Research Topics
 Radek ErbanSummaryAffiliation: University of Oxford Country: UK Publications
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Publications
 Gene regulatory networks: a coarsegrained, equationfree 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 reactiondiffusion 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)...  Taxis equations for amoeboid cellsRadek Erban
Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK
J Math Biol 54:84785. 2007..This is in contrast to the case of cells that use a "runandtumble" strategy, where adaptation is essential...  Reactive boundary conditions for stochastic simulations of reactiondiffusion processesRadek Erban
University of Oxford, Mathematical Institute, 24 29 St Giles, Oxford, UK
Phys Biol 4:1628. 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...  Variablefree 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....  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...  A higherorder 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 higherorder method with a larger stepsize can achieve the same level of accuracy as a lowerorder 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 FokkerPlanck equation approximation, we can in turn approximate average switching times in stochastic chemical systems...  The tworegime method for optimizing stochastic reactiondiffusion simulationsMark B Flegg
Mathematical Institute, University of Oxford, Oxford, UK
J R Soc Interface 9:85968. 2012..Illustrative examples and the mathematical justification of the TRM are also presented...  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 27:11701. 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 72:71962. 2010..A reactiondiffusion master equation formalism is generalised to the case of growing lattices and used in the derivation of the macroscopic PDEs...  Diffusive spatiotemporal noise in a firstpassage 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 cellphysiological firstpassage time problems with small ligand concentration and high cooperativity...  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 diagonaltorotated and rotatedtodiagonal 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 106:54649. 2009....  Spatially distributed stochastic systems: Equationfree and equationassisted 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 reactiondiffusion model capable of exhibiting Turing instabilities...