RebindingKineticsMLE

This package provides a robust framework to analyze pulling traces from single-molecule force spectroscopy experiments involving multiple unbinding-rebinding events. It makes use of numerically efficient and asymptotically exact maximum likelihood estimators for the parameters of the force-dependent unbinding and rebinding Bell-like rates.

For more details on the theoretical framework, please refer to the associated preprint:

J. T. Bullerjahn and G. Hummer, "Rebinding kinetics from single-molecule force spectroscopy experiments close to equilibrium", arXiv:2205.05991 (2022). https://doi.org/10.48550/arXiv.2205.05991

Please cite the reference above if you use RebindingKineticsMLE to analyze your data.

Installation

The package is written in the open-source programming language Julia, which can be downloaded from their webpage.

Currently, the package is not in a registry. It must therefore be added by specifying a URL to the repository:

using Pkg; Pkg.add(url="https://github.com/bio-phys/RebindingKineticsMLE")

Users of older versions of Julia may need to wrap the contents of the brackets with PackageSpec().

Usage

A detailed example on how to apply the code and compare its output to rate maps can be found in the examples directory.

Importing data

Every pulling trace (Array{Float64,2}) is defined by two columns. The first column lists the applied force (in pN) at each time step, whereas the second column defines the associated state the system occupies (0.0 for bound state, 1.0 for unbound state). A collection of pulling traces should therefore be of the type Array{Array{Float64,2},1}.

Assuming that each pulling trace is saved in a separate file, stored in the directory pulling_traces, we can use something like the following code snippet to import the data:

using DelimitedFiles

function read_data(dir)
    files = readdir(dir)
    N = length(files)
    data = Array{Array{Float64,2},1}(undef, N)
    for n = 1 : N
        data[n] = readdlm(string(dir,files[n]))
    end
    return data
end

data = read_data("./pulling_traces/")

Note that the pulling traces do not have to be of equal length or have been generated using the same force protocol. The only requirement is that the time step Δt between two subsequent force measurements has to be constant and the same for all pulling traces.

Parameter and error estimation

The Bell rate has two parameters, a rate and a length scale. We therefore have four parameters, Δx_off, k_off, Δx_on and k_on (lengths in nm, rates in 1/s), which can be estimated using the MLE_estimator function:

estimates, errors = MLE_estimator(data,Δt)

for a constant time step Δt between two subsequent measurements. MLE_estimator has a few optional arguments:

MLE_estimator(data,Δt,β=1/4,δF=0.0,interval=[0.0,10.0])

where β=1/(k_B*T) [in 1/(pN nM)] denotes the inverse thermal energy scale with the Boltzmann constant k_B and temperature T, δF characterizes the experimentally determined mean-squared fluctuations of the applied force, which we assume to be constant, and interval sets the search range used by the optimizer to determine Δx_off and Δx_on (both in nm).