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

Abstract

The ligand migration network for O2–diffusion in truncated Hemoglobin N is analyzed based on three different clustering schemes. For coordinate-based clustering, the conventional k–means and the kinetics-based Markov Clustering (MCL) methods are employed, whereas the locally scaled diffusion map (LSDMap) method is a collective-variable-based approach. It is found that all three methods agree well in their geometrical definition of the most important docking site, and all experimentally known docking sites are recovered by all three methods. Also, for most of the states, their population coincides quite favourably, whereas the kinetics of and between the states differs. One of the major differences between k–means and MCL clustering on the one hand and LSDMap on the other is that the latter finds one large primary cluster containing the Xe1a, IS1, and ENT states. This is related to the fact that the motion within the state occurs on similar time scales, whereas structurally the state is found to be quite diverse. In agreement with previous explicit atomistic simulations, the Xe3 pocket is found to be a highly dynamical site which points to its potential role as a hub in the network. This is also highlighted in the fact that LSDMap cannot identify this state. First passage time distributions from MCL clusterings using a one- (ligand-position) and two-dimensional (ligand-position and protein-structure) descriptor suggest that ligand- and protein-motions are coupled. The benefits and drawbacks of the three methods are discussed in a comparative fashion and highlight that depending on the questions at hand the best-performing method for a particular data set may differ.

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

“…The fpt is a distribution of times which characterizes the duration to reach a given target state from any other snapshot along the trajectory. For the MD trajectory the fpt distribution can be calculated in a straightforward way by taking as a target one of the states known from k-means clustering [10]. For the Markov-state-model a suitable random walk on the transition matrix was generated.…”

“…In the following two different methods are employed: the structure-based k-means clustering and the kinetic-based complex network analysis rooted in the MCL algorithm. 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.…”

“…Transition network analysis was previously used to characterize the ligand O 2 migration in truncated hemoglobin trHbN [10]. Clustering of the states included only the O 2 -positions and neglected the influence of protein fluctuation.…”

“…The transition between such pockets is a thermally activated process and coupling to the protein motion was found for similar situations in myoglobin (Mb), another topologically related globular protein [2,4]. Finally, ligand migration in trHbN was characterized from transition networks which is an effective way of investigating available states and their populations in complex systems [9,10].…”

“…To gain insight into whether and how protein dynamics is coupled to ligand motion a recently completed study on ligand motion in trHbN was extended to include the protein degrees of freedom [10] and the dynamics of multiple unbound ligands is characterized from explicit atomistic simulations. Both aspects employ state-of-the art simulation and analysis techniques suitable for quantitative investigations of condensed-phase systems.…”