Why do we need to find minimum energy in a protein chain?

Question

• High–quality protein backbone reconstruction from alpha carbons using Gaussian mixture models

The above research paper is about a software tool for reconstructing a protein's main chain model only from its alpha-carbon backbone (aka, C-alpha trace).

This tool provides two options: conversion (1) with energy minimization, and (2) without energy minimization.

• Energy Minimization

The above paper says that:

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The goal of energy Minimization is to find a set of coordinates representing the minimum energy conformation for the given structure.
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In molecular modeling we tend to are particularly curious about minimum points on the energy surface. Minimum energy arrangements of the atoms correspond to stable states of the system; any movement off from a minimum provides a configuration with a better energy.
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I haven't understood the quote from the second paper.

Why do we need to know the minimum energy conformation of a protein chain? I.e., why do we want to do energy minimization?

Answer 1

After translation, proteins fold to achieve a specific 3D structure which allows them to perform their specific functions. The structure of a protein computationally inferred through energy minimization often corresponds quite well to that specific, real-life folded 3D structure.

If you are interested in the exact reason why proteins tend to fold to a conformation of minimal energy (even though this is an oversimplification of what's really happening) you would have to dive a bit deeper into the thermodynamics of proteins: https://en.wikipedia.org/wiki/Protein_dynamics

TL;DR: Energy minimization is often used to get an idea of the protein's real-life conformation (i.e. structure) through computational means.