title: Nonparametric estimates of drift and diffusion profiles via Fokker-Planck algebra.
abstract: Diffusion processes superimposed upon deterministic motion play a key role in understanding and controlling the transport of matter, energy, momentum, and even information in physics, chemistry, material science, biology, and communications technology. Given functions defining these random and deterministic components, the Fokker-Planck (FP) equation is often used to model these diffusive systems. Many methods exist for estimating the drift and diffusion profiles from one or more identifiable diffusive trajectories; however, when many identical entities diffuse simultaneously, it may not be possible to identify individual trajectories. Here we present a method capable of simultaneously providing nonparametric estimates for both drift and diffusion profiles from evolving density profiles, requiring only the validity of Langevin/FP dynamics. This algebraic FP manipulation provides a flexible and robust framework for estimating stationary drift and diffusion coefficient profiles, is not based on fluctuation theory or solved diffusion equations, and may facilitate predictions for many experimental systems. We illustrate this approach on experimental data obtained from a model lipid bilayer system exhibiting free diffusion and electric field induced drift. The wide range over which this approach provides accurate estimates for drift and diffusion profiles is demonstrated through simulation.
authors.affiliation: Statistical Engineering Division and ‡Biosystems and Biomaterials Division, National Institute of Standards and Technology , 100 Bureau Drive, Stop 8980, Gaithersburg, Maryland 20899, United States.
authors.forename: Steven P
authors.initials: SP
authors.lastname: Lund
authors.forename: Joseph B
authors.initials: JB
authors.lastname: Hubbard
authors.forename: Michael
authors.initials: M
authors.lastname: Halter
mesh_terms: D001692:Biological Transport; D003198:Computer Simulation; D004058:Diffusion; D004560:Electricity; D004735:Energy Transfer; D008051:Lipid Bilayers / Q000737:chemistry*; D015233:Models, Statistical; D009038:Motion; D013997:Time Factors
chemical_list: D008051:Lipid Bilayers