The FOF1 ATP synthase: from atomistic three-dimensional structure to the rotary-chemical function.

Molecular motors are multi-subunit complexes that are indispensable for accomplishing various tasks of the living cells. One such molecular motor is the FOF1 ATP synthase that synthesizes ATP at the expense of the membrane proton gradient. Elucidating the molecular origin of the motor function is challenging despite significant advances in various experimental fields. Currently atomic simulations of whole motor complexes cannot reach to functionally relevant time scales that extend beyond the millisecond regime. Moreover, to reveal the underlying molecular origin of the function, one must model the coupled chemical and conformational events using physically and chemically meaningful multiscaling techniques. In this review, we discuss our approach to model the action of the F1 and FO molecular motors, where emphasis is laid on elucidating the molecular origin of the driving force that leads to directional rotation at the expense of ATP hydrolysis or proton gradients. We have used atomic structures of the motors and used hierarchical multiscaling techniques to generate low dimensional functional free energy surfaces of the complete mechano-chemical process. These free energy surfaces were studied further to calculate important characteristics of the motors, such as, rotational torque, temporal dynamics, occurrence of intermittent dwell states, etc. We also studied the result of mutating various parts of the motor domains and our observations correspond very well with the experimental findings. Overall, our studies have generated a cumulative understanding of the motor action, and especially highlight the crucial role of electrostatics in establishing the mechano-chemical coupling.

Simulating the dynamics of the mechanochemical cycle of myosin-V.

The detailed dynamics of the cycle of myosin-V are explored by simulation approaches, examining the nature of the energy-driven motion. Our study started with Langevin dynamics (LD) simulations on a very coarse landscape with a single rate-limiting barrier and reproduced the stall force and the hand-over-hand dynamics. We then considered a more realistic landscape and used time-dependent Monte Carlo (MC) simulations that allowed trajectories long enough to reproduce the force/velocity characteristic sigmoidal correlation, while also reproducing the hand-over-hand motion. Overall, our study indicated that the notion of a downhill lever-up to lever-down process (popularly known as the powerstroke mechanism) is the result of the energetics of the complete myosin-V cycle and is not the source of directional motion or force generation on its own. The present work further emphasizes the need to use well-defined energy landscapes in studying molecular motors in general and myosin in particular.

The Physics and Physical Chemistry of Molecular Machines.

The concept of a "power stroke"-a free-energy releasing conformational change-appears in almost every textbook that deals with the molecular details of muscle, the flagellar rotor, and many other biomolecular machines. Here, it is shown by using the constraints of microscopic reversibility that the power stroke model is incorrect as an explanation of how chemical energy is used by a molecular machine to do mechanical work. Instead, chemically driven molecular machines operating under thermodynamic constraints imposed by the reactant and product concentrations in the bulk function as information ratchets in which the directionality and stopping torque or stopping force are controlled entirely by the gating of the chemical reaction that provides the fuel for the machine. The gating of the chemical free energy occurs through chemical state dependent conformational changes of the molecular machine that, in turn, are capable of generating directional mechanical motions. In strong contrast to this general conclusion for molecular machines driven by catalysis of a chemical reaction, a power stroke may be (and often is) an essential component for a molecular machine driven by external modulation of pH or redox potential or by light. This difference between optical and chemical driving properties arises from the fundamental symmetry difference between the physics of optical processes, governed by the Bose-Einstein relations, and the constraints of microscopic reversibility for thermally activated processes.

Torque, chemistry and efficiency in molecular motors: a study of the rotary-chemical coupling in F1-ATPase.

Detailed understanding of the action of biological molecular machines must overcome the challenge of gaining a clear knowledge of the corresponding free-energy landscape. An example for this is the elucidation of the nature of converting chemical energy to torque and work in the rotary molecular motor of F1-ATPase. A major part of the challenge involves understanding the rotary-chemical coupling from a non-phenomenological structure/energy description. Here we focused on using a coarse-grained model of F1-ATPase to generate a structure-based free-energy landscape of the rotary-chemical process of the whole system. In particular, we concentrated on exploring the possible impact of the position of the catalytic dwell on the efficiency and torque generation of the molecular machine. It was found that the experimentally observed torque can be reproduced with landscapes that have different positions for the catalytic dwell on the rotary-chemical surface. Thus, although the catalysis is undeniably required for torque generation, the experimentally observed position of the catalytic dwell at 80° might not have a clear advantage for the force generation by F1-ATPase. This further implies that the rotary-chemical couplings in these biological motors are quite robust and their efficiencies do not depend explicitly on the position of the catalytic dwells. Rather, the specific positioning of the dwells with respect to the rotational angle is a characteristic arising due to the structural construct of the molecular machine and might not bear any clear connection to the thermodynamic efficiency for the system.

Dissecting the role of the γ-subunit in the rotary-chemical coupling and torque generation of F1-ATPase.

Unraveling the molecular nature of the conversion of chemical energy (ATP hydrolysis in the α/ß-subunits) to mechanical energy and torque (rotation of the γ-subunit) in F1-ATPase is very challenging. A major part of the challenge involves understanding the rotary-chemical coupling by a nonphenomenological structure-energy description, while accounting for the observed torque generated on the γ-subunit and its change due to mutation of this unit. Here we extend our previous study that used a coarse-grained model of the F1-ATPase to generate a structure-based free energy landscape of the rotary-chemical process. Our quantitative analysis of the landscape reproduced the observed torque for the wild-type enzyme. In doing so, we found that there are several possibilities of torque generation from landscapes with various shapes and demonstrated that a downhill slope along the chemical coordinate could still result in negligible torque, due to ineffective coupling of the chemistry to the γ-subunit rotation. We then explored the relationship between the functionality and the underlying sequence through systematic examination of the effect of various parts of the γ-subunit on free energy surfaces of F1-ATPase. Furthermore, by constructing several types of γ-deletion systems and calculating the corresponding torque generation, we gained previously unknown insights into the molecular nature of the F1-ATPase rotary motor. Significantly, our results are in excellent agreement with recent experimental findings and indicate that the rotary-chemical coupling is primarily established through electrostatic effects, although specific contacts through γ-ionizable residue side chains are not essential for establishing the basic features of the coupling.

An effective coarse-grained model for biological simulations: recent refinements and validations.

Exploring the free energy landscape of proteins and modeling the corresponding functional aspects presents a major challenge for computer simulation approaches. This challenge is due to the complexity of the landscape and the enormous computer time needed for converging simulations. The use of various simplified coarse grained (CG) models offers an effective way of sampling the landscape, but most current models are not expected to give a reliable description of protein stability and functional aspects. The main problem is associated with insufficient focus on the electrostatic features of the model. In this respect, our recent CG model offers significant advantage as it has been refined while focusing on its electrostatic free energy. Here we review the current state of our model, describing recent refinements, extensions, and validation studies while focusing on demonstrating key applications. These include studies of protein stability, extending the model to include membranes, electrolytes and electrodes, as well as studies of voltage-activated proteins, protein insertion through the translocon, the action of molecular motors, and even the coupling of the stalled ribosome and the translocon. The examples discussed here illustrate the general potential of our approach in overcoming major challenges in studies of structure function correlation in proteins and large macromolecular complexes.

Electrostatic origin of the unidirectionality of walking myosin V motors.

Understanding the basis for the action of myosin motors and related molecular machines requires a quantitative energy-based description of the overall functional cycle. Previous theoretical attempts to do so have provided interesting insights on parts of the cycle but could not generate a structure-based free energy landscape for the complete cycle of myosin. In particular, a nonphenomenological structure/energy-based understanding of the unidirectional motion is still missing. Here we use a coarse-grained model of myosin V and generate a structure-based free energy surface of the largest conformational change, namely the transition from the post- to prepowerstroke movement. We also couple the observed energetics of ligand binding/hydrolysis and product release to that of the conformational surface and reproduce the energetics of the complete mechanochemical cycle. It is found that the release in electrostatic free energy upon changing the conformation of the lever arm and the convertor domain from its post- to prepowerstroke state provides the necessary energy to bias the system towards the unidirectional movement of myosin V on the actin filament. The free energy change of 11 kcal is also in the range of ∼2-3 pN, which is consistent with the experimentally observed stalling force required to stop the motor completely on its track. The conformational-chemical coupling generating a successful powerstroke cycle is believed to be conserved among most members of the myosin family, thus highlighting the importance of the previously unknown role of electrostatics free energy in guiding the functional cycle in other actin-based myosin motors.

Simulating the pulling of stalled elongated peptide from the ribosome by the translocon.

The nature of the coupling between the stalling of the elongated nascent peptide chain in the ribosome and its insertion through the translocon is analyzed, focusing on the recently discovered biphasic force that overcomes the stalling barrier. The origin of this long-range coupling is explored by coarse-grained simulations that combine the translocon (TR) insertion profile and the effective chemical barrier for the extension of the nascent chain in the ribosome. Our simulation determined that the inserted H segment is unlikely to climb the TR barrier in parallel with the peptide synthesis chemical step and that the nascent chain should first overcome the chemical barriers and move into the ribosome-TR gap region before the insertion into the TR tunnel. Furthermore, the simulations indicate that the coupled TR-chemistry free energy profile accounts for the biphasic force. Apparently, although the overall elongation/insertion process can be depicted as a tug-of-war between the forces of the TR and the ribosome, it is actually a reflection of the combined free-energy landscape. Most importantly, the present study helps to relate the experimental observation of the biphasic force to crucial information about the elusive path and barriers of the TR insertion process.

DNA bending propensity in the presence of base mismatches: implications for DNA repair.

DNA bending is believed to facilitate the initial recognition of the mismatched base for repair. The repair efficiencies are dependent on both the mismatch type and neighboring nucleotide sequence. We have studied bending of several DNA duplexes containing canonical matches: A:T and G:C; various mismatches: A:A, A:C, G:A, G:G, G:T, C:C, C:T, and T:T; and a bis-abasic site: X:X. Free-energy profiles were generated for DNA bending using umbrella sampling. The highest energetic cost associated with DNA bending is observed for canonical matches while bending free energies are lower in the presence of mismatches, with the lowest value for the abasic site. In all of the sequences, DNA duplexes bend toward the major groove with widening of the minor groove. For homoduplexes, DNA bending is observed to occur via smooth deformations, whereas for heteroduplexes, kinks are observed at the mismatch site during strong bending. In general, pyrimidine:pyrimidine mismatches are the most destabilizing, while purine:purine mismatches lead to intermediate destabilization, and purine:pyrimidine mismatches are the least destabilizing. The ease of bending is partially correlated with the binding affinity of MutS to the mismatch pairs and subsequent repair efficiencies, indicating that intrinsic DNA bending propensities are a key factor of mismatch recognition.

Electrostatic origin of the catalytic effect of a supramolecular host catalyst.

The development of enzyme mimetic catalysts as well as the analysis of the catalytic effects of such catalysts has been a major challenge for synthetic chemists. One of the impressive examples of artificial catalysts has been the development of a highly charged host compound that provides a significant acceleration to the hydrolysis of orthoformates and other systems. However, the origin of the catalytic effect has not been quantified, and its origin remains somewhat unclear. The understanding of the corresponding supramolecular catalysis has thus become a major challenge, both in terms of computational modeling and in terms of the analysis of the corresponding acid-catalyzed reaction. Here we present a computer simulation study and kinetic analyses that reproduce the experimentally observed catalytic effect, establishing that this effect is due to electrostatic stabilization of the positively charged transition state (relative to the uncharged bound complex). Our study illustrates the crucial need for careful analysis of the complex kinetics of the catalytic effect and the host system, as well as the need for computational modeling in analyzing the catalytic effect and in the potential design of better catalysts. Finally, our finding of the large stabilization of the bound H(3)O(+) points out the very low "local pH" inside the host system even when the solvent is kept at a high pH.

Realistic simulations of the coupling between the protomotive force and the mechanical rotation of the F0-ATPase.

The molecular origin of the action of the F(0) proton gradient-driven rotor presents a major puzzle despite significant structural advances. Although important conceptual models have provided guidelines of how such systems should work, it has been challenging to generate a structure-based molecular model using physical principles that will consistently lead to the unidirectional proton-driven rotational motion during ATP synthesis. This work uses a coarse-grained (CG) model to simulate the energetics of the F(0)-ATPase system in the combined space defined by the rotational coordinate and the proton transport (PTR) from the periplasmic side (P) to the cytoplasmic side (N). The model establishes the molecular origin of the rotation, showing that this effect is due to asymmetry in the energetics of the proton path rather than only the asymmetry of the interaction of the Asp on the c-ring helices and Arg on the subunit-a. The simulation provides a clear conceptual background for further exploration of the electrostatic basis of proton-driven mechanochemical systems.

Electrostatic origin of the mechanochemical rotary mechanism and the catalytic dwell of F1-ATPase.

Understanding the nature of energy transduction in life processes requires a quantitative description of the energetics of the conversion of ATP to ADP by ATPases. Previous attempts to do so have provided an interesting insight but could not account for the rotary mechanism by a nonphenomenological structure/energy description. In particular it has been very challenging to account for the observations of the 80° and 40° rotational substates, without any prior information about such states in the simulation procedure. Here we use a coarse-grained model of F1-ATPase and generate, without the adjustment of phenomenological parameters, a structure-based free energy landscape that reproduces the energetics of the mechanochemical process. It is found that the landscape along the relevant rotary path is determined by the electrostatic free energy and not by steric effects. Furthermore, the generated surface and the corresponding Langevin dynamics simulations identify a hidden conformational barrier that provides a new fundamental interpretation of the catalytic dwell and illuminate the nature of the energy conversion process.

Molecular mechanism by which palmitate inhibits PKR autophosphorylation.

PKR (double-stranded RNA-activated protein kinase) is an important component of the innate immunity, antiviral, and apoptotic pathways. Recently, our group found that palmitate, a saturated fatty acid, is involved in apoptosis by reducing the autophosphorylation of PKR at the Thr451 residue; however, the molecular mechanism by which palmitate reduces PKR autophosphorylation is not known. Thus, we investigated how palmitate affects the phosphorylation of the PKR protein at the molecular and biophysical levels. Biochemical and computational studies show that palmitate binds to PKR, near the ATP-binding site, thereby inhibiting its autophosphorylation at Thr451 and Thr446. Mutation studies suggest that Lys296 and Asp432 in the ATP-binding site on the PKR protein are important for palmitate binding. We further confirmed that palmitate also interacts with other kinases, due to the conserved ATP-binding site. A better understanding of how palmitate interacts with the PKR protein, as well as other kinases, could shed light onto possible mechanisms by which palmitate mediates kinase signaling pathways that could have implications on the efficacy of current drug therapies that target kinases.

PRIMO/PRIMONA: a coarse-grained model for proteins and nucleic acids that preserves near-atomistic accuracy.

The new coarse graining model PRIMO/PRIMONA for proteins and nucleic acids is proposed. This model combines one to several heavy atoms into coarse-grained sites that are chosen to allow an analytical, high-resolution reconstruction of all-atom models based on molecular bonding geometry constraints. The accuracy of proposed reconstruction method in terms of structure and energetics is tested and compared with other popular reconstruction methods for a variety of protein and nucleic acid test sets.

Conformational change in MSH2-MSH6 upon binding DNA coupled to ATPase activity.

Postreplication DNA mismatch repair is initiated by the eukaryotic protein MSH2-MSH6 or the prokaryotic protein MutS, both showing overall conserved structure and functionality. Crystal structures of MSH2-MSH6 and MutS bound to the mismatch DNA reveal a closed architecture of the clamp and the lever domains exhibiting strong contacts with the bent DNA backbone. Long molecular dynamics simulations of the human MSH2-MSH6 protein in the absence of a DNA show an altered conformation of the protein that reflects the protein's state before binding to DNA. The clamp and the lever domains of both MSH6 and MSH2 open in an asymmetric and dramatic fashion. The opening of the clamp and the lever domains in the absence of DNA is coupled to changes in the ATPase domains, which explains the experimentally observed diminished ATPase activity in DNA-free MSH2-MSH6 and illustrates the allosteric coupling between DNA binding and ATPase activity.

Deciphering the mismatch recognition cycle in MutS and MSH2-MSH6 using normal-mode analysis.

Postreplication DNA mismatch repair is essential for maintaining the integrity of genomic information in prokaryotes and eukaryotes. The first step in mismatch repair is the recognition of base-base mismatches and insertions/deletions by bacterial MutS or eukaryotic MSH2-MSH6. Crystal structures of both proteins bound to mismatch DNA reveal a similar molecular architecture but provide limited insight into the detailed molecular mechanism of long-range allostery involved in mismatch recognition and repair initiation. This study describes normal-mode calculations of MutS and MSH2-MSH6 with and without DNA. The results reveal similar protein flexibilities and suggest common dynamic and functional characteristics. A strongly correlated motion is present between the lever domain and ATPase domains, which suggests a pathway for long-range allostery from the N-terminal DNA binding domain to the C-terminal ATPase domains, as indicated by experimental studies. A detailed analysis of individual low-frequency modes of both MutS and MSH2-MSH6 shows changes in the DNA-binding domains coupled to the ATPase sites, which are interpreted in the context of experimental data to arrive at a complete molecular-level mismatch recognition cycle. Distinct conformational states are proposed for DNA scanning, mismatch recognition, repair initiation, and sliding along DNA after mismatch recognition. Hypotheses based on the results presented here form the basis for further experimental and computational studies.

Conformational specificity of non-canonical base pairs and higher order structures in nucleic acids: crystal structure database analysis.

Non-canonical base pairs contribute immensely to the structural and functional variability of RNA, which calls for a detailed characterization of their spatial conformation. Intra-base pair parameters, namely propeller, buckle, open-angle, stagger, shear and stretch describe structure of base pairs indicating planarity and proximity of association between the two bases. In order to study the conformational specificities of non-canonical base pairs occurring in RNA crystal structures, we have upgraded NUPARM software to calculate these intra-base pair parameters using a new base pairing edge specific axis system. Analysis of base pairs and base triples with the new edge specific axis system indicate the presence of specific structural signatures for different classes of non-canonical pairs and triples. Differentiating features could be identified for pairs in cis or trans orientation, as well as those involving sugar edges or C-H-mediated hydrogen bonds. It was seen that propeller for all types of base pairs in cis orientation are generally negative, while those for trans base pairs do not have any preference. Formation of a base triple is seen to reduce propeller of the associated base pair along with reduction of overall flexibility of the pairs. We noticed that base pairs involving sugar edge are generally more non-planar, with large propeller or buckle values, presumably to avoid steric clash between the bulky sugar moieties. These specific conformational signatures often provide an insight into their role in the structural and functional context of RNA.

Non-canonical base pairs and higher order structures in nucleic acids: crystal structure database analysis.

Non-canonical base pairs, mostly present in the RNA, often play a prominent role towards maintaining their structural diversity. Higher order structures like base triples are also important in defining and stabilizing the tertiary folded structure of RNA. We have developed a new program BPFIND to analyze different types of canonical and non-canonical base pairs and base triples involving at least two direct hydrogen bonds formed between polar atoms of the bases or sugar O2' only. We considered 104 possible types of base pairs, out of which examples of 87 base pair types are found to occur in the available RNA crystal structures. Analysis indicates that approximately 32.7% base pairs in the functional RNA structures are non-canonical, which include different types of GA and GU Wobble base pairs apart from a wide range of base pair possibilities. We further noticed that more than 10.4% of these base pairs are involved in triplet formation, most of which play important role in maintaining long-range tertiary contacts in the three-dimensional folded structure of RNA. Apart from detection, the program also gives a quantitative estimate of the conformational deformation of detected base pairs in comparison to an ideal planar base pair. This helps us to gain insight into the extent of their structural variations and thus assists in understanding their specific role towards structural and functional diversity.