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IGME

Integrative Generalized Master Equation (IGME): A Theory to Study Long-timescale Biomolecular Dynamics via the Integrals of Memory Kernels.

This code is used to generate Integrative-Generalized-Master-Equation (IGME) models for large molcular systems with the steepest descent optimization based on the initial guess of least-square-fitting. Three theories have been provided:

do_igme_sd2.py : based on the second-order solution of IGME: T_IGME(t) = A T_hat^t

do_igme_sd3a.py : based on a three-order solution of IGME: T_IGME(t) = (A T_hat^t + T_hat^t A) / 2

do_igme_sd3a.py : based on another three-order solution of IGME: T_IGME(t) = sqrt{A} T_hat^t sqrt{A}

Usage

perform IGME with specified beginning and end points of fitting:

input=TPM_file_name [begin=fit_range_begin end=fit_range_end epoch=number_of_epochs] do_igme_sd2.py
export input=TPM_file_name 
export begin=fit_range_begin
export end=fit_range_end
export epoch=number_of_epochs
python do_igme_sd2.py

scan parameters of IGME

export TPM_file=...;
for ((i=2;i<=`cat $TPM_file|wc -l`;i++)); do
  for ((j=1;j<i=1;j++)); do
    input=$TPM_file begin=$j end=$i python do_igme_sd2.py
  done
done

note

format for input TPM_file

The TPM_file is a single file contains multiple TPMs. Each line in TPM_file represent a transition probability matrix. Each line has N^2 elements (N is the dimension of TPMs or number of states) seperated by spaces or tabs.

required packages

numpy

pyTorch

scipy

Reference

[1] Siqin Cao, Yunrui Qiu, Michael Kalin, and Xuhui Huang, Integrative Generalized Master Equation: A Theory to Study Long-timescale Biomolecular Dynamics via the Integrals of Memory Kernels, https://doi.org/10.26434/chemrxiv-2022-0n9ld