Application of N-particle random walk to geminate recombination of a hemeprotein with a ligand

The N-particle random walk in the presence of a trap at the origin is applied to the geminate recombination of hemeprotein-ligand dynamics within the diffusion approximation in one dimension. Analytical expressions for the survival probabilities of the unbound heme are procured in terms of the span 〈SN(t)〉 of the multiparticle walk. The behaviour of the span is studied in the asymptotic limit of t→∞. When N is large 〈SN(t)〉 depends linearly on t1/2 with no dependence on N, but when N is small, 〈SN(t)〉 varies linearly with N and has a logarithmic dependence on t.