Non-Markovian modeling of protein folding

<jats:title>Significance</jats:title> <jats:p> Protein-folding kinetics is often described as Markovian (i.e., memoryless) diffusion in a one-dimensional free energy landscape, governed by an instantaneous friction coefficient that is fitted to reproduce experimental or simulated folding times. For the <jats:inline-formula> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mi>α</mml:mi> </mml:math> </jats:inline-formula> -helix forming polypeptide <jats:inline-formula> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">l</mml:mi> <mml:mi mathvariant="normal">a</mml:mi> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">i</mml:mi> <mml:mi mathvariant="normal">n</mml:mi> <mml:mi mathvariant="normal">e</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>9</mml:mn> </mml:mrow> </mml:msub> </mml:math> </jats:inline-formula> and a specific reaction coordinate that consists of the summed native hydrogen-bond lengths, we demonstrate that the friction extracted from molecular dynamics simulations exhibits significant memory with a decay time that is in the nanosecond range and thus, of the same order as the folding and unfolding times. Our non-Markovian modeling not only reproduces the molecular dynamics simulations accurately but also demonstrates that memory friction effects lead to anomalous and drastically accelerated protein kinetics. </jats:p>