deltaG_BierAstumian.m
author: Natalia Martin Sabanés
Date: october 2024
Cite as:  Nicolás-García T, Martín Sabanés N, Bocanegra R, Astumian RD, Perez E, Ibarra B. Transition-path times of molecular shuttles under mechanical equilibrium show symmetry. ChemRxiv. 2024; doi:10.26434/chemrxiv-2024-w3twb

1. Inputs: 
 - path and file name of the trace to be analysed (baseline corrected and centered, recovered from baseline_correction.m). 
 - format type of data: .dat and .txt allowed
 - name: name for the legends and titles of figures
 - time_steps: 1/acquisition rate, in s. Time between two consecutive datapoints
 - deltax: extension interval in which starting and final point will be searched, ie, given a starting point a, the code considers that the point has been crossed for all extension values within the interval (a-deltax,a+deltax)
 - deltat: time interval in transistion probability accroding to Bier-Astumian relation. Probability P[a→b,Δt] as the probability of the macrocycle reaching a spatial point b starting at a (completing successfully the trajectory a→b), within a time interval Δt.
 - a: starting point (in nm), several values can be computed simultaneously, so a might be a value, a list of values, or a vector
 - b: final point (in nm), several values can be computed simultaneously, so b might be a value, a list of values, or a vector
 
2. Outputs: 
- Figure 1: P[a→b,Δt] as a function of b. Each curve represents a different value of a.
- Figure 2: P[b→a,Δt] as a function of b. Each curve represents a different value of a.
- Figure 3: P[a→b,Δt]/P[b→a,Δt as a function of b. Each curve represents a different value of a.
- Figure 4: Individual ΔG/K_bT as a function of b. Each curve represents a different value of a.
- Figure 5: Mean ΔG/K_bT as a function of b (average of all curves in Figure 4)