## Research Topics- stochastic processes
- algorithms
- statistical models
- chemical models
- diffusion
- dictyostelium
- computer simulation
- biochemistry
- molecular biology
- chemotaxis
- proteome
- cyclic amp
- enzymes
- monte carlo method
- genetic models
- gene expression regulation
- software
- computational biology
- motion
- calcium
- calcium signaling
- kinetics
- enzyme inhibitors
- systems biology
- cell movement
- crystallization
- phase transition
- animal flight
- movement
- noise
| ## Radek Erban## SummaryAffiliation: University of Oxford Country: UK ## Publications- Multiscale stochastic reaction-diffusion modeling: application to actin dynamics in filopodiaRadek Erban
Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK*Bull Math Biol*76:799-818. 2014 - Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computationRadek Erban
Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*J Chem Phys*124:084106. 2006 - Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactionsRadek Erban
Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK*Phys Biol*6:046001. 2009 - Variable-free exploration of stochastic models: a gene regulatory network exampleRadek Erban
Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, United Kingdom*J Chem Phys*126:155103. 2007 - Reactive boundary conditions for stochastic simulations of reaction-diffusion processesRadek Erban
University of Oxford, Mathematical Institute, 24 29 St Giles, Oxford, UK*Phys Biol*4:16-28. 2007 - Taxis equations for amoeboid cellsRadek Erban
Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK*J Math Biol*54:847-85. 2007 - The two-regime method for optimizing stochastic reaction-diffusion simulationsMark B Flegg
Mathematical Institute, University of Oxford, Oxford, UK*J R Soc Interface*9:859-68. 2012 - Going from microscopic to macroscopic on nonuniform growing domainsChristian A Yates
Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*Phys Rev E Stat Nonlin Soft Matter Phys*86:021921. 2012 - Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium releaseMark B Flegg
Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*J Chem Phys*138:154103. 2013 - A higher-order numerical framework for stochastic simulation of chemical reaction systemsTamás Székely
Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK*BMC Syst Biol*6:85. 2012
| ## Collaborators |

## Detail Information

### Publications

- Multiscale stochastic reaction-diffusion modeling: application to actin dynamics in filopodiaRadek Erban

Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK*Bull Math Biol*76:799-818. 2014..The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model. .. - Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computationRadek Erban

Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*J Chem Phys*124:084106. 2006.... - Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactionsRadek Erban

Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK*Phys Biol*6:046001. 2009..This implementation uses a new formula for the rate of bimolecular reactions per compartment (lattice site)... - Variable-free exploration of stochastic models: a gene regulatory network exampleRadek Erban

Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, United Kingdom*J Chem Phys*126:155103. 2007.... - Reactive boundary conditions for stochastic simulations of reaction-diffusion processesRadek Erban

University of Oxford, Mathematical Institute, 24 29 St Giles, Oxford, UK*Phys Biol*4:16-28. 2007..g. on the rate constant of the adsorbing chemical reaction and on the number of available receptors), and on the stochastic model used. This dependence is derived for each model... - Taxis equations for amoeboid cellsRadek Erban

Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK*J Math Biol*54:847-85. 2007..This is in contrast to the case of cells that use a "run-and-tumble" strategy, where adaptation is essential... - The two-regime method for optimizing stochastic reaction-diffusion simulationsMark B Flegg

Mathematical Institute, University of Oxford, Oxford, UK*J R Soc Interface*9:859-68. 2012..Illustrative examples and the mathematical justification of the TRM are also presented... - Going from microscopic to macroscopic on nonuniform growing domainsChristian A Yates

Centre for Mathematical Biology, Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*Phys Rev E Stat Nonlin Soft Matter Phys*86:021921. 2012..Through application of the master equation formalism we derive a PDE for particle density on this growing domain and corroborate our findings with numerical simulations... - Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium releaseMark B Flegg

Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*J Chem Phys*138:154103. 2013..The presented approach and results may also be relevant for other cell-physiological first-passage time problems with small ligand concentration and high cooperativity... - A higher-order numerical framework for stochastic simulation of chemical reaction systemsTamás Székely

Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK*BMC Syst Biol*6:85. 2012..In practical terms, a higher-order method with a larger stepsize can achieve the same level of accuracy as a lower-order method with a smaller one, potentially reducing the computational time of the system... - A constrained approach to multiscale stochastic simulation of chemically reacting systemsSimon L Cotter

Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*J Chem Phys*135:094102. 2011..We then show how using the ensuing Fokker-Planck equation approximation, we can in turn approximate average switching times in stochastic chemical systems... - STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLABGuido Klingbeil

Centre for Mathematical Biology, Oxford Man Institute of Quantitative Finance, University of Oxford, Oxford OX1 3LB, UK*Bioinformatics*27:1170-1. 2011..It is integrated into MATLAB and works with the Systems Biology Toolbox 2 (SBTOOLBOX2) for MATLAB... - From microscopic to macroscopic descriptions of cell migration on growing domainsRuth E Baker

Centre for Mathematical Biology, Mathematical Institute, University of Oxford, Oxford OX1 3LB, UK*Bull Math Biol*72:719-62. 2010..A reaction-diffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs... - Multistability in planar liquid crystal wellsChong Luo

Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*Phys Rev E Stat Nonlin Soft Matter Phys*85:061702. 2012..For sufficiently strong external electric fields, we numerically demonstrate diagonal-to-rotated and rotated-to-diagonal switching by allowing for variable anchoring strength across the domain boundary... - Inherent noise can facilitate coherence in collective swarm motionChristian A Yates

Centre for Mathematical Biology, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom*Proc Natl Acad Sci U S A*106:5464-9. 2009.... - Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computationsLiang Qiao

Department of Chemical Engineering, Princeton University, Princeton, NJ 08544, USA*J Chem Phys*125:204108. 2006..Our model problem is a stochastic reaction-diffusion model capable of exhibiting Turing instabilities...