Optimal Reaction Coordinate as a Biomarker for the Dynamics of Recovery from Kidney Transplant

The Journal of Chemical Physics

2015

Self Cite

State of the art realistic simulations of complex atomic processes commonly produce trajectories of large size, making the development of automated analysis tools very important. A popular approach aimed at extracting dynamical information consists of projecting these trajectories into optimally selected reaction coordinates or collective variables. For equilibrium dynamics between any two boundary states, the committor function also known as the folding probability in protein folding studies is often considered as the optimal coordinate. To determine it, one selects a functional form with many parameters and trains it on the trajectories using various criteria. A major problem with such an approach is that a poor initial choice of the functional form may lead to sub-optimal results. Here, we describe an approach which allows one to optimize the reaction coordinate without selecting its functional form and thus avoiding this source of error.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonparametric variational optimization of reaction coordinates

The Journal of Chemical Physics

2015

Self Cite

“…Then, one numerically optimizes the weights w ij or the cutoff distances

r_{i j}^{0}

for contacts by optimizing a particular functional, so that in the end, the putative RC accurately approximates the committor. The following optimization functionals have been suggested: the probability of being on a transition path, the likelihood functional, the cut profiles, and the total squared displacement (TSD) …”

Section: Validation and Determination Of Optimal Rcsmentioning

confidence: 99%

“…A different functional with analogous properties, which was used originally, is

true {false\int}_{r_{A}}^{r_{B}} Z_{H} ((), r) d r false/ Z_{C} ((), r)

. Another option is to minimize

true {false\int}_{r_{A}}^{r_{B}} Z_{C, 1} ((), r) d r = 1 false/ 2 true {false\sum}_{k} {[r (Δ t + k Δ t) - r (k Δ t)]}^{2}

, i.e., the TSD under constraints r A = 0 and r B = 1 . The fact that the minimum of the TSD is attained for the committor can be easily verified using the following expression for the TSD for an MSM ∑ ij n ij ( r i − r j ) 2 , where n ij = n ji = P ij (Δ t ) P eq , j is the equilibrium number of transitions between states i and j .…”

Section: Validation and Determination Of Optimal Rcsmentioning

confidence: 99%

“…The main contribution to the TSD functional comes from the points with high Z C ,1 ( r ), i.e., the optimization is focused on free‐energy minima. An advantage of such a functional is that its optimum can be found analytically when the RC is a weighted sum of basis functions . This feature lead to a new method which optimizes the RC over the entire range, not just around the transition state regions .…”

Section: Validation and Determination Of Optimal Rcsmentioning

confidence: 99%

See 1 more Smart Citation

Optimal reaction coordinates

2016

WIREs Comput Mol Sci

Self Cite

The dynamic behavior of complex systems with many degrees of freedom is often analyzed by projection onto one or a few reaction coordinates. The dynamics is then described in a simple and intuitive way as diffusion on the associated free energy profile. In order to use such a picture for a quantitative description of the dynamics one needs to select the coordinate in an optimal way so as to minimize non-Markovian effects due to the projection. For equilibrium dynamics between two boundary states (e.g., a reaction) the optimal coordinate is known as the committor or the pfold coordinate in protein folding studies. While the dynamics projected on the committor is not Markovian, many important quantities of the original multidimensional dynamics on an arbitrarily complex landscape can be computed exactly. Here we summarize the derivation of this result, discuss different approaches to determine and validate the committor coordinate and present three illustrative applications: protein folding, the game of chess, and patient recovery dynamics after kidney transplant.

Fep1d: A script for the analysis of reaction coordinates

2015

J Comput Chem

Self Cite

The dynamics of complex systems with many degrees of freedom can be analyzed by projecting it onto one or few coordinates (collective variables). The dynamics is often described then as diffusion on a free energy landscape associated with the coordinates.Fep1d is a script for the analysis of such one-dimensional coordinates. The script allows one to construct conventional and cut-based free energy profiles, to assess the optimality of a reaction coordinate, to inspect whether the dynamics projected on the coordinate is diffusive, to transform (re-scale) the reaction coordinate to more convenient ones, and to compute such quantities as the mean first passage time, the transition path times, the coordinate dependent diffusion coefficient, etc. Here we describe the implemented functionality together with the underlying theoretical framework.