An exact mapping is established between sequence alignment, one of the most commonly used tools of computational biology, and the asymmetric exclusion process, one of the few exactly solvable models of nonequilibrium physics. The statistical significance of sequence alignments is characterized through studying the total hopping current of the discrete time and space version of the asymmetric exclusion process.

Asymmetric exclusion process and extremal statistics of random sequences

We discuss the exact solvability of a lattice model with a flow within the matrix product ansatz to interacting many-body systems from the point of view of a tridiagonal boundary algebra. It reveals deep symmetry properties of the multiparticle process which allow for the exact solution in the stationary state and puts the description of the dynamics into perspective.

Exact solvability of a model of nonequilibrium physics

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Exact solvability of a model of nonequilibrium physics