What the structures of the cytochrome c oxidase tell us about its mechanism

Cytochrome c oxidase (CcO) reduces molecular oxygen in a process coupled with proton pumping [1,2]. Models for proton pumping activity of CcO can be divided into two groups: one in which haem a is the key player, and another where this role is covered by the oxygen reduction site [1-3]. However, all currently accepted models require, more or less explicitly, an ordered sequence of events. We show that available structures of CcO can be clustered in four groups. These structural observations, and the experimental data on which there is a general consensus, suggest a four-state, stochastic pump model [4]. This model implies the observed convex dependence of the stoichiometry of the pump on the electron transfer rate [5], while to explain this phenomenon strictly deterministic models require a series of ad hoc assumptions (e.g. slipping mechanisms) [1,3,5]. Therefore, these results lead us to conclude that a stochastic conformational coupling could be in action in the energy transduction operated by this protein machine [4]. [1] M. Wikström, K. Krab, V. Sharma, Oxygen activation and energy conservation by cytochrome c oxidase, Chem, Rev. 118 (2018) 2469-2490. [2] S. Yoshikawa, A. Shimada, Reaction mechanism of cytochrome c oxidase, Chem. Rev. 115 (2015) 1936-1989. [3] N. Capitanio, L.L. Palese, G. Capitanio, et al., Allosteric interactions and proton conducting pathways in proton pumping aa(3) oxidases: heme a as a key coupling element, Biochim. Biophys. Acta 1817 (2012) 558-566. [4] L.L. Palese, Cytochrome c oxidase structures suggest a four-state stochastic pump mechanism, Phys. Chem. Chem. Phys. 21 (2019) 4822-4830. [5] N. Capitanio, G. Capitanio, D.A. Demarinis, et al., Factors affecting the H+/e- stoichiometry in mitochondrial cytochrome c oxidase: influence of the rate of electron flow and transmembrane delta pH. Biochemistry 35 (1996) 10800-10806

Protein dynamics: complex by itself

Biological functions are intimately rooted in biopolymer dynamics. It is commonly accepted that proteins can be considered as complex systems, but the origin of such complexity is still not fully understood. Moreover, it is still not really clear if proteins are true complex systems or complicated ones. Here, molecular dynamics simulations on a two helix bundle protein have been performed, and protein trajectories have been analyzed by using correlation functions in the frequency domain. We show that even a simple protein exhibits the hallmarks of complex systems. Moreover, the molecular bases of this complex behavior are possessed completely by the protein itself, because such complexity emerges without considering the solvent explicitly

Conformations of the HIV-1 protease: A crystal structure data set analysis

The HIV protease is an important drug target for HIV/AIDS therapy, and its structure and function have been extensively investigated. This enzyme performs an essential role in viral maturation by processing specific cleavage sites in the Gag and Gag-Pol precursor polyproteins so as to release their mature forms. This 99 amino acid aspartic protease works as a homodimer, with the active site localized in a central cavity capped by two flexible flap regions. The dimer presents closed or open conformations, which are involved in the substrate binding and release. Here the results of the analysis of a HIV-1 protease data set containing 552 dimer structures are reported. Different dimensionality reduction methods have been used in order to get information from this multidimensional database. Most of the structures in the data set belong to two conformational clusters. An interesting observation that comes from the analysis of these data is that some protease sequences are localized preferentially in specific areas of the conformational landscape of this protein

Cytochrome c oxidase structures suggest a four-state stochastic pump mechanism

Cytochrome c oxidase catalyses the terminal step of cellular respiration in eukaryotes and in many prokaryotes. This enzyme reduces molecular oxygen by means of a process coupled with proton pumping. Models for proton pumping activity in cytochrome c oxidase can be divided into two groups, which are still strongly debated to date: one in which haem a is the key player, and another where this role is covered by the oxygen reduction site. Current models share the fact of requesting, more or less explicitly, an ordered sequence of events. Here, we show that all the available subunit I structures of this enzyme can be clustered in four groups. Starting from these structural observations, and considering the large corpus of available experimental data and theoretical considerations, a simple four-state (stochastic) pump model is proposed. This model implies a series of characteristics that reflect the behavior of the real enzyme in a natural way, where strictly sequential models require ad hoc assumptions (e.g. slipping mechanisms). Our results suggest that the stochastic conformational coupling could be a mechanism for energy transduction used by the protein machines

Heme-copper oxidases: could they be stochastic machines?

Heme-copper oxidases (HCOs) are the terminal enzymes of many aerobic respiratory chains, including the mitochondrial one. HCOs reduce molecular oxygen in a process coupled with proton pumping [1,2]. Despite decades of intense work, some features of this proton pump mechanism still remain controversial [1-3]. Currently accepted models require, more or less explicitly, an ordered sequence of events, and can be considered deterministic. Taking into account the cytochrome c oxidase clusters of structures and experimental data on which there is a general consensus, we suggested a stochastic pump mechanism for this enzyme class [4]. From a biochemical point of view, the model is essentially based on the decoupling of the redox linked events at the proton loading site from the fluctuations of the access barriers to the intramolecular proton conduction pathways. This model predicts some pump features that can be hardly explained by deterministic models, such as the convex dependence of the stoichiometry of the pump on the electron transfer rate [1,3,5]. Furthermore, this stochastic model provides a rational explanation for contrasting evidences from single-molecule experiments performed on HCOs incorporated in proteoliposomes and predicts when it is more likely to observe leak states during HCO turnover [6,7]. [1] M. Wikström, K. Krab, V. Sharma, Chem. Rev. 118 (2018) 2469-2490. [2] S. Yoshikawa, A. Shimada, Chem. Rev. 115 (2015) 1936-1989. [3] N. Capitanio, L.L. Palese, G. Capitanio, et al., Biochim. Biophys. Acta 1817 (2012) 558-566. [4] L.L. Palese, Phys. Chem. Chem. Phys. 21 (2019) 4822-4830. [5] N. Capitanio, G. Capitanio, D.A. Demarinis, et al., Biochemistry 35 (1996) 10800-10806. [6] Li M, Jørgensen SK, McMillan DG, et al., J. Am. Chem. Soc. 137 (2015) 16055-16063. [7] Berg J, Block S, Höök F, et al., Isr. J. Chem. 57 (2017) 437 – 445

Protein States as Symmetry Transitions in the Correlation Matrices

Over the last few years, there has been significant progress in the knowledge on protein folding. However, some aspects of protein folding still need further attention. One of these is the exact relationship between the folded and unfolded states and the differences between them. Whereas the folded state is well known, at least from a structural point of view (just think of the thousands of structures in online databases), the unfolded state is more elusive. Also, these are dynamic states of matter, and this aspect cannot be overlooked. Molecular dynamics-derived correlation matrices are an invaluable source of information on the protein dynamics. Here, bulk eigenvalue spectra of the correlation matrices obtained from the Trp-cage dynamics in the folded and unfolded states have been analyzed. The associated modes represent localized vibrations and are significantly affected by the fine details of the structure and interactions. Therefore, these bulk modes can be used as probes of the protein local dynamics in different states. The results of these analyses show that the correlation matrices describing the folded and unfolded dynamics belong to different symmetry classes. This finding provides new support to the phase-transition models of protein folding

Random Matrix Theory in molecular dynamics analysis

It is well known that, in some situations, principal component analysis (PCA) carried out on molecular dynamics data results in the appearance of cosine-shaped low index projections. Because this is reminiscent of the results obtained by performing PCA on a multidimensional Brownian dynamics, it has been suggested that short-time protein dynamics is essentially nothing more than a noisy signal. Here we use Random Matrix Theory to analyze a series of short-time molecular dynamics experiments which are specifically designed to be simulations with high cosine content. We use as a model system the protein apoCox17, a mitochondrial copper chaperone. Spectral analysis on correlation matrices allows to easily differentiate random correlations, simply deriving from the finite length of the process, from non-random signals reflecting the intrinsic system properties. Our results clearly show that protein dynamics is not really Brownian also in presence of the cosine-shaped low index projections on principal axes

A random version of principal component analysis in data clustering

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance/correlation matrix of the analyzed data. However, to properly work with high-dimensional data sets, PCA poses severe mathematical constraints on the minimum number of different replicates, or samples, that must be included in the analysis. Generally, improper sampling is due to a small number of data respect to the number of the degrees of freedom that characterize the ensemble. In the field of life sciences it is often important to have an algorithm that can accept poorly dimensioned data sets, including degenerated ones. Here a new random projection algorithm is proposed, in which a random symmetric matrix surrogates the covariance/correlation matrix of PCA, while maintaining the data clustering capacity. We demonstrate that what is important for clustering efficiency of PCA is not the exact form of the covariance/correlation matrix, but simply its symmetry

Analysis of the conformations of the HIV-1 protease from a large crystallographic data set

The HIV-1 protease performs essential roles in viral maturation by processing specific cleavage sites in the Gag and Gag-Pol precursor polyproteins to release their mature forms. Here the analysis of a large HIV-1 protease data set (containing 552 dimer structures) are reported. These data are related to article entitled “Conformations of the HIV-1 protease: a crystal structure data set analysis” (Palese, 2017) [1]