scholarly journals Making High-Dimensional Molecular Distribution Functions Tractable through Belief Propagation on Factor Graphs

2021 ◽  
Vol 125 (40) ◽  
pp. 11150-11158
Author(s):  
Zachary Smith ◽  
Pratyush Tiwary
Keyword(s):  
Belief Propagation ◽  
Distribution Functions ◽  
High Dimensional ◽  
Factor Graphs ◽  
Molecular Distribution

scholarly journals Making high-dimensional molecular distribution functions tractable through Belief Propagation on Factor Graphs

2021 ◽  
Author(s):  
Zachary Smith ◽  
Pratyush Tiwary
Keyword(s):  
Belief Propagation ◽  
Conformational Dynamics ◽  
Joint Probability ◽  
Md Simulations ◽  
Distribution Functions ◽  
Factor Graph ◽  
High Dimensional ◽  
Enhanced Sampling ◽  
Small Peptides ◽  
Approximate Probability

Molecular dynamics (MD) simulations provide a wealth of high-dimensional data at all-atom and femtosecond resolution but deciphering mechanistic information from this data is an ongoing challenge in physical chemistry and biophysics. Theoretically speaking, joint probabilities of the equilibrium distribution contain all thermodynamic information, but they prove increasingly difficult to compute and interpret as the dimensionality increases. Here, inspired by tools in probabilistic graphical modeling, we develop a factor graph trained through belief propagation that helps factorize the joint probability into an approximate tractable form that can be easily visualized and used. We validate the study through the analysis of the conformational dynamics of two small peptides with 5 and 9 residues. Our validations include testing the conditional dependency predictions through an intervention scheme inspired by Judea Pearl. Secondly we directly use the belief propagation based approximate probability distribution as a high-dimensional static bias for enhanced sampling, where we achieve spontaneous back-and-forth motion between metastable states that is up to 350 times faster than unbiased MD. We believe this work opens up useful ways to thinking about and dealing with high-dimensional molecular simulations.

Molecular Distribution Functions in a One‐Dimensional Fluid

1953 ◽  
Vol 21 (6) ◽  
pp. 1098-1107 ◽  
Author(s):  
Zevi W. Salsburg ◽  
Robert W. Zwanzig ◽  
John G. Kirkwood
Keyword(s):  
Distribution Functions ◽  
One Dimensional ◽  
Molecular Distribution

Contour Reconstruction

2020 ◽  
pp. 584-618
Author(s):  
Dariusz Jacek Jakóbczak
Keyword(s):  
Probability Distribution ◽  
Image Retrieval ◽  
Probability Distribution Function ◽  
Feature Space ◽  
Linear Interpolation ◽  
Distribution Functions ◽  
High Dimensional ◽  
Feature Spaces ◽  
Contour Reconstruction ◽  
Multidimensional Feature Spaces

The method of Probabilistic Features Combination (PFC) enables interpolation and modeling of high-dimensional N data using features' combinations and different coefficients γ: polynomial, sinusoidal, cosinusoidal, tangent, cotangent, logarithmic, exponential, arc sin, arc cos, arc tan, arc cot or power function. Functions for γ calculations are chosen individually at each data modeling and it is treated as N-dimensional probability distribution function: γ depends on initial requirements and features' specifications. PFC method leads to data interpolation as handwriting or signature identification and image retrieval via discrete set of feature vectors in N-dimensional feature space. So PFC method makes possible the combination of two important problems: interpolation and modeling in a matter of image retrieval or writer identification. Main features of PFC method are: PFC interpolation develops a linear interpolation in multidimensional feature spaces into other functions as N-dimensional probability distribution functions.

Virial expansions in an inhomogeneous system

1985 ◽  
Vol 402 (1822) ◽  
pp. 67-82 ◽  
Keyword(s):  
External Field ◽  
Isosteric Heat ◽  
Distribution Functions ◽  
Harmonic Potential ◽  
Inhomogeneous System ◽  
Pressure Tensor ◽  
Arbitrary Size ◽  
Molecular Distribution ◽  
Grand Potential

The grand potential, the density and the molecular distribution functions are obtained in the form of virial expansions for systems of arbitrary size and inhomogeneity by using an external field to replace the conventional fixed geometric boundaries of a system. The equations are applied first to the calculation of the density and of different representations of the pressure tensor for a system of gaussian (repulsive) molecules in a simple harmonic potential, and, secondly, to obtaining an expression for the isosteric heat of absorption of interacting molecules in the pores of a zeolite.

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