Fortuitous Correlations in Molecular Dynamics Simulations: Their Harmful Influence on the Probability Distributions of the Main Principal Components.

Nonsense correlations frequently develop between independent random variables that evolve with time. Therefore, it is not surprising that they appear between the components of vectors carrying out multidimensional random walks, such as those describing the trajectories of biomolecules in molecular dynamics simulations. The existence of these correlations does not imply in itself a problem. Still, it can present a problem when the trajectories are analyzed with an algorithm such as the Principal Component Analysis (PCA) because it seeks to maximize correlations without discriminating whether they have physical origin or not. In this Article, we employ random walks occurring on multidimensional harmonic potentials to evaluate the influence of fortuitous correlations in PCA. We demonstrate that, because of them, this algorithm affords misleading results when applied to a single trajectory. The errors do not only affect the directions of the first eigenvectors and their eigenvalues, but the very definition of the molecule's "essential space" may be wrong. Additionally, the main principal component's probability distributions present artificial structures which do not correspond with the shape of the potential energy surface. Finally, we show that the PCA of two realistic protein models, human serum albumin and lysozyme, behave similarly to the simple harmonic models. In all cases, the problems can be mitigated and eventually eliminated by doing PCA on concatenated trajectories formed from a large enough number of individual simulations.

The dynamics of the flavin, NADPH, and active site loops determine the mechanism of activation of class B flavin-dependent monooxygenases.

Flavin-dependent monooxygenases (FMOs) constitute a diverse enzyme family that catalyzes crucial hydroxylation, epoxidation, and Baeyer-Villiger reactions across various metabolic pathways in all domains of life. Due to the intricate nature of this enzyme family's mechanisms, some aspects of their functioning remain unknown. Here, we present the results of molecular dynamics computations, supplemented by a bioinformatics analysis, that clarify the early stages of their catalytic cycle. We have elucidated the intricate binding mechanism of NADPH and L-Orn to a class B monooxygenase, the ornithine hydroxylase from Aspergillus $$ Aspergillus $$ fumigatus $$ fumigatus $$ known as SidA. Our investigation involved a comprehensive characterization of the conformational changes associated with the FAD (Flavin Adenine Dinucleotide) cofactor, transitioning from the out to the in position. Furthermore, we explored the rotational dynamics of the nicotinamide ring of NADPH, shedding light on its role in facilitating FAD reduction, supported by experimental evidence. Finally, we also analyzed the extent of conservation of two Tyr-loops that play critical roles in the process.

Dynamics and Function of sRNA/mRNAs Under the Scrutiny of Computational Simulation Methods.

Molecular dynamics simulations have proved extremely useful in investigating the functioning of proteins with atomic-scale resolution. Many applications to the study of RNA also exist, and their number increases by the day. However, implementing MD simulations for RNA molecules in solution faces challenges that the MD practitioner must be aware of for the appropriate use of this tool. In this chapter, we present the fundamentals of MD simulations, in general, and the peculiarities of RNA simulations, in particular. We discuss the strengths and limitations of the technique and provide examples of its application to elucidate small RNA's performance.

On the Uses of PCA to Characterise Molecular Dynamics Simulations of Biological Macromolecules: Basics and Tips for an Effective Use.

Principal Component Analysis (PCA) is a procedure widely used to examine data collected from molecular dynamics simulations of biological macromolecules. It allows for greatly reducing the dimensionality of their configurational space, facilitating further qualitative and quantitative analysis. Its simplicity and relatively low computational cost explain its extended use. However, a judicious implementation of PCA requires the knowledge of its theoretical grounds as well as its weaknesses and capabilities. In this article, we review these issues and discuss several strategies developed over the last years to mitigate the main PCA flaws and enhance the reproducibility of its results.

Recognition and Binding of RsmE to an AGGAC Motif of RsmZ: Insights from Molecular Dynamics Simulations.

CsrA/RsmE is a post-transcriptional regulator protein widely distributed in bacteria. It impedes the expression of target mRNAs by attaching their 5' untranslated region. The translation is restored by small, noncoding RNAs that sequester CsrA/RsmE acting as sponges. In both cases, the protein recognizes and attaches to specific AGGAX and AXGGAX motifs, where X refers to any nucleotide. RsmZ of Pseudomonas protegens is one of these small RNAs. The structures of some of its complexes with RsmE were disclosed a few years ago. We have used umbrella sampling simulations to force the unbinding of RsmE from the AGGAC motif located in the single-stranded region sited between stem loops 2 and 3 of RsmZ. The calculations unveiled the identity of the main residues and nucleotides involved in the process. They also showed that the region adopts a hairpin-like conformation during the initial stages of the binding. The ability to acquire this conformation requires that the region has a length of at least nine nucleotides. Besides, we performed standard molecular dynamics simulations of the isolated fragments, analyzed their typical conformations, and characterized their movements. This analysis revealed that the free molecules oscillate along specific collective coordinates that facilitate the initial stages of the binding. The results strongly suggest that the flexibility of the single-stranded region of RsmZ crucially affects the ability of its binding motif to catch RsmE.

Ion Selectivity in P2X Receptors: A Comparison between hP2X3 and zfP2X4.

Charge discrimination in P2X receptors occurs in two stages. The first stage takes place in the extracellular vestibule. The second one happens as the ions travel across the pore. The search of the amino acids required to achieve these goals has focused on negatively charged residues conserved among the family members. This strategy, however, has afforded baffling results since residues that strongly influence ion selectivity in a given member are not present in others. This finding suggests that alternative family members could achieve the same goal using different molecular approaches. We have compared the mechanisms of charge discrimination in the extracellular vestibule of zebrafish P2X4 (zfP2X4) and human P2X3 (hP2X3), employing molecular dynamics simulations. In particular, we have analyzed how the mutation of residues D59 and D61 of zfP2X4 and residues E46, D53, and E57 of hP2X3 influence ion behavior. The results indicate that both D59 and D61 are required to confer the extracellular vestibule of zfP2X4 a preference for cations. In contrast, the presence of D53 suffices to provide that capacity to hP2X3. We also computed the potentials of mean force for the passage of Na+ and Cl- through the pore of hP2X3. These profiles were compared against those already available for zfP2X4. Altogether, the results provide a detailed description of the mechanisms employed by these receptors to discriminate between cations and anions.

Molecular Dynamics Simulations Unveil the Basis of the Sequential Binding of RsmE to the Noncoding RNA RsmZ.

CsrA/RsmE are dimeric proteins that bind to targeted mRNAs repressing translation. This mechanism modulates several metabolic pathways and allows bacteria to efficiently adjust their responses to environmental changes. In turn, small RNAs (sRNA) such as CsrB or RsmZ, restore translation by sequestering CsrA/RsmE dimers. Thus, these molecules act in tandem as a gene-expression regulatory system. Recently, a combined NMR-EPR approach solved the structure of part of RsmZ of Pseudomonas fluorescens, attached to three RsmE dimers. The study demonstrated that RsmE assembles onto RsmZ following a specific sequential order. The reasons underlying this peculiar behavior are still unclear. Here, we present a molecular dynamics analysis that explores the conformational diversity of RsmZ and RsmZ-RsmE complexes. The results reveal a clear pattern regarding the exposure of the alternative GGA binding motifs of RsmZ. This pattern is tuned by the attachment of RsmE dimers. Altogether, the observations provide a simple and convincing explanation for the order observed in the sequestration of RsmE dimers. Typical structures for RsmZ and RsmZ-RsmE complexes have been identified. Their characteristics concerning the exposure of the GGA sequences are presented and their most significant interactions are described.

Positively Charged Residues in the Head Domain of P2X4 Receptors Assist the Binding of ATP.

P2X receptors are a family of trimeric cationic channels located in the membrane of mammalian cells. They open in response to the binding of ATP. The differences between the closed and open structures have been described in detail for some members of the family. However, the order in which the conformational changes take place as ATP enters the binding cleft, and the residues involved in the intermediate stages, are still unknown. Here, we present the results of umbrella sampling simulations aimed to elucidate the sequence of conformational changes that occur during the reversible binding of ATP to the P2X4 receptor. The simulations also provided information about the interactions that develop in the course of the process. In particular, they revealed the existence of a metastable state which assists the binding. This state is stabilized by positively charged residues located in the head domain of the receptor. Based on these findings, we propose a novel mechanism for the capture of ATP by P2X4 receptors.

Molecular Dynamics Simulations of Substrate Release from Trypanosoma cruzi UDP-Galactopyranose Mutase.

The enzyme UDP-galactopyranose mutase (UGM) represents a promising drug target for the treatment of infections with Trypanosoma cruzi. We have computed the Potential of Mean Force for the release of UDP-galactopyranose from UGM, using Umbrella Sampling simulations. The simulations revealed the conformational changes that both substrate and enzyme undergo during the process. It was determined that the galactopyranose portion of the substrate is highly mobile and that the opening/closing of the active site occurs in stages. Previously uncharacterized interactions with highly conserved residues were also identified. These findings provide new pieces of information that contribute to the rational design of drugs against T. cruzi.

Charge Discrimination in P2X4 Receptors Occurs in Two Consecutive Stages.

P2X receptors are a group of trimeric cationic channels that are activated by adenosine 5'-triphosphate. They perform critical roles in the membranes of mammalian cells, and their improper functioning is associated with numerous diseases. Despite the vast amount of research devoted to them, several aspects of their operation are currently unclear, including the causes of their charge selectivity. We present the results of molecular dynamics simulation, which shed light on this issue for the case of P2X4 channels. We examined in detail the behavior of Na+ and Cl- ions inside the receptor. The examination reveals that charge discrimination occurs in two stages. First, cations bear precedence over anions to enter the extracellular vestibule. Then, cations at the extracellular vestibule are more likely to cross the pore than anions in an equivalent position. In this manner, a thorough but straightforward analysis of computational simulations suggests a stepwise mechanism, without a unique determinant factor.

Steric Control of the Rate-Limiting Step of UDP-Galactopyranose Mutase.

Galactose is an abundant monosaccharide found exclusively in mammals as galactopyranose (Gal p), the six-membered ring form of this sugar. In contrast, galactose appears in many pathogenic microorganisms as the five-membered ring form, galactofuranose (Gal f). Gal f biosynthesis begins with the conversion of UDP-Gal p to UDP-Gal f catalyzed by the flavoenzyme UDP-galactopyranose mutase (UGM). Because UGM is essential for the survival and proliferation of several pathogens, there is interest in understanding the catalytic mechanism to aid inhibitor development. Herein, we have used kinetic measurements and molecular dynamics simulations to explore the features of UGM that control the rate-limiting step (RLS). We show that UGM from the pathogenic fungus Aspergillus fumigatus also catalyzes the isomerization of UDP-arabinopyranose (UDP-Ara p), which differs from UDP-Gal p by lacking a -CH2-OH substituent at the C5 position of the hexose ring. Unexpectedly, the RLS changed from a chemical step for the natural substrate to product release with UDP-Ara p. This result implicated residues that contact the -CH2-OH of UDP-Gal p in controlling the mechanistic path. The mutation of one of these residues, Trp315, to Ala changed the RLS of the natural substrate to product release, similar to the wild-type enzyme with UDP-Ara p. Molecular dynamics simulations suggest that steric complementarity in the Michaelis complex is responsible for this distinct behavior. These results provide new insight into the UGM mechanism and, more generally, how steric factors in the enzyme active site control the free energy barriers along the reaction path.

Consistent Principal Component Modes from Molecular Dynamics Simulations of Proteins.

Principal component analysis is a technique widely used for studying the movements of proteins using data collected from molecular dynamics simulations. In spite of its extensive use, the technique has a serious drawback: equivalent simulations do not afford the same PC-modes. In this article, we show that concatenating equivalent trajectories and calculating the PC-modes from the concatenated one significantly enhances the reproducibility of the results. Moreover, the consistency of the modes can be systematically improved by adding more individual trajectories to the concatenated one.

Theoretical Insights into the Reaction and Inhibition Mechanism of Metal-Independent Retaining Glycosyltransferase Responsible for Mycothiol Biosynthesis.

Understanding enzymatic reactions with atomic resolution has proven in recent years to be of tremendous interest for biochemical research, and thus, the use of QM/MM methods for the study of reaction mechanisms is experiencing a continuous growth. Glycosyltransferases (GTs) catalyze the formation of glycosidic bonds, and are important for many biotechnological purposes, including drug targeting. Their reaction product may result with only one of the two possible stereochemical outcomes for the reacting anomeric center, and therefore, they are classified as either inverting or retaining GTs. While the inverting GT reaction mechanism has been widely studied, the retaining GT mechanism has always been controversial and several questions remain open to this day. In this work, we take advantage of our recent GPU implementation of a pure QM(DFT-PBE)/MM approach to explore the reaction and inhibition mechanism of MshA, a key retaining GT responsible for the first step of mycothiol biosynthesis, a low weight thiol compound found in pathogens like Mycobacterium tuberculosis that is essential for its survival under oxidative stress conditions. Our results show that the reaction proceeds via a front-side SNi-like concerted reaction mechanism (DNAN in IUPAC nomenclature) and has a 17.5 kcal/mol free energy barrier, which is in remarkable agreement with experimental data. Detailed analysis shows that the key reaction step is the diphosphate leaving group dissociation, leading to an oxocarbenium-ion-like transition state. In contrast, fluorinated substrate analogues increase the reaction barrier significantly, rendering the enzyme effectively inactive. Detailed analysis of the electronic structure along the reaction suggests that this particular inhibition mechanism is associated with fluorine's high electronegative nature, which hinders phosphate release and proper stabilization of the transition state.

The Dynamic Behavior of the P2X4 Ion Channel in the Closed Conformation.

We present the results of a detailed molecular dynamics study of the closed form of the P2X4 receptor. The fluctuations observed in the simulations were compared with the changes that occur in the transition from the closed to the open structure. To get further insight on the opening mechanism, the actual displacements were decomposed into interchain motions and intrachain deformations. This analysis revealed that the iris-like expansion of the transmembrane helices mainly results from interchain motions that already take place in the closed conformation. However, these movements cannot reach the amplitude required for the opening of the channel because they are impeded by interactions occurring around the ATP binding pocket. This suggests that the union of ATP produces distortions in the chains that eliminate the restrictions on the interchain displacements, leading to the opening of the pore.

New insights into the meaning and usefulness of principal component analysis of concatenated trajectories.

A comparison between different conformations of a given protein, relating both structure and dynamics, can be performed in terms of combined principal component analysis (combined-PCA). To that end, a trajectory is obtained by concatenating molecular dynamics trajectories of the individual conformations under comparison. Then, the principal components are calculated by diagonalizing the correlation matrix of the concatenated trajectory. Since the introduction of this approach in 1995 it has had a large number of applications. However, the interpretation of the eigenvectors and eigenvalues so obtained is based on intuitive foundations, because analytical expressions relating the concatenated correlation matrix with those of the individual trajectories under consideration have not been provided yet. In this article, we present such expressions for the cases of two, three, and an arbitrary number of concatenated trajectories. The formulas are simple and show what is to be expected and what is not to be expected from a combined-PCA. Their correctness and usefulness is demonstrated by discussing some representative examples. The results can be summarized in a simple sentence: the correlation matrix of a concatenated trajectory is given by the average of the individual correlation matrices plus the correlation matrix of the individual averages. From this it follows that the combined-PCA of trajectories belonging to different free energy basins provides information that could also be obtained by alternative and more straightforward means.

QM/MM molecular dynamics study of the galactopyranose → galactofuranose reaction catalysed by Trypanosoma cruzi UDP-galactopyranose mutase.

The enzyme UDP-Galactopyranose Mutase (UGM) catalyses the conversion of galactopyranose into galactofuranose. It is known to be critical for the survival and proliferation of several pathogenic agents, both prokaryotic and eukaryotic. Among them is Trypanosoma cruzi, the parasite responsible for Chagas' disease. Since the enzyme is not present in mammals, it appears as a promising target for the design of drugs to treat this illness. A precise knowledge of the mechanism of the catalysed reaction would be crucial to assist in such design. In this article we present a detailed study of all the putative steps of the mechanism. The study is based on QM/MM free energy calculations along properly selected reaction coordinates, and on the analysis of the main structural changes and interactions taking place at every step. The results are discussed in connection with the experimental evidence and previous theoretical studies.

Unraveling the differences of the hydrolytic activity of Trypanosoma cruzi trans-sialidase and Trypanosoma rangeli sialidase: a quantum mechanics-molecular mechanics modeling study.

Chagas' disease, also known as American trypanosomiasis, is a lethal, chronic disease that currently affects more than 10 million people in Central and South America. The trans-sialidase from Trypanosoma cruzi (T. cruzi, TcTS) is a crucial enzyme for the survival of this parasite: sialic acids from the host are transferred to the cell surface glycoproteins of the trypanosome, thereby evading the host's immune system. On the other hand, the sialidase of T. rangeli (TrSA), which shares 70% sequence identity with TcTS, is a strict hydrolase and shows no trans-sialidase activity. Therefore, TcTS and TrSA represent an excellent framework to understand how different catalytic activities can be achieved with extremely similar structures. By means of combined quantum mechanics-molecular mechanics (QM/MM, SCC-DFTB/Amberff99SB) calculations and umbrella sampling simulations, we investigated the hydrolysis mechanisms of TcTS and TrSA and computed the free energy profiles of these reactions. The results, together with our previous computational investigations, are able to explain the catalytic mechanism of sialidases and describe how subtle differences in the active site make TrSA a strict hydrolase and TcTS a more efficient trans-sialidase.

Free-energy computations identify the mutations required to confer trans-sialidase activity into Trypanosoma rangeli sialidase.

Trypanosoma rangeli's sialidase (TrSA) and Trypanosoma cruzi's trans-sialidase (TcTS) are members of the glycoside hydrolase family 33 (GH-33). They share 70% of sequence identity and their crystallographic Cα RMSD is 0.59 Å. Despite these similarities they catalyze different reactions. TcTS transfers sialic acid between glycoconjugates while TrSA can only cleave sialic acid from sialyl-glyconjugates. Significant effort has been invested into unraveling the differences between TrSA and TcTS, and into conferring TrSA with trans-sialidase activity through appropriate point mutations. Recently, we calculated the free-energy change for the formation of the covalent intermediate (CI) in TcTS and performed an energy decomposition analysis of that process. In this article we present a similar study for the formation of the CI in TrSA, as well as in a quintuple mutant (TrSA5mut), which has faint trans-sialidase activity. The comparison of these new results with those previously obtained for TcTS allowed identifying five extra mutations to be introduced in TrSA5mut that should create a mutant (TrSA10mut ) with high trans-sialidase activity.

Free energy study of the catalytic mechanism of Trypanosoma cruzi trans-sialidase. From the Michaelis complex to the covalent intermediate.

Trypanosoma cruzi trans-sialidase (TcTS) is a crucial enzyme for the infection of Trypanosoma cruzi, the protozoa responsible for Chagas' disease in humans. It catalyzes the transfer of sialic acids from the host's glycoconjugates to the parasite's glycoconjugates. Based on kinetic isotope effect (KIE) studies, a strong nucleophilic participation at the transition state could be determined, and recently, elaborate experiments used 2-deoxy-2,3-difluorosialic acid as substrate and were able to trap a long-lived covalent intermediate (CI) during the catalytic mechanism. In this paper, we compute the KIE and address the entire mechanistic pathway of the CI formation step in TcTS using computational tools. Particularly, the free energy results indicate that in the transition state there is a strong nucleophilic participation of Tyr342, and after this, the system collapsed into a stable CI. We find that there is no carbocation intermediate for this reaction. By means of the energy decomposition method, we identify the residues that have the biggest influence on catalysis. This study facilitates the understanding of the catalytic mechanism of TcTS and can serve as a guide for future inhibitor design studies.

Proton transfer facilitated by ligand binding. An energetic analysis of the catalytic mechanism of Trypanosoma cruzi trans-sialidase.

Trans-sialidase is a crucial enzyme for the infection of Trypanosoma cruzi, the protozoa responsible for Chagas' disease in humans. This enzyme catalyzes the transfer of sialic acids from mammalian host cells to parasitic cell surfaces in order to mask the infection from the host's immune system. It represents a promising target for the development of therapeutics to treat the disease and has been subject of extensive structural studies. Elaborate experiments suggested formation of a long-lived covalent intermediate in the catalytic mechanism and identified a Tyr/Glu pair as an unusual catalytic couple. This requires that the tyrosine hydroxyl proton is transferred to the carboxylate group of glutamate before the nucleophilic attack. Since the solution pK(a)s of tyrosine and glutamate are very different, this transfer can only be accomplished if the reaction environment selectively stabilizes the product state. We compute the free energy profile for the proton transfer in different environments, and our results indicate that it can take place in the active site of trans-sialidase, but only after substrate binding. By means of the energy decomposition method, we explain the influence that the active site residues exert on the reaction and how the pattern is changed when the substrate is present. This study represents an initial step that can shed light on our understanding of the catalytic mechanism of this reaction.