# Asymmetric exclusion process and extremal statistics of random sequences.

@article{Bundschuh2002AsymmetricEP, title={Asymmetric exclusion process and extremal statistics of random sequences.}, author={Ralf Bundschuh}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2002}, volume={65 3 Pt 1}, pages={ 031911 } }

A mapping is established between sequence alignment, one of the most commonly used tools of computational biology, at a certain choice of scoring parameters 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.

## 53 Citations

### Exact solution of the Bernoulli matching model of sequence alignment

- Mathematics
- 2008

Through a series of exact mappings we reinterpret the Bernoulli model of sequence alignment in terms of the discrete-time totally asymmetric exclusion process with backward sequential update and step…

### Replica model for an unusual directed polymer in 1+1 dimensions and prediction of the extremal parameter of gapped sequence alignment statistics.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

Two classes of solutions for the gapped alignment statistics are presented by explicitly calculating the evolution of the few-replica partition function in 1+1 dimensions by obtaining the conditions under which the more important extremal parameter lambda, characterizing the alignment score statistics, becomes predictable.

### Bethe Ansatz Solution of the Finite Bernoulli Matching Model of Sequence Alignment

- Mathematics
- 2011

We map the Bernoulli matching model of sequence alignment to the discrete-time totally asymmetric exclusion process with backward sequential update and step function initial condition. The Bethe…

### Tableaux combinatorics for the asymmetric exclusion process and Askey-Wilson polynomials

- Mathematics
- 2009

Introduced in the late 1960's, the asymmetric exclusion process (ASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a…

### A Markov Chain on Permutations which Projects to the PASEP

- Mathematics
- 2006

The partially asymmetric exclusion process (PASEP) is an important model from statistical mechanics which describes a system of interacting particles hopping left and right on a one-dimensional…

### Score statistics of global sequence alignment from the energy distribution of a modified directed polymer and directed percolation problem.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

This work investigates the score statistics of global sequence alignment taking into account, in particular, the compositional bias of the sequences compared, and the possibility of characterizing score statistics for modest system size (sequence lengths), via proper reparametrization of alignment scores, is illustrated.

### Path reversal, islands, and the gapped alignment of random sequences

- Mathematics
- 2004

In bioinformatics, the notion of an 'island' enhances the efficient simulation of gapped local alignment statistics. This paper generalizes several results relevant to gapless local alignment…

### Hidden symmetries in the asymmetric exclusion process

- Physics
- 2004

We present a spectral study of the evolution matrix of the totally asymmetric exclusion process on a ring at half filling. The natural symmetries (translation, charge conjugation combined with…

### Symmetry and Fractal-like Structures in the Statistics of Sequence Comparison

- Computer Science, Mathematics
- 2002

The iterative value in fact converges more rapidly to the Chvátal-Sankoff constant ac (the proportionality constant for the linear growth of the expected length of the LCS with sequence length) as the sequence length increases.

## References

SHOWING 1-10 OF 29 REFERENCES

### The Asymptotic Theory of Extreme Order Statistics

- Mathematics
- 1977

Abstract. Let X j denote the life length of the j th component of a machine. In reliability theory, one is interested in the life length Z n of the machine where n signifies its number of components.…

### Proceedings : Sixth International Conference on Intelligent Systems for Molecular Biology

- Engineering
- 1998

### Proceedings of the second annual international conference on Computational molecular biology

- BiologyRECOMB 1998
- 1998

### Proceedings of the Seventh International Conference on Intelligent Systems for Molecular Biology

- Engineering, Computer ScienceISMB 1999
- 1993

### Expected length of longest common subsequences

- Computer Science, Mathematics
- 1994

The methods used for producing bounds on the expected length of a common subsequences of two sequences are also used for other problems, namely a longest common subsequence of several sequences, a shortest common supersequence and a maximal adaptability.