Bayesian Inference for Jump-Diffusion Approximations of Biochemical Reaction Networks

Biochemical reaction networks are an amalgamation of reactions where each reaction represents the interaction of different species. Generally, these networks exhibit a multi-scale behavior caused by the high variability in reaction rates and abundances of species. The so-called jump-diffusion approximation is a valuable tool in the modeling of such systems. The approximation is constructed by partitioning the reaction network into a fast and slow subgroup of fast and slow reactions, respectively. This enables the modeling of the dynamics using a Langevin equation for the fast group, while a Markov jump process model is kept for the dynamics of the slow group. Most often biochemical processes are poorly characterized in terms of parameters and population states. As a result of this, methods for estimating hidden quantities are of significant interest. In this paper, we develop a tractable Bayesian inference algorithm based on Markov chain Monte Carlo. The presented blocked Gibbs particle smoothing algorithm utilizes a sequential Monte Carlo method to estimate the latent states and performs distinct Gibbs steps for the parameters of a biochemical reaction network, by exploiting a jump-diffusion approximation model. The presented blocked Gibbs sampler is based on the two distinct steps of state inference and parameter inference. We estimate states via a continuous-time forward-filtering backward-smoothing procedure in the state inference step. By utilizing bootstrap particle filtering within a backward-smoothing procedure, we sample a smoothing trajectory. For estimating the hidden parameters, we utilize a separate Markov chain Monte Carlo sampler within the Gibbs sampler that uses the path-wise continuous-time representation of the reaction counters. Finally, the algorithm is numerically evaluated for a partially observed multi-scale birth-death process example

Finding Multiple Reaction Pathways of Ligand Unbinding

Searching for reaction pathways describing rare events in large systems presents a long-standing challenge in chemistry and physics. Incorrectly computed reaction pathways result in the degeneracy of microscopic configurations and inability to sample hidden energy barriers. To this aim, we present a general enhanced sampling method to find multiple diverse reaction pathways of ligand unbinding through non-convex optimization of a loss function describing ligand-protein interactions. The method successfully overcomes large energy barriers using an adaptive bias potential, and constructs possible reaction pathways along transient tunnels without the initial guesses of intermediate or final states, requiring crystallographic information only. We examine the method on the T4 lysozyme L99A mutant which is often used as a model system to study ligand binding to proteins, provide a previously unknown reaction pathway, and show that using the bias potential and the tunnel widths it is possible to capture heterogeneity of the unbinding mechanisms between the found transient protein tunnels

Fast, Robust, and Versatile Event Detection through HMM Belief State Gradient Measures

Event detection is a critical feature in data-driven systems as it assists with the identification of nominal and anomalous behavior. Event detection is increasingly relevant in robotics as robots operate with greater autonomy in increasingly unstructured environments. In this work, we present an accurate, robust, fast, and versatile measure for skill and anomaly identification. A theoretical proof establishes the link between the derivative of the log-likelihood of the HMM filtered belief state and the latest emission probabilities. The key insight is the inverse relationship in which gradient analysis is used for skill and anomaly identification. Our measure showed better performance across all metrics than related state-of-the art works. The result is broadly applicable to domains that use HMMs for event detection.Comment: 8 pages, 7 figures, double col, ieee conference forma

An immune network approach to learning qualitative models of biological pathways

ACKNOWLEDGMENT GMC is supported by the CRISP project (Combinatorial Responses In Stress Pathways) funded by the BBSRC (BB/F00513X/1) under the Systems Approaches to Biological Research (SABR) Initiative. WP and GMC are also supported by the partnership fund from dot.rural, RCUK Digital Economy research.Postprin

Penta-quark states with hidden charm and beauty

More and more hadron states are found to be difficult to be accommodated by the quenched quark models which describe baryons as 3-quark states and mesons as antiquark-quark states. Dragging out an antiquark-quark pair from the gluon field in hadrons should be an important excitation mechanism for hadron spectroscopy. Our recent progress on the penta-quark states with hidden charm and beauty is reviewed.Comment: Plenary talk at the 5th Asia-Pacific Conference on Few-Body Problems in Physics 2011 (APFB2011), 22-26 Aug., 2011, Seoul, Kore