Augmented Modelling with Natural Move Monte Carlo Simulations

In the last group meeting I reported on the progress that I have made regarding the development of a protocol for the systematic use of Natural Move Monte Carlo simulations.

Natural Move Monte Carlo simulations
Natural Moves are degrees of freedom that describe the collective motion of groups of residues. In DNA this might be the concerted motion of a double helix; in proteins this could be the movement of a stable secondary structure element such as a beta-sheet. These segments are joined by so called melting areas. At each simulation step the segments are propagated independently in an MC fashion. The resulting chain breaks are resolved by a chain closure algorithm that acts on the melting areas. This results in a reduction of degrees of freedom of several orders of magnitude. Therefore, large complexes and conformational changes can be sampled more effectively.

In order to get sensible results, however, the initial decomposition of the system is important. The challenge is to accurately represent the plasticity of the system, while keeping the number of degrees of freedom as small as possible. Detailed insight into the flexibility of the system might be gained from experimental sources such as NMR or computational methods such as MD simulations and Normal Mode Analysis. This can help with defining segments and melting areas. However, there are many systems for which this data is not available. Even if it is, there is no guarantee that the segmentation is correct.

Therefore, I am developing a protocol that allows for the evaluation of a range of different test cases that each reflect a unique set of segments and melting areas.

Augmented Modelling Protocol
This protocol is aimed at the systematic evaluation of NMMC segmentations. It allows researchers to feed experimental information, biological knowledge and educated guesses into molecular simulations and so provides a framework for testing competing hypotheses. The protocol has four steps.

Step 1: Segmentation of the system into low-level segments
The initial segmentation contains all possible areas of flexibility that may play a role in conformational changes in the system of interest. This decision may be influenced by many sources. For now, however, we only consider secondary structure information. Helices and beta strands are treated as potential segments. Unstructured regions such as kinks, loops and random coils are treated as melting areas. For a small fold with four helices we get the segmentation shown in figure 1a.

Step 2: Formulate test cases
Generate multiple test cases that reflect hypotheses about the mechanism of interest. In this step we try to narrow down the degrees of freedom as much as possible in order to retain sampling efficiency. This is done by selectively deactivating some melting areas that were defined in step 1. For a system with three melting areas that can either be on or off, 2^3 = 8 different test cases may be generated (example shown in figure 1b).

Segmentation of a small α-fold.

Figure 1 a) Segmentation of a small α-fold. The blue rectangles represent α-helices. The dashed lines indicate the presence of melting areas I, II and III. Each melting area can be switched on or off (1/0) b) Example of a test case in which the first of three melting area is switched off. c) The six degrees of freedom along which a segment is propagated.

Step 3: Perform simulations
Sample the conformational space of all test cases that were generated in step 2. We generally use Parallel Tempering or Simulated Tempering algorithm to accelerate the sampling process. These methods rely on the modulation of temperature to overcome energy barriers.

Step 4: Evaluate results
Score the results against a given control and rank the test cases accordingly. The scoring might be done by comparing experimental distributions of observables with those generated by simulations (e.g. Kullback-Leibler divergence). A test case that reproduces desired expectation values of observables might then be considered as a candidate hypothesis for a certain structural mechanism.

What’s next?
I am currently working on example uses for this protocol. These include questions regarding aspects of protein folding and the stability of the empty MHC II binding groove.

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