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Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems.

Johnson ME, Hummer G - Phys Rev X (2014 Jul-Sep)

Bottom Line: FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone.With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events.Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biophysics, The Johns Hopkins University, Baltimore, Maryland 21218, USA.

ABSTRACT

We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green's function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR) method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions.

No MeSH data available.


Related in: MedlinePlus

Irreversible reaction A + A → 0. A(t) versus time for (a) absorbing BC, Δt = 0.001 μs and DAB = 200 nm2/μs. RD simulations are shown in red for a 16.6 mM concentration of A particles. The solution to Eq. (27), , is plotted in black dashed lines. In pink, we show RD simulations for ka = 1000 nm3/μs, Δt = 0.001 μs, and DAB = 100 nm2/μs, and the theoretical solution to Eq. (27) given by  in dashed black. For comparison, we show results from Gillespie simulations for simple chemical kinetics (cyan, no symbols) of both reactions and the corresponding solution to Eq. (27) with the steady-state rate in blue dashed lines. (b) RD simulations with ka = 10 nm3/μs, Δt = 0.1μs, Δt = 0.01 μs, and DAB = 20 nm2/μs demonstrating the long-time steady-state decay at 332 μM concentration of A particles (red circles) and 3.3 mM (orange and yellow data simulated with different time steps).
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Figure 8: Irreversible reaction A + A → 0. A(t) versus time for (a) absorbing BC, Δt = 0.001 μs and DAB = 200 nm2/μs. RD simulations are shown in red for a 16.6 mM concentration of A particles. The solution to Eq. (27), , is plotted in black dashed lines. In pink, we show RD simulations for ka = 1000 nm3/μs, Δt = 0.001 μs, and DAB = 100 nm2/μs, and the theoretical solution to Eq. (27) given by in dashed black. For comparison, we show results from Gillespie simulations for simple chemical kinetics (cyan, no symbols) of both reactions and the corresponding solution to Eq. (27) with the steady-state rate in blue dashed lines. (b) RD simulations with ka = 10 nm3/μs, Δt = 0.1μs, Δt = 0.01 μs, and DAB = 20 nm2/μs demonstrating the long-time steady-state decay at 332 μM concentration of A particles (red circles) and 3.3 mM (orange and yellow data simulated with different time steps).

Mentions: In Fig. 8, we compare numerical simulations using FPR to the theoretical results for A(t) and find extremely good agreement. To highlight the contribution of diffusion to the relaxation process, we also show the relaxation from chemical kinetics simulations, where the steady-state rate k(t → ∞) is used in the solution to Eq. (27). The effect of diffusion on the relaxation process is most pronounced with absorbing boundaries, but is also visible for radiation boundaries [Fig. 8(a)]. At longer times, and for systems with slower reaction rates and faster diffusion, the processes converge to the steady-state relaxation of chemical kinetics [Fig. 8(b)].


Free-Propagator Reweighting Integrator for Single-Particle Dynamics in Reaction-Diffusion Models of Heterogeneous Protein-Protein Interaction Systems.

Johnson ME, Hummer G - Phys Rev X (2014 Jul-Sep)

Irreversible reaction A + A → 0. A(t) versus time for (a) absorbing BC, Δt = 0.001 μs and DAB = 200 nm2/μs. RD simulations are shown in red for a 16.6 mM concentration of A particles. The solution to Eq. (27), , is plotted in black dashed lines. In pink, we show RD simulations for ka = 1000 nm3/μs, Δt = 0.001 μs, and DAB = 100 nm2/μs, and the theoretical solution to Eq. (27) given by  in dashed black. For comparison, we show results from Gillespie simulations for simple chemical kinetics (cyan, no symbols) of both reactions and the corresponding solution to Eq. (27) with the steady-state rate in blue dashed lines. (b) RD simulations with ka = 10 nm3/μs, Δt = 0.1μs, Δt = 0.01 μs, and DAB = 20 nm2/μs demonstrating the long-time steady-state decay at 332 μM concentration of A particles (red circles) and 3.3 mM (orange and yellow data simulated with different time steps).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4440698&req=5

Figure 8: Irreversible reaction A + A → 0. A(t) versus time for (a) absorbing BC, Δt = 0.001 μs and DAB = 200 nm2/μs. RD simulations are shown in red for a 16.6 mM concentration of A particles. The solution to Eq. (27), , is plotted in black dashed lines. In pink, we show RD simulations for ka = 1000 nm3/μs, Δt = 0.001 μs, and DAB = 100 nm2/μs, and the theoretical solution to Eq. (27) given by in dashed black. For comparison, we show results from Gillespie simulations for simple chemical kinetics (cyan, no symbols) of both reactions and the corresponding solution to Eq. (27) with the steady-state rate in blue dashed lines. (b) RD simulations with ka = 10 nm3/μs, Δt = 0.1μs, Δt = 0.01 μs, and DAB = 20 nm2/μs demonstrating the long-time steady-state decay at 332 μM concentration of A particles (red circles) and 3.3 mM (orange and yellow data simulated with different time steps).
Mentions: In Fig. 8, we compare numerical simulations using FPR to the theoretical results for A(t) and find extremely good agreement. To highlight the contribution of diffusion to the relaxation process, we also show the relaxation from chemical kinetics simulations, where the steady-state rate k(t → ∞) is used in the solution to Eq. (27). The effect of diffusion on the relaxation process is most pronounced with absorbing boundaries, but is also visible for radiation boundaries [Fig. 8(a)]. At longer times, and for systems with slower reaction rates and faster diffusion, the processes converge to the steady-state relaxation of chemical kinetics [Fig. 8(b)].

Bottom Line: FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone.With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events.Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Biophysics, The Johns Hopkins University, Baltimore, Maryland 21218, USA.

ABSTRACT

We present a new algorithm for simulating reaction-diffusion equations at single-particle resolution. Our algorithm is designed to be both accurate and simple to implement, and to be applicable to large and heterogeneous systems, including those arising in systems biology applications. We combine the use of the exact Green's function for a pair of reacting particles with the approximate free-diffusion propagator for position updates to particles. Trajectory reweighting in our free-propagator reweighting (FPR) method recovers the exact association rates for a pair of interacting particles at all times. FPR simulations of many-body systems accurately reproduce the theoretically known dynamic behavior for a variety of different reaction types. FPR does not suffer from the loss of efficiency common to other path-reweighting schemes, first, because corrections apply only in the immediate vicinity of reacting particles and, second, because by construction the average weight factor equals one upon leaving this reaction zone. FPR applications include the modeling of pathways and networks of protein-driven processes where reaction rates can vary widely and thousands of proteins may participate in the formation of large assemblies. With a limited amount of bookkeeping necessary to ensure proper association rates for each reactant pair, FPR can account for changes to reaction rates or diffusion constants as a result of reaction events. Importantly, FPR can also be extended to physical descriptions of protein interactions with long-range forces, as we demonstrate here for Coulombic interactions.

No MeSH data available.


Related in: MedlinePlus