9,337 research outputs found
Model reduction for stochastic CaMKII reaction kinetics in synapses by graph-constrained correlation dynamics.
A stochastic reaction network model of Ca(2+) dynamics in synapses (Pepke et al PLoS Comput. Biol. 6 e1000675) is expressed and simulated using rule-based reaction modeling notation in dynamical grammars and in MCell. The model tracks the response of calmodulin and CaMKII to calcium influx in synapses. Data from numerically intensive simulations is used to train a reduced model that, out of sample, correctly predicts the evolution of interaction parameters characterizing the instantaneous probability distribution over molecular states in the much larger fine-scale models. The novel model reduction method, 'graph-constrained correlation dynamics', requires a graph of plausible state variables and interactions as input. It parametrically optimizes a set of constant coefficients appearing in differential equations governing the time-varying interaction parameters that determine all correlations between variables in the reduced model at any time slice
A reaction network scheme which implements inference and learning for Hidden Markov Models
With a view towards molecular communication systems and molecular multi-agent
systems, we propose the Chemical Baum-Welch Algorithm, a novel reaction network
scheme that learns parameters for Hidden Markov Models (HMMs). Each reaction in
our scheme changes only one molecule of one species to one molecule of another.
The reverse change is also accessible but via a different set of enzymes, in a
design reminiscent of futile cycles in biochemical pathways. We show that every
fixed point of the Baum-Welch algorithm for HMMs is a fixed point of our
reaction network scheme, and every positive fixed point of our scheme is a
fixed point of the Baum-Welch algorithm. We prove that the "Expectation" step
and the "Maximization" step of our reaction network separately converge
exponentially fast. We simulate mass-action kinetics for our network on an
example sequence, and show that it learns the same parameters for the HMM as
the Baum-Welch algorithm.Comment: Accepted at 25th International Conference on DNA Computing and
Molecular Programmin
Perfect Sampling of the Master Equation for Gene Regulatory Networks
We present a Perfect Sampling algorithm that can be applied to the Master
Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's
Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo
methods and combines it with the Dominated Coupling From The Past (DCFTP)
algorithm to provide guaranteed sampling from the stationary distribution. We
show how the DCFTP-SSA can be generically applied to genetic networks with
feedback formed by the interconnection of linear enzymatic reactions and
nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the
error and convergence of the DCFTP-SSA, as compared to the standard SSA,
through a set of increasingly complex examples. Once the building blocks for
GRNs have been introduced, the algorithm is applied to study properly averaged
dynamic properties of two experimentally relevant genetic networks: the toggle
switch, a two-dimensional bistable system, and the repressilator, a
six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa
Tackling Exascale Software Challenges in Molecular Dynamics Simulations with GROMACS
GROMACS is a widely used package for biomolecular simulation, and over the
last two decades it has evolved from small-scale efficiency to advanced
heterogeneous acceleration and multi-level parallelism targeting some of the
largest supercomputers in the world. Here, we describe some of the ways we have
been able to realize this through the use of parallelization on all levels,
combined with a constant focus on absolute performance. Release 4.6 of GROMACS
uses SIMD acceleration on a wide range of architectures, GPU offloading
acceleration, and both OpenMP and MPI parallelism within and between nodes,
respectively. The recent work on acceleration made it necessary to revisit the
fundamental algorithms of molecular simulation, including the concept of
neighborsearching, and we discuss the present and future challenges we see for
exascale simulation - in particular a very fine-grained task parallelism. We
also discuss the software management, code peer review and continuous
integration testing required for a project of this complexity.Comment: EASC 2014 conference proceedin
Complete-Graph Tensor Network States: A New Fermionic Wave Function Ansatz for Molecules
We present a new class of tensor network states that are specifically
designed to capture the electron correlation of a molecule of arbitrary
structure. In this ansatz, the electronic wave function is represented by a
Complete-Graph Tensor Network (CGTN) ansatz which implements an efficient
reduction of the number of variational parameters by breaking down the
complexity of the high-dimensional coefficient tensor of a
full-configuration-interaction (FCI) wave function. We demonstrate that CGTN
states approximate ground states of molecules accurately by comparison of the
CGTN and FCI expansion coefficients. The CGTN parametrization is not biased
towards any reference configuration in contrast to many standard quantum
chemical methods. This feature allows one to obtain accurate relative energies
between CGTN states which is central to molecular physics and chemistry. We
discuss the implications for quantum chemistry and focus on the spin-state
problem. Our CGTN approach is applied to the energy splitting of states of
different spin for methylene and the strongly correlated ozone molecule at a
transition state structure. The parameters of the tensor network ansatz are
variationally optimized by means of a parallel-tempering Monte Carlo algorithm
New Approaches for ab initio Calculations of Molecules with Strong Electron Correlation
Reliable quantum chemical methods for the description of molecules with
dense-lying frontier orbitals are needed in the context of many chemical
compounds and reactions. Here, we review developments that led to our
newcomputational toolbo x which implements the quantum chemical density matrix
renormalization group in a second-generation algorithm. We present an overview
of the different components of this toolbox.Comment: 19 pages, 1 tabl
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