Multibind

Thermodynamic cycles which are defined by a set of individually determined free energy differences are not guaranteed to be thermodynamically consistent. This criterion is only satisfied when all the differences in a closed loop vanish. Multibind is a Python package that allows for the combination of these differences, along with their variances, into a set of data-informed and thermodynamically consistent state free energies. Additionally, multibind supports cycles whose free energies are dependent on multiple ligand concentrations.

State definitions

States are minimally defined by a name and should be added to a csv file. Macrostate classes can be added as additional columns with the name of the class being the column header.

name,n_protons,n_sodium
1,0,0
2,0,1
3,1,0
4,1,1

Graph definition

States are not enough to define the graph, you'll need edges. These edges are the free energy differences between states and are characterized by a specific type of process.

Multibind allows for three process type, which are specified under the ligand column:

• "H+": proton binding which takes as its free energy value, the pKa.
• general ligand: binding of a general ligand. The standard state free energy in kT. By defining the concentration to build the cycle, this free energy becomes concentration dependent.
• "helm": undefined process which takes a free energy directly in kT.

In defining the edges, always treat the free energies as going from state 1 to state 2 for that process. For 'H+', state 1 should be the deprotonated state and state 2 is the protonated state. For a general ligand, state 1 is the unbound state and state 2 is the bound state. Failure to do so will assign the negative of the desired free energy to that edge.

# graph.csv
state1,state2,value,variance,ligand,standard_state
1,2,-10,0.1,Na+,1
2,3,5.697116,0.1,H+,1
4,3,-6,0.1,Na+,1
1,4,7.434294,0.1,H+,1

Example code

The standard Multibind object is used to solve the graph at one point in concentration space.

import multibind as mb

concentrations = {'Na': 0.150}

c = mb.Multibind()
c.read_graph("examples/input/4-state-diamond/graph.csv",comment="#")
c.read_states("examples/input/4-state-diamond/states.csv")
c.concentrations = concentrations
c.build_cycle(pH=7)
c.MLE(svd=True) 
# compute the effective energy difference between two macrostates
# if you are unsure of the values to pass to the function, look
# at either your state file or the contents of c.states
c.effective_energy_difference("N_protons",1,2)

The MultibindScanner can be used to scan across a bunch of concentrations.

import multibind as mb

state_file = 'examples/input/4-state-diamond/states.csv'
graph_file = 'examples/input/4-state-diamond/graph.csv'

scanner = mb.MultibindScanner(state_file, graph_file, comment_char='#')

concentrations = {'H+': [7, 8, 9], 'Na+': [0.200, 0.150, 0.100]}
# This will MLE calculations across 9 points in concentration space
# the results will be in an xarray Dataset that can be accessed with
# scanner.results
scanner.run(concentrations, svd=True)

Citation

When using multibind in published works, please cite the following preprint:

Kenney, Ian Michael, and Oliver Beckstein. Thermodynamically Consistent Determination of Free Energies and Rates in Kinetic Cycle Models. 2023. doi:10.1101/2023.04.08.536126.