Jesús A. Izaguirre

Langevin stabilization of molecular dynamics

In this paper we show the possibility of using very mild stochastic damping to stabilize long time step integrators for Newtonian molecular dynamics. More specifically, stable and accurate integrations are obtained for damping coefficients that are only a few percent of the natural decay rate of processes of interest, such as the velocity autocorrelation function. Two new multiple time stepping integrators, Langevin Molly (LM) and Brunger–Brooks–Karplus–Molly (BBK–M), are introduced in this paper. Both use the mollified impulse method for the Newtonian term. LM uses a discretization of the Langevin equation that is exact for the constant force, and BBK–M uses the popular Brunger–Brooks–Karplus integrator (BBK). These integrators, along with an extrapolative method called LN, are evaluated across a wide range of damping coefficient values. When large damping coefficients are used, as one would for the implicit modeling of solvent molecules, the method LN is superior, with LM closely following. However, with mild damping of 0.2 ps−1, LM produces the best results, allowing long time steps of 14 fs in simulations containing explicitly modeled flexible water. With BBK–M and the same damping coefficient, time steps of 12 fs are possible for the same system. Similar results are obtained for a solvated protein–DNA simulation of estrogen receptor ER with estrogen response element ERE. A parallel version of BBK–M runs nearly three times faster than the Verlet-I/r-RESPA (reversible reference system propagator algorithm) when using the largest stable time step on each one, and it also parallelizes well. The computation of diffusion coefficients for flexible water and ER/ERE shows that when mild damping of up to 0.2 ps−1 is used the dynamics are not significantly distorted.

CompuCell, a multi-model framework for simulation of morphogenesis

MOTIVATION CompuCell is a multi-model software framework for simulation of the development of multicellular organisms known as morphogenesis. It models the interaction of the gene regulatory network with generic cellular mechanisms, such as cell adhesion, division, haptotaxis and chemotaxis. A combination of a state automaton with stochastic local rules and a set of differential equations, including subcellular ordinary differential equations and extracellular reaction-diffusion partial differential equations, model gene regulation. This automaton in turn controls the differentiation of the cells, and cell-cell and cell-extracellular matrix interactions that give rise to cell rearrangements and pattern formation, e.g. mesenchymal condensation. The cellular Potts model, a stochastic model that accurately reproduces cell movement and rearrangement, models cell dynamics. All these models couple in a controllable way, resulting in a powerful and flexible computational environment for morphogenesis, which allows for simultaneous incorporation of growth and spatial patterning. RESULTS We use CompuCell to simulate the formation of the skeletal architecture in the avian limb bud. AVAILABILITY Binaries and source code for Microsoft Windows, Linux and Solaris are available for download from http://sourceforge.net/projects/compucell/

An impulse integrator for Langevin dynamics

The best simple method for Newtonian molecular dynamics is indisputably the leapfrog Stormer-Verlet method. The appropriate generalization to simple Langevin dynamics is unclear. An analysis is presented comparing an ‘impulse method’ (kick; fluctuate; kick), the 1982 method of van Gunsteren and Berendsen, and the Brünger-Brooks-Karplus (BBK) method. It is shown how the impulse method and the van Gunsteren-Berendsen methods can be implemented as efficiently as the BBK method. Other considerations suggest that the impulse method is the best basic method for simple Langevin dynamics, with the van Gunsteren-Berendsen method a close contender.

A Framework for Three-Dimensional Simulation of Morphogenesis

We present COMPUCELL3D, a software framework for three-dimensional simulation of morphogenesis in different organisms. COMPUCELL3D employs biologically relevant models for cell clustering, growth, and interaction with chemical fields. COMPUCELL3D uses design patterns for speed, efficient memory management, extensibility, and flexibility to allow an almost unlimited variety of simulations. We have verified COMPUCELL3D by building a model of growth and skeletal pattern formation in the avian (chicken) limb bud. Binaries and source code are available, along with documentation and input files for sample simulations, at http:// compucell.sourceforge.net.

On multiscale approaches to three-dimensional modelling of morphogenesis

In this paper we present the foundation of a unified, object-oriented, three-dimensional biomodelling environment, which allows us to integrate multiple submodels at scales from subcellular to those of tissues and organs. Our current implementation combines a modified discrete model from statistical mechanics, the Cellular Potts Model, with a continuum reaction–diffusion model and a state automaton with well-defined conditions for cell differentiation transitions to model genetic regulation. This environment allows us to rapidly and compactly create computational models of a class of complex-developmental phenomena. To illustrate model development, we simulate a simplified version of the formation of the skeletal pattern in a growing embryonic vertebrate limb.

ProtoMol, an object-oriented framework for prototyping novel algorithms for molecular dynamics

ProtoMol is a high-performance framework in C++ for rapid prototyping of novel algorithms for molecular dynamics and related applications. Its flexibility is achieved primarily through the use of inheritance and design patterns (object-oriented programming). Performance is obtained by using templates that enable generation of efficient code for sections critical to performance (generic programming). The framework encapsulates important optimizations that can be used by developers, such as parallelism in the force computation. Its design is based on domain analysis of numerical integrators for molecular dynamics (MD) and of fast solvers for the force computation, particularly due to electrostatic interactions. Several new and efficient algorithms are implemented in ProtoMol. Finally, it is shown that ProtoMols sequential performance is excellent when compared to a leading MD program, and that it scales well for moderate number of processors. Binaries and source codes for Windows, Linux, Solaris, IRIX, HP-UX, and AIX platforms are available under open source license at http://protomol.sourceforge.net.

A parallel implementation of the Cellular Potts Model for simulation of cell-based morphogenesis

The Cellular Potts Model (CPM) has been used in a wide variety of biological simulations. However, most current CPM implementations use a sequential modified Metropolis algorithm which restricts the size of simulations. In this paper we present a parallel CPM algorithm for simulations of morphogenesis, which includes cell–cell adhesion, a cell volume constraint, and cell haptotaxis. The algorithm uses appropriate data structures and checkerboard subgrids for parallelization. Communication and updating algorithms synchronize properties of cells simulated on different processor nodes. Tests show that the parallel algorithm has good scalability, permitting large-scale simulations of cell morphogenesis (107 or more cells) and broadening the scope of CPM applications. The new algorithm satisfies the balance condition, which is sufficient for convergence of the underlying Markov chain.

Predicting Protein-Protein Interactions from Protein Domains Using a Set Cover Approach

One goal of contemporary proteome research is the elucidation of cellular protein interactions. Based on currently available protein-protein interaction and domain data, we introduce a novel method, maximum specificity set cover (MSSC), for the prediction of protein-protein interactions. In our approach, we map the relationship between interactions of proteins and their corresponding domain architectures to a generalized weighted set cover problem. The application of a greedy algorithm provides sets of domain interactions which explain the presence of protein interactions to the largest degree of specificity. Utilizing domain and protein interaction data of S. cerevisiae, MSSC enables prediction of previously unknown protein interactions, links that are well supported by a high tendency of coexpression and functional homogeneity of the corresponding proteins. Focusing on concrete examples, we show that MSSC reliably predicts protein interactions in well-studied molecular systems, such as the 26S proteasome and RNA polymerase II of S. cerevisiae. We also show that the quality of the predictions is comparable to the maximum likelihood estimation while MSSC is faster. This new algorithm and all data sets used are accessible through a Web portal at http://ppi-cse.nd.edu

Modeling Conformational Ensembles of Slow Functional Motions in Pin1-WW

Protein-protein interactions are often mediated by flexible loops that experience conformational dynamics on the microsecond to millisecond time scales. NMR relaxation studies can map these dynamics. However, defining the network of inter-converting conformers that underlie the relaxation data remains generally challenging. Here, we combine NMR relaxation experiments with simulation to visualize networks of inter-converting conformers. We demonstrate our approach with the apo Pin1-WW domain, for which NMR has revealed conformational dynamics of a flexible loop in the millisecond range. We sample and cluster the free energy landscape using Markov State Models (MSM) with major and minor exchange states with high correlation with the NMR relaxation data and low NOE violations. These MSM are hierarchical ensembles of slowly interconverting, metastable macrostates and rapidly interconverting microstates. We found a low population state that consists primarily of holo-like conformations and is a “hub” visited by most pathways between macrostates. These results suggest that conformational equilibria between holo-like and alternative conformers pre-exist in the intrinsic dynamics of apo Pin1-WW. Analysis using MutInf, a mutual information method for quantifying correlated motions, reveals that WW dynamics not only play a role in substrate recognition, but also may help couple the substrate binding site on the WW domain to the one on the catalytic domain. Our work represents an important step towards building networks of inter-converting conformational states and is generally applicable.

From Genes to Organisms Via the Cell: A Problem-Solving Environment for Multicellular Development

To gain performance, developers often build scientific applications in procedural languages, such as C or Fortran, which unfortunately reduces flexibility. To address this imbalance, the authors present CompuCell3D, a multitiered, flexible, and scalable problem-solving environment for morphogenesis simulations thats written in C++ using object-oriented design patterns.