A Kalman Filter Approach for Biomolecular Systems with Noise Covariance Updating

An important part of system modeling is determining parameter values, particularly for biomolecular systems, where direct measurements of individual parameters are typically hard. While Extended Kalman Filters have been used for this purpose, the choice of the process noise covariance is generally unclear. In this chapter, we address this issue for biomolecular systems using a combination of Monte Carlo simulations and experimental data, exploiting the dependence of the process noise covariance on the states and parameters, as given in the Langevin framework. We adapt a Hybrid Extended Kalman Filtering technique by updating the process noise covariance at each time step based on estimates. We compare the performance of this framework with different fixed values of process noise covariance in biomolecular system models, including an oscillator model, as well as in experimentally measured data for a negative transcriptional feedback circuit. We find that the Extended Kalman Filter with such process noise covariance update is closer to the optimality condition in the sense that the innovation sequence becomes white and in achieving a balance between the mean square estimation error and parameter convergence time. The results of this chapter may help in the use of Extended Kalman Filters for systems where process noise covariance depends on states and/or parameters.Comment: 23 pages, 9 figure

GPU-powered Simulation Methodologies for Biological Systems

The study of biological systems witnessed a pervasive cross-fertilization between experimental investigation and computational methods. This gave rise to the development of new methodologies, able to tackle the complexity of biological systems in a quantitative manner. Computer algorithms allow to faithfully reproduce the dynamics of the corresponding biological system, and, at the price of a large number of simulations, it is possible to extensively investigate the system functioning across a wide spectrum of natural conditions. To enable multiple analysis in parallel, using cheap, diffused and highly efficient multi-core devices we developed GPU-powered simulation algorithms for stochastic, deterministic and hybrid modeling approaches, so that also users with no knowledge of GPUs hardware and programming can easily access the computing power of graphics engines.Comment: In Proceedings Wivace 2013, arXiv:1309.712

Archiving and disseminating integrative structure models.

Limitations in the applicability, accuracy, and precision of individual structure characterization methods can sometimes be overcome via an integrative modeling approach that relies on information from all available sources, including all available experimental data and prior models. The open-source Integrative Modeling Platform (IMP) is one piece of software that implements all computational aspects of integrative modeling. To maximize the impact of integrative structures, the coordinates should be made publicly available, as is already the case for structures based on X-ray crystallography, NMR spectroscopy, and electron microscopy. Moreover, the associated experimental data and modeling protocols should also be archived, such that the original results can easily be reproduced. Finally, it is essential that the integrative structures are validated as part of their publication and deposition. A number of research groups have already developed software to implement integrative modeling and have generated a number of structures, prompting the formation of an Integrative/Hybrid Methods Task Force. Following the recommendations of this task force, the existing PDBx/mmCIF data representation used for atomic PDB structures has been extended to address the requirements for archiving integrative structural models. This IHM-dictionary adds a flexible model representation, including coarse graining, models in multiple states and/or related by time or other order, and multiple input experimental information sources. A prototype archiving system called PDB-Dev ( https://pdb-dev.wwpdb.org ) has also been created to archive integrative structural models, together with a Python library to facilitate handling of integrative models in PDBx/mmCIF format

Process Calculi Abstractions for Biology

Several approaches have been proposed to model biological systems by means of the formal techniques and tools available in computer science. To mention just a few of them, some representations are inspired by Petri Nets theory, and some other by stochastic processes. A most recent approach consists in interpreting the living entities as terms of process calculi where the behavior of the represented systems can be inferred by applying syntax-driven rules. A comprehensive picture of the state of the art of the process calculi approach to biological modeling is still missing. This paper goes in the direction of providing such a picture by presenting a comparative survey of the process calculi that have been used and proposed to describe the behavior of living entities. This is the preliminary version of a paper that was published in Algorithmic Bioprocesses. The original publication is available at http://www.springer.com/computer/foundations/book/978-3-540-88868-

Dynamic control of selectivity in the ubiquitination pathway revealed by an ASP to GLU substitution in an intra-molecular salt-bridge network

Ubiquitination relies on a subtle balance between selectivity and promiscuity achieved through specific interactions between ubiquitin-conjugating enzymes (E2s) and ubiquitin ligases (E3s). Here, we report how a single aspartic to glutamic acid substitution acts as a dynamic switch to tip the selectivity balance of human E2s for interaction toward E3 RING-finger domains. By combining molecular dynamic simulations, experimental yeast-two-hybrid screen of E2-E3 (RING) interactions and mutagenesis, we reveal how the dynamics of an internal salt-bridge network at the rim of the E2-E3 interaction surface controls the balance between an “open”, binding competent, and a “closed”, binding incompetent state. The molecular dynamic simulations shed light on the fine mechanism of this molecular switch and allowed us to identify its components, namely an aspartate/glutamate pair, a lysine acting as the central switch and a remote aspartate. Perturbations of single residues in this network, both inside and outside the interaction surface, are sufficient to switch the global E2 interaction selectivity as demonstrated experimentally. Taken together, our results indicate a new mechanism to control E2-E3 interaction selectivity at an atomic level, highlighting how minimal changes in amino acid side-chain affecting the dynamics of intramolecular salt-bridges can be crucial for protein-protein interactions. These findings indicate that the widely accepted sequence-structure-function paradigm should be extended to sequence-structure-dynamics-function relationship and open new possibilities for control and fine-tuning of protein interaction selectivity

BioNetGen 2.2: Advances in Rule-Based Modeling

BioNetGen is an open-source software package for rule-based modeling of complex biochemical systems. Version 2.2 of the software introduces numerous new features for both model specification and simulation. Here, we report on these additions, discussing how they facilitate the construction, simulation, and analysis of larger and more complex models than previously possible.Comment: 3 pages, 1 figure, 1 supplementary text file. Supplementary text includes a brief discussion of the RK-PLA along with a performance analysis, two tables listing all new actions/arguments added in BioNetGen 2.2, and the "BioNetGen Quick Reference Guide". Accepted for publication in Bioinformatic

Investigation of Structural Dynamics of Enzymes and Protonation States of Substrates Using Computational Tools.

This review discusses the use of molecular modeling tools, together with existing experimental findings, to provide a complete atomic-level description of enzyme dynamics and function. We focus on functionally relevant conformational dynamics of enzymes and the protonation states of substrates. The conformational fluctuations of enzymes usually play a crucial role in substrate recognition and catalysis. Protein dynamics can be altered by a tiny change in a molecular system such as different protonation states of various intermediates or by a significant perturbation such as a ligand association. Here we review recent advances in applying atomistic molecular dynamics (MD) simulations to investigate allosteric and network regulation of tryptophan synthase (TRPS) and protonation states of its intermediates and catalysis. In addition, we review studies using quantum mechanics/molecular mechanics (QM/MM) methods to investigate the protonation states of catalytic residues of β-Ketoacyl ACP synthase I (KasA). We also discuss modeling of large-scale protein motions for HIV-1 protease with coarse-grained Brownian dynamics (BD) simulations

Projected and Hidden Markov Models for calculating kinetics and metastable states of complex molecules

Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has therefore been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase- space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs / PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, an 1 ms Anton MD simulation of the BPTI protein, and an optical tweezer force probe trajectory of an RNA hairpin