind. Molecular dynamics simulations were used to elucidate the dynamics of this crucial protein in three different states: apo, Ca2+-bound, and Ca2+-TnI-bound. Dynamics between the states are compared, and the Ca2+-bound system is investigated for opening motions. On the basis of the simulations, NMR chemical shifts and order parameters are calculated and compared with experimental observables. Agreement indicates that the simulations sample the relevant dynamics of the system. Brownian dynamics simulations are used to investigate the calcium association of TnC. We find that calcium binding gives rise to correlative motions involving the EF hand and collective motions conducive of formation of the TnI-binding interface. We furthermore indicate the essential role of electrostatic steering in facilitating diffusion-limited binding of Ca2+.

Solvation Effect on the Conformations of Alanine Dipeptide: Integral Equation Approach.

We present an implicit solvent model based on the extended reference interaction site model (XRISM) integral equation theory, which is a molecular theory of solvation. The solvation free energy is composed of additive potentials of mean force (PMF) of various functional groups. The XRISM theory is applied to determine the PMF of each group in water and NaBr electrolyte solutions. The method has been coupled to Brownian dynamics (BD) and is illustrated here on alanine dipeptide. The results of the method are compared with those obtained by explicit water simulations and other popular implicit solvent models for detailed discussion. The comparison of our model with other methods indicates that the intramolecular correlation and the solvation structure influence the stability of the PII and αR conformers. The results of NaBr electrolyte solutions show that the concentration of electrolyte also has a substantial effect on the favored conformations.

Brownian dynamics study of the association between the 70S ribosome and elongation factor G

Protein synthesis on the ribosome involves a number of external protein factors that bind at its functional sites. One key factor is the elongation factor G (EF-G) that facilitates the translocation of transfer RNAs between their binding sites, as well as advancement of the messenger RNA by one codon. The details of the EF-G/ribosome diffusional encounter and EF-G association pathway still remain unanswered. Here, we applied Brownian dynamics methodology to study bimolecular association in the bacterial EF-G/70S ribosome system. We estimated the EF-G association rate constants at 150 and 300 mM monovalent ionic strengths and obtained reasonable agreement with kinetic experiments. We have also elucidated the details of EF-G/ribosome association paths and found that positioning of the L11 protein of the large ribosomal subunit is likely crucial for EF-G entry to its binding site.

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Assessing the two-body diffusion tensor calculated by the bead models

The diffusion tensor of complex macromolecules in Stokes flow is often approximated by the bead models. The bead models are known to reproduce the experimental diffusion coefficients of a single macromolecule, but the accuracy of their calculation of the whole multi-body diffusion tensor, which is important for Brownian dynamics simulations, has not been closely investigated. As a first step, we assess the accuracy of the bead model calculated diffusion tensor of two spheres. Our results show that the bead models produce very accurate diffusion tensors for two spheres where a reasonable number of beads are used and there is no bead overlap.

An Efficient Algorithm for Polarizable Interactions: A Uniformly Distributed One-Dimensional Case

We present details of an algorithm for the solution of the one-dimensional atom–dipole interactions problem for a uniform distribution that is based on the combination of the full multigrid and cell multipole methods. The rate of convergence of this technique is faster than current iterative methods used to solve this problem. It can be extended to a three-dimensional algorithm that will allow people to include polarizable interactions in simulations for a more accurate description of simulated systems.