Transition probabilities between conformational states

ENCoM can be used to compute transition probabilities between two conformational states of the same macromolecule. These probabilities do not represent actual thermodynamic properties but give an indication of which state is favored by the computed normal modes. For a detailed explanation of the metric, see the following paper: Modelling conformational state dynamics and its role on infection for SARS-CoV-2 Spike protein variants.

In the nrgten_examples repository, the open and closed forms of the citrate synthase enzyme have been cleaned up from water and solvent molecules and are called open_clean.pdb and closed_clean.pdb. The transition probabilities between the states can be computed in the following way:

from nrgten.encom import ENCoM
from nrgten.metrics import get_transit_probs

open_cs = ENCoM("open_clean.pdb")
closed_cs = ENCoM("closed_clean.pdb")
prob_open, prob_closed = get_transit_probs(open_cs, closed_cs, gamma=1)

The gamma parameter is a Boltzmann scaling factor. Lower values of gamma translate to a bigger contribution of the slow-frequency normal modes. The default value is 1, but you may have to explore different values for your system and fit against experimental data like described in our paper mentioned above.

If we print the probabilities:

print("prob_open: {}, prob_closed: {}".format(prob_open, prob_closed))

We get the following values:

prob_open : 0.28940086631043577, prob_closed : 0.43081399660689834

The aspartic acid in position 239 has been mutated to a lysine in both conformations using MODELLER (doi.org/10.1002/cpbi.3). We can compute the same transition probabilities using the mutated forms:

from nrgten.encom import ENCoM
from nrgten.metrics import get_transit_probs

open_cs_mut = ENCoM("open_clean_LYS239.pdb")
closed_cs_mut = ENCoM("closed_clean_LYS239.pdb")
prob_open_mut, prob_closed_mut = get_transit_probs(open_cs_mut, closed_cs_mut, gamma=1)
print("prob_open_mut: {}, prob_closed_mut: {}".format(prob_open_mut, prob_closed_mut))

This gives:

prob_open_mut : 0.2903252666753628, prob_closed_mut : 0.4304065571363618

So we can see that the mutation slightly favors the open state. Here is the full documentation for the get_transit_probs method:

nrgten.metrics.get_transit_probs(enm_a, enm_b, gamma=1, alignment=None)

Computes the transition ‘probabilities’ of reaching state B from state A and vice versa.

Parameters:

  • enm_a (ENM) – The ENM object representing state A.

  • enm_b (ENM) – The ENM object representing state B.

  • gamma (float, optional) – The Boltzmann scaling factor.

  • alignment (list, optional) – list of 2 lists of matching indices. Example: The alignment of sequences enm_a: -XYY-Z and enm_b: ZXYYXZ would give alignment=[[0,1,2,3],[1,2,3,5]]

Returns:

tuple containing:

p_a(float): the probability of reaching state A from state B

p_b(float): the probability of reaching state B from state A

Return type:

tuple