Multiscale reaction-diffusion simulations with Smoldyn

“…In order to focus on observations around the expected peak observation time, the receiver always samples the number of molecules within its space every t p /30 seconds over an interval of at least [0, 3t p ], where t p is found using ( 10) and (11) for the 1D and 3D environments, respectively. Thus, each simulation has at least M = 91 samples, though for clarity of presentation we do not show every sample time in every plot.…”

“…To improve the efficiency of simulations further, one can then coarse-grain such a generalized Langevin description using a Brownian dynamics approach [14,60]. Brownian dynamics modelling can be further coupled with stochastic reaction-diffusion modelling based on lattice-based (compartment-based) methods [22]. Lattice-based models are very attractive for simulations of intracellular processes, because they enable modelling of spatio-temporal processes in the whole cell or its significant parts [61].…”

“…In this paper, we have investigated multi-resolution approaches, schematically described in figure 1a royalsocietypublishing.org/journal/rsfs Interface Focus 9: 20180070 class of multi-resolution approaches in the literature considers a fixed subdomain of the computational domain where a detailed modelling approach is used, which is coupled with a coarser model in the rest of the simulation domain [21,22]. Such an approach is useful, for example, when modelling intracellular ion dynamics.…”

“…Moreover, if we are far away from the MD domain Ω 1 , we can further increase the efficiency of BD simulations by using different BD timesteps in different parts of the BD subdomain Ω 5 [ 12 ], or by using event-based BD algorithms [ 35 , 37 ]. The computational intensity of BD simulations can be further decreased by using multiscale methods which efficiently and accurately combine BD models with lattice-based (compartment-based) models [ 43 , 44 ]. Such a strategy has been previously used for modelling intracellular calcium dynamics [ 3 , 7 ] or actin dynamics in filopodia [ 45 ], and enables us to extend both temporal and spatial extents of the simulation.…”

“…In order to focus on observations around the expected peak observation time, the receiver always samples the number of molecules within its space every t p /30 seconds over an interval of at least [0, 3t p ], where t p is found using ( 10) and (11) for the 1D and 3D environments, respectively. Thus, each simulation has at least M = 91 samples, though for clarity of presentation we do not show every sample time in every plot.…”

“…To improve the efficiency of simulations further, one can then coarse-grain such a generalized Langevin description using a Brownian dynamics approach [14,60]. Brownian dynamics modelling can be further coupled with stochastic reaction-diffusion modelling based on lattice-based (compartment-based) methods [22]. Lattice-based models are very attractive for simulations of intracellular processes, because they enable modelling of spatio-temporal processes in the whole cell or its significant parts [61].…”

“…In this paper, we have investigated multi-resolution approaches, schematically described in figure 1a royalsocietypublishing.org/journal/rsfs Interface Focus 9: 20180070 class of multi-resolution approaches in the literature considers a fixed subdomain of the computational domain where a detailed modelling approach is used, which is coupled with a coarser model in the rest of the simulation domain [21,22]. Such an approach is useful, for example, when modelling intracellular ion dynamics.…”

“…Moreover, if we are far away from the MD domain Ω 1 , we can further increase the efficiency of BD simulations by using different BD timesteps in different parts of the BD subdomain Ω 5 [ 12 ], or by using event-based BD algorithms [ 35 , 37 ]. The computational intensity of BD simulations can be further decreased by using multiscale methods which efficiently and accurately combine BD models with lattice-based (compartment-based) models [ 43 , 44 ]. Such a strategy has been previously used for modelling intracellular calcium dynamics [ 3 , 7 ] or actin dynamics in filopodia [ 45 ], and enables us to extend both temporal and spatial extents of the simulation.…”

“…In order to focus on observations around the expected peak observation time, the receiver always samples the number of molecules within its space every t p /30 seconds over an interval of at least [0, 3t p ], where t p is found using ( 10) and (11) for the 1D and 3D environments, respectively. Thus, each simulation has at least M = 91 samples, though for clarity of presentation we do not show every sample time in every plot.…”

“…To improve the efficiency of simulations further, one can then coarse-grain such a generalized Langevin description using a Brownian dynamics approach [14,60]. Brownian dynamics modelling can be further coupled with stochastic reaction-diffusion modelling based on lattice-based (compartment-based) methods [22]. Lattice-based models are very attractive for simulations of intracellular processes, because they enable modelling of spatio-temporal processes in the whole cell or its significant parts [61].…”

“…In this paper, we have investigated multi-resolution approaches, schematically described in figure 1a royalsocietypublishing.org/journal/rsfs Interface Focus 9: 20180070 class of multi-resolution approaches in the literature considers a fixed subdomain of the computational domain where a detailed modelling approach is used, which is coupled with a coarser model in the rest of the simulation domain [21,22]. Such an approach is useful, for example, when modelling intracellular ion dynamics.…”

“…Moreover, if we are far away from the MD domain Ω 1 , we can further increase the efficiency of BD simulations by using different BD timesteps in different parts of the BD subdomain Ω 5 [ 12 ], or by using event-based BD algorithms [ 35 , 37 ]. The computational intensity of BD simulations can be further decreased by using multiscale methods which efficiently and accurately combine BD models with lattice-based (compartment-based) models [ 43 , 44 ]. Such a strategy has been previously used for modelling intracellular calcium dynamics [ 3 , 7 ] or actin dynamics in filopodia [ 45 ], and enables us to extend both temporal and spatial extents of the simulation.…”