Modeling of Multi-Modal Diffusion Processes with Applications to Protein Folding

• Activity Number: 131
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Julie Forman*+ and Michael Sørensen
• Companies: University of Copenhagen and Department of Mathematical Science, University of Copenhagen
• Keywords: diffusion model ; martingale estimating function ; measurement error ; multi-modality ; protein folding

Abstract

Double well potential models are standard for modeling multi-state behavior in e.g. molecular dynamics data and financial time series. However, the usual assumption of a constant diffusions coefficient is often in conflict with the data [2]. In this talk we present a transformation approach to modeling stationary multi-modal diffusions that complies well with the non-constant diffusion coefficients found in molecular dynamics data [1]. Due to a simple latent structure, our model allows for fast estimation of model parameters by means of explicit martingale estimating equations. Our methodology extends to the situation where the diffusion is observed with measurement error. We apply the models to estimate the folding rate of the small Trp-zipper protein. The estimated folding rate may be severely biased if measurement error in the data is disregarded.

[1] Forman, J. L., S{\o}rensen, M.: A new approach to multi-modal diffusions with applications to protein folding, University of Copenhagen, submitted 2012. [2] Best, R.B., Hummer, G.:Coordinate-dependent diffusion in protein folding, PNAS, 107, 1088--1093, 2010.