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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

Time-dependent probability of association of particle pairs for the system of Fig. 5 with Δt = 0.001 μs and DAB = 1 nm2/μs, the parameter combination with the largest error, but now with the simulations adapted to reduce error. The RD simulations with absorbing BCs are in magenta and for ka = 10 nm3/μs in light and dark green, with the exact solution shown as a black dashed line. To reduce the error for these conditions, we lowered the distance over which reweighting is applied. The magenta lines are simulations with the reweighting separation decreased from  to , but with the same reaction zone size. This means trajectories are reweighted for a shorter length of time. The light green lines are for ka = 10 nm3/μs and the reweighting separation decreased from  to . Another way to reduce error is to simply increase ka, and in dark green we show association for ka increased from 10 to 10.3 nm3/μs. This approach is not applicable to absorbing BCs (ka cannot be increased) but works well for finite rates. The inset shows the difference between exact and simulated results.
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Figure 6: Time-dependent probability of association of particle pairs for the system of Fig. 5 with Δt = 0.001 μs and DAB = 1 nm2/μs, the parameter combination with the largest error, but now with the simulations adapted to reduce error. The RD simulations with absorbing BCs are in magenta and for ka = 10 nm3/μs in light and dark green, with the exact solution shown as a black dashed line. To reduce the error for these conditions, we lowered the distance over which reweighting is applied. The magenta lines are simulations with the reweighting separation decreased from to , but with the same reaction zone size. This means trajectories are reweighted for a shorter length of time. The light green lines are for ka = 10 nm3/μs and the reweighting separation decreased from to . Another way to reduce error is to simply increase ka, and in dark green we show association for ka increased from 10 to 10.3 nm3/μs. This approach is not applicable to absorbing BCs (ka cannot be increased) but works well for finite rates. The inset shows the difference between exact and simulated results.

Mentions: We propose two ways to deal with the error arising from trajectory undersampling when small time steps are necessary and also diffusion constants are slow (DΔt ∼ 0.001σ2). First, using the same size reaction zone Rmax, a smaller radial separation can be used inside which reweighting is applied, such that Rrewgt < Rmax. This will shorten the length of reweighted trajectories and can improve overall association rates, because fewer trajectories will be reweighted with low (approximately 0) ratios. In Fig. 6, we see that this approach improves agreement for simulations with D = 1 nm2/μs, Δt = 0.001 μs, and ka = ∞ and ka = 10 nm3/μs, although not perfectly. Second, a larger intrinsic rate constant ka could be input to the program to bring the total association up to the desired level. In Fig. 6, the dark green lines report simulations with ka = 10.3 nm3/μs and very small error. However, the choice of reweighting zone radius Rrewgt, or increased association rates, was only determined through trial and error.


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)

Time-dependent probability of association of particle pairs for the system of Fig. 5 with Δt = 0.001 μs and DAB = 1 nm2/μs, the parameter combination with the largest error, but now with the simulations adapted to reduce error. The RD simulations with absorbing BCs are in magenta and for ka = 10 nm3/μs in light and dark green, with the exact solution shown as a black dashed line. To reduce the error for these conditions, we lowered the distance over which reweighting is applied. The magenta lines are simulations with the reweighting separation decreased from  to , but with the same reaction zone size. This means trajectories are reweighted for a shorter length of time. The light green lines are for ka = 10 nm3/μs and the reweighting separation decreased from  to . Another way to reduce error is to simply increase ka, and in dark green we show association for ka increased from 10 to 10.3 nm3/μs. This approach is not applicable to absorbing BCs (ka cannot be increased) but works well for finite rates. The inset shows the difference between exact and simulated results.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 6: Time-dependent probability of association of particle pairs for the system of Fig. 5 with Δt = 0.001 μs and DAB = 1 nm2/μs, the parameter combination with the largest error, but now with the simulations adapted to reduce error. The RD simulations with absorbing BCs are in magenta and for ka = 10 nm3/μs in light and dark green, with the exact solution shown as a black dashed line. To reduce the error for these conditions, we lowered the distance over which reweighting is applied. The magenta lines are simulations with the reweighting separation decreased from to , but with the same reaction zone size. This means trajectories are reweighted for a shorter length of time. The light green lines are for ka = 10 nm3/μs and the reweighting separation decreased from to . Another way to reduce error is to simply increase ka, and in dark green we show association for ka increased from 10 to 10.3 nm3/μs. This approach is not applicable to absorbing BCs (ka cannot be increased) but works well for finite rates. The inset shows the difference between exact and simulated results.
Mentions: We propose two ways to deal with the error arising from trajectory undersampling when small time steps are necessary and also diffusion constants are slow (DΔt ∼ 0.001σ2). First, using the same size reaction zone Rmax, a smaller radial separation can be used inside which reweighting is applied, such that Rrewgt < Rmax. This will shorten the length of reweighted trajectories and can improve overall association rates, because fewer trajectories will be reweighted with low (approximately 0) ratios. In Fig. 6, we see that this approach improves agreement for simulations with D = 1 nm2/μs, Δt = 0.001 μs, and ka = ∞ and ka = 10 nm3/μs, although not perfectly. Second, a larger intrinsic rate constant ka could be input to the program to bring the total association up to the desired level. In Fig. 6, the dark green lines report simulations with ka = 10.3 nm3/μs and very small error. However, the choice of reweighting zone radius Rrewgt, or increased association rates, was only determined through trial and error.

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