Identifiability analysis for stochastic differential equation models in systems biology by Browning, AP, Warne, DJ, Burrage, K, Baker, RE, Simpson, MJ

“…We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. …”

Modeling ion channel dynamics through reflected stochastic differential equations. by Dangerfield, C, Kay, D, Burrage, K

“…Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. …”

Modeling ion channel dynamics through reflected stochastic differential equations by Dangerfield, C, Kay, D, Burrage, K

Modeling ion channel dynamics through reflected stochastic differential equations by Dangerfield, C, Kay, D, Burrage, K

“…Continuous stochastic methods that use stochastic differential equations (SDEs) to model the system are more efficient but can lead to simulations that have no biological meaning. …”

A boundary preserving numerical algorithm for the Wright-Fisher model with mutation by Dangerfield, C, Kay, D, MacNamara, S, Burrage, K

“…The Wright-Fisher model is an Itô stochastic differential equation that was originally introduced to model genetic drift within finite populations and has recently been used as an approximation to ion channel dynamics within cardiac and neuronal cells. …”

Fast stochastic simulation of biochemical reaction systems by alternative formulations of the Chemical Langevin Equation by Mélykúti, B, Burrage, K, Zygalakis, K

“…The Chemical Langevin Equation (CLE), which is a stochastic differential equation (SDE) driven by a multidimensional Wiener process, acts as a bridge between the discrete Stochastic Simulation Algorithm and the deterministic reaction rate equation when simulating (bio)chemical kinetics. …”

Application of stochastic phenomenological modelling to cell-to-cell and beat-to-beat electrophysiological variability in cardiac tissue by Walmsley, J, Mirams, GR, Pitt-Francis, J, Rodriguez, B, Burrage, K

“…We developed four cell-specific parameterizations of a phenomenological stochastic differential equation AP model exhibiting intrinsic variability using APs recorded from isolated guinea pig ventricular myocytes exhibiting BVR. …”

Stochastic Models and Simulation of Ion Channel Dynamics by Dangerfield, C, Kay, D, Burrage, K, ICCS

“…By assuming that such transition rates are constant over each time step, it is possible to derive a stochastic differential equation (SDE), in the same manner as for biochemical reaction networks, that describes the stochastic dynamics of ion channels. …”

Application of stochastic phenomenological modelling to cell−to−cell and beat−to−beat electrophysiological variability in cardiac tissue by Walmsley, J, Mirams, G, Pitt−Francis, J, Rodriguez, B, Burrage, K

“…We developed four cell-specific parameterizations of a phenomenological stochastic differential equation AP model exhibiting intrinsic variability using APs recorded from isolated guinea pig ventricular myocytes exhibiting BVR. …”

Higher-order numerical methods for stochastic simulation of chemical reaction systems by Székely Jr., T, Burrage, K, Erban, R, Zygalakis, K

“…This approach, as in the case of ordinary and stochastic differential equations, can be repeated to obtain even higher-order approximations. …”

A higher-order numerical framework for stochastic simulation of chemical reaction systems. by Székely, T, Burrage, K, Erban, R, Zygalakis, K

“…As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations. …”

A higher-order numerical framework for stochastic simulation of chemical reaction systems by Szekely, T, Burrage, K, Erban, R, Zygalakis, K

“…As in the case of ordinary and stochastic differential equations, extrapolation can be repeated to obtain even higher-order approximations.…”

Stochastic models of ion channel dynamics and their role in short-term repolarisation variability in cardiac cells by Dangerfield, CE

“…Two different models of stochastic ion channel behaviour, both based on a system of stochastic differential equations (SDEs), are developed and compared. …”