### Introduction

RaTrav tool was designed to support computational biology studies where where Markovian dynamics takes place and mean first-passage times (MFPTs) between initial and single or multiple final states in network-like systems are used. Two methods are made available for which their efficiency is strongly dependent on the topology of the defined network: the combinatorial Hill technique and the Monte Carlo simulation. The user simply prepares a text file with the structure of a given network, along with some additional basic parameters such as transition probabilities, waiting probabilities (if any) and local time scales (weights of edges), which define explicitly the stochastic dynamics on the network. The RaTrav tool can then be applied in order to compute desired MFPTs. For the provided examples, we were able to find the favourable binding path within a protein-protein docking funnel and to calculate the degree of coupling for two chemical reactions catalysed simultaneously by the same protein enzyme. However, the list of possible applications is much wider; more in Ref. (1).Accurate determination of mean first-passage times (MFPTs) between any two states of a complex network still attracts considerable attention. Appropriate methods should take into account the discrepancy in MFPTs when a random walker moves first from a source to a target and then in the opposite direction. In addition, it is desirable to allow fast evaluation of mean first-passage times when transition probabilities are allowed to vary over time. When given a fixed distance to travel, the calculation of a particular MFPT depends on the choice of source and target points and their relative position on a lattice. When the network contains a relatively low number of cycles, Hill's deterministic technique provides exact results much faster in comparison to the more standard, but computationally demanding, stochastic Monte Carlo simulation method, where only approximate results can be obtained that are highly dependent on the number of walkers; more in Ref. (2).

### If you find the RaTrav tool useful please cite

- M. Torchala
**(*)**, P. Chelminiak**(*)**, M. Kurzynski and P. A. Bates, 'RaTrav: a tool for calculating mean first-passage times on biochemical networks',*BMC Syst. Biol.***7**, 130 (2013).**(*)***Joint First Authors.* - M. Torchala, P. Chelminiak and P. A. Bates, 'Mean first-passage time calculations: comparison of the deterministic Hill's algorithm with Monte Carlo simulations',
*Eur. Phys. J. B***85**, 116 (2012).

### Please send any comments or/and bug reports directly to the developers

- Mieczyslaw.Torchala@gmail.com (RaTrav.xx.xx.xx.cpp and MC.xx.xx.xx.cpp)
- Przemyslaw.Chelminiak@amu.edu.pl (HI.xx.xx.xx.cpp)

### RaTrav is distributed under GNU General Public License, version 3 (GPL-3.0) or any later version

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or any later version.This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

**Developers of this code will appreciate further modifications. If upon testing, the authors feel that the additions are valuable, they may be included in further versions; full acknowledgment will be given to all developers.**

### Input files

Examples of input files in**basic**input file format (structures may be found in

**Ref. (2)**):

- Bethe lattice with two shells, waiting times in leaves: MC_Bethe2shells_Wait.in
- Bethe lattice with two shells, without waiting: MC_Bethe2shells_NoWait.in
- 2nd order Sierpinski gasket: MC_Sierpinski2order.in
- A square (2D hypercube): MC_Hypercube2D.in
- A square (2D hypercube) with MFPT keyword: MC_Hypercube2D_01.in
- A square (2D hypercube) with OCCU keyword: MC_Hypercube2D_OCCU.in
- expnet10: MC_expnet10.in
- sfnet10: MC_sfnet10.in

Examples of input files in

**advanced**input file format:

- A square (2D hypercube): MC_Hypercube2D_PRO.in or MC_Hypercube2D_PRO2.in
- A square (2D hypercube) with MFPT keyword: MC_Hypercube2D_PRO3.in or MC_Hypercube2D_PRO4.in
- A square (2D hypercube) with various transition probabilities: MC_Hypercube2D_PRO5.in
- A square (2D hypercube) with all weights of edges equal to 5.0: MC_Hypercube2D_PRO6.in
- A square (2D hypercube) with various weights and transition probabilities: MC_Hypercube2D_PRO7.in

Network depicted in the Manual (S = 0, E1 = 7, E2 = 8):

- input: ratrav_fig1.in (choose run parameters [0/1] 1 0; see below);

output from Monte Carlo method: MC_ratrav_fig1.out, output from Hill's method: HI_ratrav_fig1.out - input: ratrav_fig1_078.in (choose run parameters [0/1] 1 1; see below);

output from Monte Carlo method: MC_ratrav_fig1_078.out, output from Hill's method: HI_ratrav_fig1_078.out