# Monte Carlo simulation of a statistical mechanical model of multiple protein sequence alignment

## TL;DR

This paper introduces a Monte Carlo simulation method for a lattice gas model of multiple protein sequence alignment, enabling detailed exploration of sequence space with long-range interactions and insertions, and reveals a two-state transition in the SH3 domain family.

## Contribution

It presents a novel grand canonical Monte Carlo algorithm for the lattice gas model of protein sequences, incorporating long-range interactions and variable insertions, and compares it with mean-field approximations.

## Key findings

- Identification of a two-state transition in the SH3 domain family
- Demonstration of the inaccuracy of mean-field approximation for the model
- Preliminary results across various temperatures and chemical potentials

## Abstract

A grand canonical Monte Carlo (MC) algorithm is presented for studying the lattice gas model (LGM) of multiple protein sequence alignment, which coherently combines long-range interactions and variable-length insertions. MC simulations are used for both parameter optimization of the model and production runs to explore the sequence subspace around a given protein family. In this Note, I describe the details of the MC algorithm as well as some preliminary results of MC simulations with various temperatures and chemical potentials, and compare them with the mean-field approximation. The existence of a two-state transition in the sequence space is suggested for the SH3 domain family, and inappropriateness of the mean-field approximation for the LGM is demonstrated.