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101b

Multiscale Stochastic Dynamical Models Calibrated from AFM Single-Molecule Time Series and Computer Simulations

Christopher P. Calderon1, Ching-Hwa Kiang2, Dennis D. Cox3, Nolan C. Harris2, Wei-Hung Chen2, and Kuan-Jiuh Lin4. (1) Computational and Applied Mathematics, Rice University, 6100 Main St, Houston, TX 77251-1892, (2) Physics & Astronomy, Rice University, 6100 Main St, Houston, TX 77251-1892, (3) Statistics, Rice University, 6100 Main St, Houston, TX 77251-1892, (4) Chemistry, National Chung-Hsing University

The stochastic dynamics associated with stretching both single-stranded poly(dA) DNA and synthetic titin molecules (each molecule contained 8 identical serially linked I27 domains) were approximated using maximum likelihood state-space techniques. The models were fit using experimental atomic force microscopy (AFM) time series. The measurement noise associated with the AFM apparatus was quantified using time domain techniques which exploited a time scale separation that exists in the data [1,2]. All results reported in this study analyzed repeat experiments on the same underlying molecule, i.e. once a single-molecule is captured by the AFM tip, it is retained and a series of experiments are conducted with the same molecule. The fitted stochastic models are fairly flexible, the major assumptions made about the dynamics were that overdamped diffusion models can be used to adequately approximate the true process and that the drift and diffusion coefficient (whose global functional form is assumed unknown) of these models are well-behaved, e.g. twice differentiable. The assumptions are tested in an a posteriori fashion using goodness-of-fit tests given the data and the models estimated from the observed data (the tests employed check for non-Markovian effects). The unfolding of the I27 domain of titin was also investigated [2] using steered molecule dynamics simulations in order to test a variety of hypothesis suggested by the experiments.

The estimated pathwise dynamical models can be used for a variety of purposes. They can be used to simulate and quantify how solvent induced thermal noise would affect the distribution of certain observables like the nonequilibrium work associated with stretching the captured molecule. This is relevant in situations where collecting a large number of force extension curves (FECs) is difficult due to experimental complications (e.g., in some systems retaining the same molecule for a large number of repeated force extension cycles is difficult).

The models can also be used to indirectly determine when certain important structural transitions occur and also quantify how conformational degrees of freedom (which typically are associated with slower time scales) influence the multiscale stochastic dynamics [1,2,3]. This indirect inference requires one to collect a batch of FECs and compare the “rules” governing the resulting models. In some cases, the measured drift contains a signature of a transition and in others a sudden thermal noise magnitude change acts as a fingerprint of a structural change. The primary appeal of this type of work is that the methods developed more fully utilize the wealth of information contained in the time series collected from single-molecule force spectroscopy and computer simulations. The diffusion model functions facilitate physical understanding of the process dynamics and aid in interpreting the experiment and simulation results. Quantitative information about stochastic dynamical responses of single-molecules induced by different stimuli (mechanical and/or chemical) can possibly enhance targeted drug design which exploit recent rapid advances in nanotechnology.

[1] C.P. Calderon, W.-H. Chen, K-.J. Lin , and C.-H. Kiang (submitted).

[2] C.P. Calderon, N.C. Harris, C.-H. Kiang and D. D. Cox (in preparation).

[3] C.P. Calderon and R. Chelli. J. Chem. Phys., 128:145103 (2008).



Web Page: www.stat.rice.edu/~cpc1/