Accounting for the kinetics in order parameter analysis: Lessons from theoretical models and a disordered peptide

Abstract

Molecular simulations as well as single molecule experiments have been widely analyzed in terms of order parameters, the latter representing candidate probes for the relevant degrees of freedom. Notwithstanding this approach is very intuitive, mounting evidence showed that such description is not accurate, leading to ambiguous definitions of states and wrong kinetics. To overcome these limitations a framework making use of order parameter fluctuations in conjunction with complex network analysis is investigated. Derived from recent advances in the analysis of single molecule time traces, this approach takes into account of the fluctuations around each time point to distinguish between states that have similar values of the order parameter but different dynamics. Snapshots with similar fluctuations are used as nodes of a transition network, the clusterization of which into states provides accurate Markov-State-Models of the system under study. Application of the methodology to theoretical models with a noisy order parameter as well as the dynamics of a disordered peptide illustrates the possibility to build accurate descriptions of molecular processes on the sole basis of order parameter time series without using any supplementary information.

A comparative analysis of clustering algorithms: O2 migration in truncated hemoglobin I from transition networks

“…67 Within MCL, several methods have been proposed so far for the definition of these microstates, ranging from secondary structure strings, 67 RMSD clustering, 68 and order parameter fluctuations. 69 The discrete microstates time series built from the continuous O 2 trajectories were then mapped onto a transition network 67,70 with the properties described further below. In this network, nodes (i.e., microstates) are weighted with the total number of times they appear along the discrete trajectories.…”

Visualization and thermodynamic encoding of single-molecule partition function projections

“…The commonality of these examples is that they rely on ensemble-or time-averaging a collection of observable macromolecular features that are fundamentally sub-molecular in nature. Therefore, microscopic thermodynamic information, that is, microstate probabilities with atomic precision, is usually lost 21,22 . However, it is clear that the exploration of the spatial degrees of freedom underlying the configurational partition function can be expressed geometrically for a given system.…”

“…With the use of classical force fields (FFs) and emerging strategies such as network projections 21,24 , MD simulations allow computing equilibrium microstate probabilities with millions of microscopic molecular states and microsecond timescales, thereby offering the possibility of full convergence to the ergodic limit. A drawback in MD modelling is the dependence on FF validation, which limits its use to well-known systems.…”

Coupled protein–ligand dynamics in truncated hemoglobin N from atomistic simulations and transition networks

“…This approach was initially applied to single molecule experiments [28][29][30] and was recently extended for studying conventional order parameter time series [26]. Also this framework was successfully applied to the description of Fip35 folding mechanism [27].…”

“…k-means clustering [24,25] was extensively employed in our previous work which focused on the study of ligand coordinates only [10] and is used here as a benchmark for defining possible states of the system. The complex network analysis previously employed [26] allowed a straightforward incorporation of several degrees of freedom [27] that turns out to be useful here for the study of coupling between ligand and protein motion. For the details of the k-means clustering methods we refer the reader to the literature [24,25].…”