Hierarchical Reaction-Diffusion Master Equation

We have developed an algorithm coupling mesoscopic simulations on different levels in a hierarchy of Cartesian meshes. Based on the multiscale nature of the chemical reactions, some molecules in the system will live on a fine-grained mesh, while others live on a coarse-grained mesh. By allowing molecules to transfer from the fine levels to the coarse levels when appropriate, we show that we can save up to three orders of magnitude of computational time compared to microscopic simulations or highly resolved mesoscopic simulations, without losing significant accuracy. We demonstrate this in several numerical examples with systems that cannot be accurately simulated with a coarse-grained mesoscopic model

Apache Spark Streaming, Kafka and HarmonicIO: A Performance Benchmark and Architecture Comparison for Enterprise and Scientific Computing

This paper presents a benchmark of stream processing throughput comparing Apache Spark Streaming (under file-, TCP socket- and Kafka-based stream integration), with a prototype P2P stream processing framework, HarmonicIO. Maximum throughput for a spectrum of stream processing loads are measured, specifically, those with large message sizes (up to 10MB), and heavy CPU loads -- more typical of scientific computing use cases (such as microscopy), than enterprise contexts. A detailed exploration of the performance characteristics with these streaming sources, under varying loads, reveals an interplay of performance trade-offs, uncovering the boundaries of good performance for each framework and streaming source integration. We compare with theoretic bounds in each case. Based on these results, we suggest which frameworks and streaming sources are likely to offer good performance for a given load. Broadly, the advantages of Spark's rich feature set comes at a cost of sensitivity to message size in particular -- common stream source integrations can perform poorly in the 1MB-10MB range. The simplicity of HarmonicIO offers more robust performance in this region, especially for raw CPU utilization

Simulation of stochastic reaction-diffusion processes on unstructured meshes

Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered by an unstructured mesh and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology

Local error estimates for adaptive simulation of the Reaction-Diffusion Master Equation via operator splitting

The efficiency of exact simulation methods for the reaction-diffusion master equation (RDME) is severely limited by the large number of diffusion events if the mesh is fine or if diffusion constants are large. Furthermore, inherent properties of exact kinetic-Monte Carlo simulation methods limit the efficiency of parallel implementations. Several approximate and hybrid methods have appeared that enable more efficient simulation of the RDME. A common feature to most of them is that they rely on splitting the system into its reaction and diffusion parts and updating them sequentially over a discrete timestep. This use of operator splitting enables more efficient simulation but it comes at the price of a temporal discretization error that depends on the size of the timestep. So far, existing methods have not attempted to estimate or control this error in a systematic manner. This makes the solvers hard to use for practitioners since they must guess an appropriate timestep. It also makes the solvers potentially less efficient than if the timesteps are adapted to control the error. Here, we derive estimates of the local error and propose a strategy to adaptively select the timestep when the RDME is simulated via a first order operator splitting. While the strategy is general and applicable to a wide range of approximate and hybrid methods, we exemplify it here by extending a previously published approximate method, the Diffusive Finite-State Projection (DFSP) method, to incorporate temporal adaptivity

The role of dimerisation and nuclear transport in the Hes1 gene regulatory network

Hes1 is a member of the family of basic helix-loop-helix transcription factors and the Hes1 gene regulatory network (GRN) may be described as the canonical example of transcriptional control in eukaryotic cells, since it involves only the Hes1 protein and its own mRNA. Recently, the Hes1 protein has been established as an excellent target for an anti-cancer drug treatment, with the design of a small molecule Hes1 dimerisation inhibitor representing a promising if challenging approach to therapy. In this paper, we extend a previous spatial stochastic model of the Hes1 GRN to include nuclear transport and dimerisation of Hes1 monomers. Initially, we assume that dimerisation occurs only in the cytoplasm, with only dimers being imported into the nucleus. Stochastic simulations of this novel model using the URDME software show that oscillatory dynamics in agreement with experimental studies are retained. Furthermore, we find that our model is robust to changes in the nuclear transport and dimerisation parameters. However, since the precise dynamics of the nuclear import of Hes1 and the localisation of the dimerisation reaction are not known, we consider a second modelling scenario in which we allow for both Hes1 monomers and dimers to be imported into the nucleus, and we allow dimerisation of Hes1 to occur everywhere in the cell. Once again, computational solutions of this second model produce oscillatory dynamics in agreement with experimental studies. We also explore sensitivity of the numerical solutions to nuclear transport and dimerisation parameters. Finally, we compare and contrast the two different modelling scenarios using numerical experiments that simulate dimer disruption, and suggest a biological experiment that could distinguish which model more faithfully captures the Hes1 GRN.PostprintPeer reviewe

Reaction rates for mesoscopic reaction-diffusion kinetics

The mesoscopic reaction-diffusion master equation (RDME) is a popular modeling framework, frequently applied to stochastic reaction-diffusion kinetics in systems biology. The RDME is derived from assumptions about the underlying physical properties of the system, and it may produce unphysical results for models where those assumptions fail. In that case, other more comprehensive models are better suited, such as hard-sphere Brownian dynamics (BD). Although the RDME is a model in its own right, and not inferred from any specific microscale model, it proves useful to attempt to approximate a microscale model by a specific choice of mesoscopic reaction rates. In this paper we derive mesoscopic reaction rates by matching certain statistics of the RDME solution to statistics of the solution of a widely used microscopic BD model: the Smoluchowski model with a mixed boundary condition at the reaction radius of two molecules. We also establish fundamental limits for the range of mesh resolutions for which this approach yields accurate results, and show both theoretically and in numerical examples that as we approach the lower fundamental limit, the mesoscopic dynamics approach the microscopic dynamics

Orchestral: a lightweight framework for parallel simulations of cell-cell communication

We develop a modeling and simulation framework capable of massively parallel simulation of multicellular systems with spatially resolved stochastic kinetics in individual cells. By the use of operator-splitting we decouple the simulation of reaction-diffusion kinetics inside the cells from the simulation of molecular cell-cell interactions occurring on the boundaries between cells. This decoupling leverages the inherent scale separation in the underlying model to enable highly horizontally scalable parallel simulation, suitable for simulation on heterogeneous, distributed computing infrastructures such as public and private clouds. Thanks to its modular structure, our frameworks makes it possible to couple just any existing single-cell simulation software together with any cell signaling simulator. We exemplify the flexibility and scalability of the framework by using the popular single-cell simulation software eGFRD to construct and simulate a multicellular model of Notch-Delta signaling over OpenStack cloud infrastructure provided by the SNIC Science Cloud.Comment: preprint, 9 pages, 9 figures, submitted to IEEE eScience 201

Site fidelity and range size of wintering Barnacle Geese Branta leucopsis

Barnacle Geese restrict their movements to relatively few key sites and exhibit considerable variation in ranging behaviour. To examine individual and seasonal variation in site fidelity, habitat use, range size and foraging strategies of Barnacle Geese Branta leucopsis, the movements of 18 male Barnacle Geese tagged in two discrete areas were tracked for 3–6 months from late autumn until departure on the spring migration. Tagged geese concentrated their feeding in a relatively small proportion of apparently suitable habitat. Geese moved increasingly further afield in midwinter, and there was a clear predeparture shift to the largest area of relatively undisturbed, and possibly more nitrogen-rich, saltmarsh on the Solway. Birds from one of the two capture sites tended to be more sedentary and have smaller home ranges