Finite-temperature local protein sequence alignment: percolation and free-energy distribution

TL;DR

This paper investigates the phase transition in finite-temperature local protein sequence alignment, analyzing how free-energy growth shifts from logarithmic to linear, and characterizes the energy distribution near the transition using simulations.

Contribution

It introduces a detailed phase diagram for finite-temperature protein alignment, revealing temperature-dependent critical exponents and energy distribution behaviors near the transition.

Findings

Identified the phase boundary between linear and logarithmic growth regimes.

Confirmed the modified Gumbel distribution for free-energy in the logarithmic phase.

Discovered a crossover to a modified Gaussian distribution in the linear phase.

Abstract

Sequence alignment is a tool in bioinformatics that is used to find homological relationships in large molecular databases. It can be mapped on the physical model of directed polymers in random media. We consider the finite-temperature version of local sequence alignment for proteins and study the transition between the linear phase and the biologically relevant logarithmic phase, where the free-energy grows linearly or logarithmically with the sequence length. By means of numerical simulations and finite-size scaling analysis we determine the phase diagram in the plane that is spanned by the gap costs and the temperature. We use the most frequently used parameter set for protein alignment. The critical exponents that describe the parameter driven transition are found to be explicitly temperature dependent. Furthermore, we study the shape of the (free-) energy distribution close to the transition by rare-event simulations down to probabilities of the order $10^{-64}$. It is well known that, in the logarithmic region, the optimal score distribution (T=0) is described by a modified Gumbel distribution. We confirm that this also applies for the free-energy distribution ($T>0$). However, in the linear phase, the distribution crosses over to a modified Gaussian distribution.