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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

Distribution of exact to simulated trajectory probabilities on exiting the reaction zone for different initial separations r0, with each curve representing an increment of 0.1 nm in r0. These values reflect the degree of overlap between the exact and the simulated trajectories. If the reweighting-factor distributions are broad, the simulated trajectories will waste time on highly improbable trajectories, and miss out on some relevant trajectories, hence, undersampling in Eq. (19). (a) ka = 10.0 nm3/μs, DAB = 20 nm2/μs, Δt = 0.1 μs. (b) ka =1000.0 nm3/μs, DAB = 1 nm2/μs, Δt = 0.01 μs.
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Figure 4: Distribution of exact to simulated trajectory probabilities on exiting the reaction zone for different initial separations r0, with each curve representing an increment of 0.1 nm in r0. These values reflect the degree of overlap between the exact and the simulated trajectories. If the reweighting-factor distributions are broad, the simulated trajectories will waste time on highly improbable trajectories, and miss out on some relevant trajectories, hence, undersampling in Eq. (19). (a) ka = 10.0 nm3/μs, DAB = 20 nm2/μs, Δt = 0.1 μs. (b) ka =1000.0 nm3/μs, DAB = 1 nm2/μs, Δt = 0.01 μs.

Mentions: When trajectories exit the reaction zone, the value of their accumulated reweighting ratio will differ from one, but the exit ratio averaged over all trajectories will be one in the case of complete sampling. This average exit ratio, defined as , reflects the reweighting factors accumulated by trajectories that survived to the edge of the reaction zone Rmax. In Fig. 4(a), we show the distribution of these exit ratios for different initial starting positions r0. The average exit ratio is one because by construction the association probabilities of the reweighted free trajectories match those of trajectories created with the exact irreversible pair propagator. Therefore, the overall survival probabilities of the reweighted trajectories are exact. As a consequence, free trajectories with weights exceeding the probability of the exact trajectories are balanced by trajectories of low weight. The average ratio must be one to ensure the correct association probabilities.


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)

Distribution of exact to simulated trajectory probabilities on exiting the reaction zone for different initial separations r0, with each curve representing an increment of 0.1 nm in r0. These values reflect the degree of overlap between the exact and the simulated trajectories. If the reweighting-factor distributions are broad, the simulated trajectories will waste time on highly improbable trajectories, and miss out on some relevant trajectories, hence, undersampling in Eq. (19). (a) ka = 10.0 nm3/μs, DAB = 20 nm2/μs, Δt = 0.1 μs. (b) ka =1000.0 nm3/μs, DAB = 1 nm2/μs, Δt = 0.01 μs.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Distribution of exact to simulated trajectory probabilities on exiting the reaction zone for different initial separations r0, with each curve representing an increment of 0.1 nm in r0. These values reflect the degree of overlap between the exact and the simulated trajectories. If the reweighting-factor distributions are broad, the simulated trajectories will waste time on highly improbable trajectories, and miss out on some relevant trajectories, hence, undersampling in Eq. (19). (a) ka = 10.0 nm3/μs, DAB = 20 nm2/μs, Δt = 0.1 μs. (b) ka =1000.0 nm3/μs, DAB = 1 nm2/μs, Δt = 0.01 μs.
Mentions: When trajectories exit the reaction zone, the value of their accumulated reweighting ratio will differ from one, but the exit ratio averaged over all trajectories will be one in the case of complete sampling. This average exit ratio, defined as , reflects the reweighting factors accumulated by trajectories that survived to the edge of the reaction zone Rmax. In Fig. 4(a), we show the distribution of these exit ratios for different initial starting positions r0. The average exit ratio is one because by construction the association probabilities of the reweighted free trajectories match those of trajectories created with the exact irreversible pair propagator. Therefore, the overall survival probabilities of the reweighted trajectories are exact. As a consequence, free trajectories with weights exceeding the probability of the exact trajectories are balanced by trajectories of low weight. The average ratio must be one to ensure the correct association probabilities.

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