# Molecular simulations minimally restrained by experimental data

## TL;DR

This paper derives equations for restrained molecular simulations that minimally perturb unbiased distributions while fitting experimental data, improving the integration of experimental constraints into simulations.

## Contribution

It introduces a new method to restrain simulations, ensuring minimal deviation from unbiased distributions while matching experimental observable values.

## Key findings

- Provides equations for equilibrium distributions under restraints
- Suggests a method for minimally perturbing simulations
- Enables accurate reproduction of experimental data within uncertainties

## Abstract

One popular approach to incorporating experimental data into molecular simulations is to restrain the ensemble average of observables to their experimental values. Here I derive equations for the equilibrium distributions generated by restrained ensemble simulations and the corresponding expected values of observables. My results suggest a method to restrain simulations so that they generate distributions that are minimally perturbed from the unbiased distributions while reproducing the experimental values of the observables within their measurement uncertainties.