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How can nonlinear optimization model the folding of a protein molecule?

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optimization problem — optimization Constraint set bounded by the five lines x₁ = 0, x₂ = 0, x₁ = 8, x₂ = 5, and x₁ + x₂ = 10. These enclose an infinite number of points that represent feasible solutions.

Nonlinear optimization models the folding of a protein molecule by identifying the specific conformation that minimizes a nonlinear objective function. In this context, the objective function represents the energy state of the protein, which is determined by the distances between the nuclei of its component atoms.1

Because these interatomic distances are themselves nonlinear functions of the atomic positions, the problem cannot be accurately expressed using linear functions. By applying nonlinear programming, researchers can search for the optimal spatial arrangement of atoms that corresponds to the protein's stable, folded state. This process often involves navigating complex, high-dimensional landscapes where algorithms must iteratively refine guesses to identify either a global or local optimum.1