Radek Erban

Summary

Affiliation: University of Oxford
Country: UK

Publications

  1. doi request reprint Multiscale stochastic reaction-diffusion modeling: application to actin dynamics in filopodia
    Radek Erban
    Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK
    Bull Math Biol 76:799-818. 2014
  2. ncbi request reprint Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
    Radek Erban
    Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom
    J Chem Phys 124:084106. 2006
  3. doi request reprint Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions
    Radek Erban
    Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK
    Phys Biol 6:046001. 2009
  4. ncbi request reprint Variable-free exploration of stochastic models: a gene regulatory network example
    Radek Erban
    Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, United Kingdom
    J Chem Phys 126:155103. 2007
  5. ncbi request reprint Reactive boundary conditions for stochastic simulations of reaction-diffusion processes
    Radek Erban
    University of Oxford, Mathematical Institute, 24 29 St Giles, Oxford, UK
    Phys Biol 4:16-28. 2007
  6. ncbi request reprint Taxis equations for amoeboid cells
    Radek Erban
    Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, OX1 3LB, UK
    J Math Biol 54:847-85. 2007
  7. pmc The two-regime method for optimizing stochastic reaction-diffusion simulations
    Mark B Flegg
    Mathematical Institute, University of Oxford, Oxford, UK
    J R Soc Interface 9:859-68. 2012
  8. ncbi request reprint Going from microscopic to macroscopic on nonuniform growing domains
    Christian 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
  9. doi request reprint Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
    Mark B Flegg
    Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom
    J Chem Phys 138:154103. 2013
  10. pmc A higher-order numerical framework for stochastic simulation of chemical reaction systems
    Tamás Székely
    Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK
    BMC Syst Biol 6:85. 2012

Detail Information

Publications16

  1. doi request reprint Multiscale stochastic reaction-diffusion modeling: application to actin dynamics in filopodia
    Radek 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. ..
  2. ncbi request reprint Gene regulatory networks: a coarse-grained, equation-free approach to multiscale computation
    Radek Erban
    Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford OX1 3LB, United Kingdom
    J Chem Phys 124:084106. 2006
    ....
  3. doi request reprint Stochastic modelling of reaction-diffusion processes: algorithms for bimolecular reactions
    Radek 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)...
  4. ncbi request reprint Variable-free exploration of stochastic models: a gene regulatory network example
    Radek Erban
    Mathematical Institute, University of Oxford, 24 29 St Giles, Oxford, United Kingdom
    J Chem Phys 126:155103. 2007
    ....
  5. ncbi request reprint Reactive boundary conditions for stochastic simulations of reaction-diffusion processes
    Radek 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...
  6. ncbi request reprint Taxis equations for amoeboid cells
    Radek 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...
  7. pmc The two-regime method for optimizing stochastic reaction-diffusion simulations
    Mark 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...
  8. ncbi request reprint Going from microscopic to macroscopic on nonuniform growing domains
    Christian 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...
  9. doi request reprint Diffusive spatio-temporal noise in a first-passage time model for intracellular calcium release
    Mark 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...
  10. pmc A higher-order numerical framework for stochastic simulation of chemical reaction systems
    Tamás 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...
  11. doi request reprint A constrained approach to multiscale stochastic simulation of chemically reacting systems
    Simon 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...
  12. doi request reprint STOCHSIMGPU: parallel stochastic simulation for the Systems Biology Toolbox 2 for MATLAB
    Guido 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...
  13. doi request reprint From microscopic to macroscopic descriptions of cell migration on growing domains
    Ruth 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...
  14. ncbi request reprint Multistability in planar liquid crystal wells
    Chong 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...
  15. pmc Inherent noise can facilitate coherence in collective swarm motion
    Christian 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
    ....
  16. ncbi request reprint Spatially distributed stochastic systems: Equation-free and equation-assisted preconditioned computations
    Liang 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...