Mechano-chemical kinetics of DNA replication: identification of the translocation step of a replicative DNA polymerase

During DNA replication replicative polymerases move in discrete mechanical steps along the DNA template. To address how the chemical cycle is coupled to mechanical motion of the enzyme, here we use optical tweezers to study the translocation mechanism of individual bacteriophage Phi29 DNA polymerases during processive DNA replication. We determine the main kinetic parameters of the nucleotide incorporation cycle and their dependence on external load and nucleotide (dNTP) concentration. The data is inconsistent with power stroke models for translocation, instead supports a loose-coupling mechanism between chemical catalysis and mechanical translocation during DNA replication. According to this mechanism the DNA polymerase works by alternating between a dNTP/PPi-free state, which diffuses thermally between pre- and post-translocated states, and a dNTP/PPi-bound state where dNTP binding stabilizes the post-translocated state. We show how this thermal ratchet mechanism is used by the polymerase to generate work against large opposing loads (∼50 pN).     

Transition-state ensemble in enzyme catalysis: possibility, reality, or necessity?

Proteins are not rigid structures; they are dynamic entities, with numerous conformational isomers (substates). The dynamic nature of protein structures amplifies the structural variation of the transition state for chemical reactions performed by proteins. This suggests that utilizing a transition state ensemble to describe chemical reactions involving proteins may be a useful representation. Here we re-examine the nature of the transition state of protein chemical reactions (enzyme catalysis), considering both recent developments in chemical reaction theory (Marcus theory for SN2 reactions), and protein dynamics effects. The classical theory of chemical reactions relies on the assumption that a reaction must pass through an obligatory transition-state structure. The widely accepted view of enzymatic catalysis holds that there is tight binding of the substrate to the transition-state structure, lowering the activation energy. This picture, may, however, be oversimplified. The real meaning of a transition state is a surface, not a single saddle point on the potential energy surface. In a reaction with a "loose" transition-state structure, the entire transition-state region, rather than a single saddle point, contributes to reaction kinetics. Consequently, here we explore the validity of such a model, namely, the enzymatic modulation of the transition-state surface. We examine its utility in explaining enzyme catalysis. We analyse the possibility that instead of optimizing binding to a well-defined transition-state structure, enzymes are optimized by evolution to bind efficiently with a transition-state ensemble, with a broad range of activated conformations. For enzyme catalysis, the key issue is still transition state (ensemble) stabilization. The source of the catalytic power is the modulation of the transition state. However, our definition of the transition state is the entire transition-state surface rather just than a single well-defined structure. This view of the transition-state ensemble is consistent with the nature of the protein molecule, as embodied and depicted in the protein energy landscape of folding, and binding, funnels.     

The catalytic power of enzymes: conformational selection or transition state stabilization?

The mechanism by which enzymes produce enormous rate enhancements in the reactions they catalyze remains unknown. Two viewpoints, selection of ground state conformations and stabilization of the transition state, are present in the literature in apparent opposition. To provide more insight into current discussion about enzyme efficiency, a two-state model of enzyme catalysis was developed. The model was designed to include both the pre-chemical (ground state conformations) and the chemical (transition state) components of the process for the substrate both in water and in the enzyme. Although the model is of general applicability, the chorismate to prephenate reaction catalyzed by chorismate mutase was chosen for illustrative purposes. The resulting kinetic equations show that the catalytic power of enzymes, quantified as the k(cat)/k(uncat) ratio, is the product of two terms: one including the equilibrium constants for the substrate conformational states and the other including the rate constants for the uncatalyzed and catalyzed chemical reactions. The model shows that these components are not mutually exclusive and can be simultaneously present in an enzymic system, being their relative contribution a property of the enzyme. The developed mathematical expressions reveal that the conformational and reaction components of the process perform differently for the translation of molecular efficiency (changes in energy levels) into observed enzymic efficiency (changes in k(cat)), being, in general, more productive the component involving the transition state.     

The Dominant Folding Route Minimizes Backbone Distortion in SH3

Energetic frustration in protein folding is minimized by evolution to create a smooth and robust energy landscape. As a result the geometry of the native structure provides key constraints that shape protein folding mechanisms. Chain connectivity in particular has been identified as an essential component for realistic behavior of protein folding models. We study the quantitative balance of energetic and geometrical influences on the folding of SH3 in a structure-based model with minimal energetic frustration. A decomposition of the two-dimensional free energy landscape for the folding reaction into relevant energy and entropy contributions reveals that the entropy of the chain is not responsible for the folding mechanism. Instead the preferred folding route through the transition state arises from a cooperative energetic effect. Off-pathway structures are penalized by excess distortion in local backbone configurations and contact pair distances. This energy cost is a new ingredient in the malleable balance of interactions that controls the choice of routes during protein folding.     

Plasticity of acetylcholine receptor gating motions via rate-energy relationships

Like other protein conformational changes, ion channel gating requires the protein to achieve a high-energy transition-state structure. It is not known whether ion channel gating takes place on a broad energy landscape on which many alternative transition state structures are accessible, or on a narrow energy landscape where only a few transition-state structures are possible. To address this question, we measured how rate-equilibrium free energy relationships (REFERs) for di-liganded and unliganded acetylcholine receptor gating vary as a function of the gating equilibrium constant. A large slope for the REFER plot indicates an openlike transition state, whereas a small slope indicates a closedlike transition state. Due to this relationship between REFERs and transition-state structure, the sensitivity of the REFER slope to mutation-induced energetic perturbations allows estimation of the breadth of the energy landscape underlying gating. The relatively large sensitivity of di-liganded REFER slopes to energetic perturbations suggests that the motions underlying di-liganded gating take place on a broad, shallow energy landscape where many alternative transition-state structures are accessible.     

Understanding a molecular motor walking along a microtubule: an asymmetric Brownian motor driven by bubble formation with a focus on binding affinity

In recent years, many studies on a molecular motor have been conducted in the fields of biorheology and nanoengineering. The molecular motor is a molecule that converts the chemical energy obtained by ATP hydrolysis into mechanical energy. Explaining this mechanism is important for nanoengineering. A kinesin, which is a type of molecular motor, has the characteristics to move on a microtubule with hand-over-hand steps. The kinesin walking behaviour is explained by the ‘asymmetric Brownian ratchet model’. Previously, we had suggested that the walking mechanism was achieved by the bubble formation in a nanosized channel surrounded by hydrophobic atoms with the transition between the two states – bubble state and liquid state. However, the walking behaviour of the model motor was different from that of a single molecule measurement of a kinesin. In this study, we constructed a new motor system focused on the asymmetric binding affinity of a motor protein and performed a model simulation using the dissipative particle dynamics method. As a result, it was observed that hand-over-hand walking depends on the transition position ratio and the transition frequency coefficient. Moreover, the efficiency of the new motor system is higher than that of the previous motor systems. The new motor model can provide a simulation guide for the design of biomimetic nanomachines.     

Shape of the free energy barriers for protein folding probed by multiple perturbation analysis

The characterization of the free energy barriers has been a major goal in studies on the mechanism of protein folding. Testing the effect of mutations or denaturants on protein folding reactions revealed that transition state movement is rare, suggesting that folding barriers are robust and narrow maxima on the free energy landscape. Here we demonstrate that the application of multiple perturbations allows the observation of small transition state movements that escape detection in single perturbation experiments. We used tendamistat as a model protein to test the broadness of the free energy barriers. Tendamistat folds over two consecutive transition states and through a high-energy intermediate. Measuring the combined effect of temperature and denaturant on the position of the transition state in the wild-type protein and in several mutants revealed that the early transition state shows significant transition state movement. Its accessible surface area state becomes more native-like with destabilization of the native state by temperature. To the same extent, the entropy of the early transition state becomes more native-like with increasing denaturant concentration, in accordance with Hammond behavior. The position of the late transition state, in contrast, is much less sensitive to the applied perturbations. These results suggest that the barriers in protein folding become increasingly narrow as the folding polypeptide chain approaches the native state.     

Free energy landscape and transition pathways from Watson–Crick to Hoogsteen base pairing in free duplex DNA

Houghton (HG) base pairing plays a central role in the DNA binding of proteins and small ligands. Probing detailed transition mechanism from Watson–Crick (WC) to HG base pair (bp) formation in duplex DNAs is of fundamental importance in terms of revealing intrinsic functions of double helical DNAs beyond their sequence determined functions. We investigated a free energy landscape of a free B-DNA with an adenosine–thymine (A–T) rich sequence to probe its conformational transition pathways from WC to HG base pairing. The free energy landscape was computed with a state-of-art two-dimensional umbrella molecular dynamics simulation at the all-atom level. The present simulation showed that in an isolated duplex DNA, the spontaneous transition from WC to HG bp takes place via multiple pathways. Notably, base flipping into the major and minor grooves was found to play an important role in forming these multiple transition pathways. This finding suggests that naked B-DNA under normal conditions has an inherent ability to form HG bps via spontaneous base opening events.     

Capturing Transition Paths and Transition States for Conformational Rearrangements in the Ribosome

To reveal the molecular determinants of biological function, one seeks to characterize the interactions that are formed in conformational and chemical transition states. In other words, what interactions govern the molecule’s energy landscape? To accomplish this, it is necessary to determine which degrees of freedom can unambiguously identify each transition state. Here, we perform simulations of large-scale aminoacyl-transfer RNA (aa-tRNA) rearrangements during accommodation on the ribosome and project the dynamics along experimentally accessible atomic distances. From this analysis, we obtain evidence for which coordinates capture the correct number of barrier-crossing events and accurately indicate when the aa-tRNA is on a transition path. Although a commonly used coordinate in single-molecule experiments performs poorly, this study implicates alternative coordinates along which rearrangements are accurately described as diffusive movements across a one-dimensional free-energy profile. From this, we provide the theoretical foundation required for single-molecule techniques to uncover the energy landscape governing aa-tRNA selection by the ribosome.     

The brownian ratchet and power stroke models for posttranslational protein translocation into the endoplasmic reticulum

A quantitative analysis of experimental data for posttranslational translocation into the endoplasmic reticulum is performed. This analysis reveals that translocation involves a single rate-limiting step, which is postulated to be the release of the signal sequence from the translocation channel. Next, the Brownian ratchet and power stroke models of translocation are compared against the data. The data sets are simultaneously fit using a least-squares criterion, and both models are found to accurately reproduce the experimental results. A likelihood-ratio test reveals that the optimal fit of the Brownian ratchet model, which contains one fewer free parameter, does not differ significantly from that of the power stroke model. Therefore, the data considered here cannot be used to reject this import mechanism. The models are further analyzed using the estimated parameters to make experimentally testable predictions.     

Charge requirements for proton gradient-driven translocation of anthrax toxin

Anthrax lethal toxin is used as a model system to study protein translocation. The toxin is composed of a translocase channel, called protective antigen (PA), and an enzyme, called lethal factor (LF). A proton gradient (ΔpH) can drive LF unfolding and translocation through PA channels; however, the mechanism of ΔpH-mediated force generation, substrate unfolding, and establishment of directionality are poorly understood. One recent hypothesis suggests that the ΔpH may act through changes in the protonation state of residues in the substrate. Here we report the charge requirements of LF's amino-terminal binding domain (LF(N)) using planar lipid bilayer electrophysiology. We found that acidic residues are required in LF(N) to utilize a proton gradient for translocation. Constructs lacking negative charges in the unstructured presequence of LF(N) translocate independently of the ΔpH driving force. Acidic residues markedly increase the rate of ΔpH-driven translocation, and the presequence is optimized in its natural acidic residue content for efficient ΔpH-driven unfolding and translocation. We discuss a ΔpH-driven charge state Brownian ratchet mechanism for translocation, where glutamic and aspartic acid residues in the substrate are the "molecular teeth" of the ratchet. Our Brownian ratchet model includes a mechanism for unfolding and a novel role for positive charges, which we propose chaperone negative charges through the PA channel during ΔpH translocation.     

An ionic–chemical–mechanical model for muscle contraction

The dynamic process underlying muscle contraction is the parallel sliding of thin actin filaments along an immobile thick myosin fiber powered by oar‐like movements of protruding myosin cross bridges (myosin heads). The free energy for functioning of the myosin nanomotor comes from the hydrolysis of ATP bound to the myosin heads. The unit step of translational movement is based on a mechanical‐chemical cycle involving ATP binding to myosin, hydrolysis of the bound ATP with ultimate release of the hydrolysis products, stress‐generating conformational changes in the myosin cross bridge, and relief of built‐up stress in the myosin power stroke. The cycle is regulated by a transition between weak and strong actin–myosin binding affinities. The dissociation of the weakly bound complex by addition of salt indicates the electrostatic basis for the weak affinity, while structural studies demonstrate that electrostatic interactions among negatively charged amino acid residues of actin and positively charged residues of myosin are involved in the strong binding interface. We therefore conjecture that intermediate states of increasing actin–myosin engagement during the weak‐to‐strong binding transition also involve electrostatic interactions. Methods of polymer solution physics have shown that the thin actin filament can be regarded in some of its aspects as a net negatively charged polyelectrolyte. Here we employ polyelectrolyte theory to suggest how actin–myosin electrostatic interactions might be of significance in the intermediate stages of binding, ensuring an engaged power stroke of the myosin motor that transmits force to the actin filament, and preventing the motor from getting stuck in a metastable pre‐power stroke state. We provide electrostatic force estimates that are in the pN range known to operate in the cycle.     

An electromechanical model of myosin molecular motors

There is a long-running debate on the working mechanism of myosin molecular motors, which, by interacting with actin filaments, convert the chemical energy of ATP into a variety of mechanical work. After the development of technologies for observing and manipulating individual working molecules, experimental results negating the widely accepted 'lever-arm hypothesis' have been reported. In this paper, based on the experimental results so far accumulated, an alternative hypothesis is proposed, in which motor molecules are modelled as electromechanical components that interact with each other through electrostatic force. Electrostatic attractive force between myosin and actin is assumed to cause a conformational change in the myosin head during the attachment process. An elastic energy resulting from the conformational change then produces the power stroke. The energy released at the ATP hydrolysis is mainly used to detach the myosin head from actin filaments. The mechanism presented in this paper is compatible with the experimental results contradictory to the previous theories. It also explains the behavior of myosins V and VI, which are engaged in cellular transport and move processively along actin filaments.     

A survey of flexible protein binding mechanisms and their transition states using native topology based energy landscapes

Many cellular functions rely on interactions between protein pairs and higher oligomers. We have recently shown that binding mechanisms are robust and owing to the minimal frustration principle, just as for protein folding, are governed primarily by the protein's native topology, which is characterized by the network of non-covalent residue-residue interactions. The detailed binding mechanisms of nine dimers, a trimer, and a tetramer, each involving different degrees of flexibility and plasticity during assembly, are surveyed here using a model that is based solely on the protein topology, having a perfectly funneled energy landscape. The importance of flexibility in binding reactions is manifested by the fly-casting effect, which is diminished in magnitude when protein flexibility is removed. Many of the grosser and finer structural aspects of the various binding mechanisms (including binding of pre-folded monomers, binding of intrinsically unfolded monomers, and binding by domain-swapping) predicted by the native topology based landscape model are consistent with the mechanisms found in the laboratory. An asymmetric binding mechanism is often observed for the formation of the symmetric homodimers where one monomer is more structured at the binding transition state and serves as a template for the folding of the other monomer. Phi values were calculated to show how the structure of the binding transition state ensemble would be manifested in protein engineering studies. For most systems, the simulated Phi values are reasonably correlated with the available experimental values. This agreement suggests that the overall binding mechanism and the nature of the binding transition state ensemble can be understood from the network of interactions that stabilize the native fold. The Phi values for the formation of an antibody-antigen complex indicate a possible role for solvation of the interface in biomolecular association of large rigid proteins.     

Temperature dependence of the free energy landscape of the src-SH3 protein domain

The temperature dependence of the free energy landscape of the src-SH3 protein domain is investigated through fully atomic simulations in explicit solvent. Simulations are performed above and below the folding transition temperature, enabling an analysis of both protein folding and unfolding. The transition state for folding and unfolding, identified from the free energy surfaces, is found to be very similar, with structure in the central hydrophobic sheet and little structure throughout the rest of the protein. This is a result of a polarized folding (unfolding) mechanism involving early formation (late loss) of the central hydrophobic sheet at the transition state. Unfolding simulations map qualitatively well onto low-temperature free energy surfaces but appear, however, to miss important features observed in folding simulations. In particular, details of the folding mechanism involving the opening and closing of the hydrophobic core are not captured by unfolding simulations performed under strongly denaturing conditions. In addition, free energy surfaces at high temperatures do not display a desolvation barrier found at lower temperatures, involving the expulsion of water molecules from the hydrophobic core.     

How do serine proteases really work?

Recent advances in genetic engineering have led to a growing acceptance of the fact that enzymes work like other catalysts by reducing the activation barriers of the corresponding reactions. However, the key question about the action of enzymes is not related to the fact that they stabilize transition states but to the question to how they accomplish this task. This work considers the catalytic reaction of serine proteases and demonstrates how one can use a combination of calculations and experimental information to elucidate the key contributions to the catalytic free energy. Recent reports about genetic modifications of the buried aspartic group in serine proteases, which established the large effect of this group (but could not determine its origin), are analyzed. Two independent methods indicate that the buried aspartic group in serine proteases stabilizes the transition state by electrostatic interactions rather than by alternative mechanisms. Simple free energy considerations are used to eliminate the double proton-transfer mechanism (which is depicted in many textbooks as the key catalytic factor in serine proteases). The electrostatic stabilization of the oxyanion side of the transition state is also considered. It is argued that serine proteases and other enzymes work by providing electrostatic complementarity to the changes in charge distribution occurring during the reactions they catalyze.     

Bio-switches: what makes them robust?

Ideas of how a system of interacting enzymes can act as a switch are based on the concept of bistability of a biochemical network. This means that, because of the very structure of a signaling pathway, the system can be in one of two stable steady states: active or inactive. Switching from one state to another may then occur in response to external stimuli or as a result of internal development. However, the bistability of a biochemical network might not be robust enough to be the sole mechanism behind bio-switching. On the basis of recent experimental data on the cell-cycle G2/M transition during starfish oocyte meiotic maturation, it is shown that cooperative phenomena--such as phase changes associated with clustering, dissolution of aggregates and so on--may play central roles in providing a decisive and irreversible transition.     

Ligand-protein interaction in biomembrane carriers. The induced transition fit of transport catalysis

Carrier-linked transport through biomembranes is treated under the view of catalysis. As in enzymes, substrate-protein interaction yields catalytic energy in overcoming the activation barrier. At variance with enzymes, catalytic energy is concentrated on structural changes of the carrier rather than on the substrate destabilization for facilitating the global protein rearrangements during transport. A transition state is invoked in which the binding site assumes the best fit to the substrate, whereas in the two ground (internal and external) states, the fit is poor. The maximum binding energy released in the transition state provides catalytic energy to enable the large carrier protein transformations associated with transport. This "induced transition fit" (ITF) of carrier catalysis provides a framework of rules, concerning specificity, unidirectional versus exchange type transport, directing inhibitors to the ground state instead of the transition state, and excluding simultaneous chemical and transport catalysis (vectorial group translocation). The possible role of external energy sources (ATP and Deltapsi) in supplementing the catalytic energy is elucidated. The analysis of the structure-function relationship based on new carrier structures may be challenged to account for the workings of the ITF.     

Simulation study on dynamics transition in neuronal activity during sleep cycle by using asynchronous and symmetry neural network model

We have found that single neuronal activities in different regions in the brain commonly exhibit the distinct dynamics transition during sleep-waking cycle in cats. Especially, power spectral densities of single neuronal activities change their profiles from the white to the 1/f along with sleep cycle from slow wave sleep (SWS) to paradoxical sleep (PS). Each region has different neural network structure and physiological function. This suggests a globally working mechanism may be underlying the dynamics transition we concern. Pharmacological studies have shown that a change in a wide-spread serotonergic input to these regions possibly causes the neuronal dynamics transition during sleep cycle. In this paper, based on these experimental results, an asynchronous and symmetry neural network model including inhibitory input, which represents the role of the serotonergic system, is utilized to examine the reality of our idea that the inhibitory input level varying during sleep cycle induce that transition. Simulation results show that the globally applied inhibitory input can control the dynamics of single neuronal state evolution in the artificial neural network: 1/f-like power spectral density profiles result under weak inhibition, which possibly corresponds to PS, and white profiles under strong inhibition, which possibly corresponds to SWS. An asynchronous neural network is known to change its state according to its energy function. The geometrical structure of network energy function is thought to vary along with the change in inhibitory level, which is expected to cause the dynamics transition of neuronal state evolution in the network model. These simulation results support the possibility that the serotonergic system is essential for the dynamics transition of single neuronal activities during sleep cycle.