A model for dynamics of primer extension by eukaryotic DNA primase

A mathematical model is proposed for processive primer extension by eukaryotic DNA primase. The model uses available experimental data to predict rate constants for the dynamic behavior of primase activity as a function of NTP concentration. The model also predicts some data such as the binding affinities of the primase for the DNA template and for the RNA primer.     

Pre-steady-state kinetics for hydrolysis of insoluble cellulose by cellobiohydrolase Cel7A

The transient kinetic behavior of enzyme reactions prior to the establishment of steady state is a major source of mechanistic information, yet this approach has not been utilized for cellulases acting on their natural substrate, insoluble cellulose. Here, we elucidate the pre-steady-state regime for the exo-acting cellulase Cel7A using amperometric biosensors and an explicit model for processive hydrolysis of cellulose. This analysis allows the identification of a pseudo-steady-state period and quantification of a processivity number as well as rate constants for the formation of a threaded enzyme complex, processive hydrolysis, and dissociation, respectively. These kinetic parameters elucidate limiting factors in the cellulolytic process. We concluded, for example, that Cel7A cleaves about four glycosidic bonds/s during processive hydrolysis. However, the results suggest that stalling the processive movement and low off-rates result in a specific activity at pseudo-steady state that is 10-25-fold lower. It follows that the dissociation of the enzyme-substrate complex (half-time of ~30 s) is rate-limiting for the investigated system. We suggest that this approach can be useful in attempts to unveil fundamental reasons for the distinctive variability in hydrolytic activity found in different cellulase-substrate systems.     

Product binding varies dramatically between processive and nonprocessive cellulase enzymes

Cellulases hydrolyze β-1,4 glycosidic linkages in cellulose, which are among the most prevalent and stable bonds in Nature. Cellulases comprise many glycoside hydrolase families and exist as processive or nonprocessive enzymes. Product inhibition negatively impacts cellulase action, but experimental measurements of product-binding constants vary significantly, and there is little consensus on the importance of this phenomenon. To provide molecular level insights into cellulase product inhibition, we examine the impact of product binding on processive and nonprocessive cellulases by calculating the binding free energy of cellobiose to the product sites of catalytic domains of processive and nonprocessive enzymes from glycoside hydrolase families 6 and 7. The results suggest that cellobiose binds to processive cellulases much more strongly than nonprocessive cellulases. We also predict that the presence of a cellodextrin bound in the reactant site of the catalytic domain, which is present during enzymatic catalysis, has no effect on product binding in nonprocessive cellulases, whereas it significantly increases product binding to processive cellulases. This difference in product binding correlates with hydrogen bonding between the substrate-side ligand and the cellobiose product in processive cellulase tunnels and the additional stabilization from the longer tunnel-forming loops. The hydrogen bonds between the substrate- and product-side ligands are disrupted by water in nonprocessive cellulase clefts, and the lack of long tunnel-forming loops results in lower affinity of the product ligand. These findings provide new insights into the large discrepancies reported for binding constants for cellulases and suggest that product inhibition will vary significantly based on the amount of productive binding for processive cellulases on cellulose.     

Kinetic relationships with processivity in Serratia marcescens family 18 glycoside hydrolases

In nature, recalcitrant polysaccharides such as chitin and cellulose are degraded by glycoside hydrolases (GH) that act synergistically through different modes of action including attack from reducing-end and nonreducing-end (exo-mode) and random (endo-mode) on single polysaccharide chains. Both modes can be combined with a processive mechanism where the GH remain bound to the polysaccharide to perform multiple catalytic steps before dissociation into the solution. In this work, we have determined association rate constants and their activation paramaters for three co-evolved GHs from Serratia marcescens (SmChiA, SmChiB, and SmChiC) with an oligomeric substrate. Interestingly, we observe a positive correlation between the association rate constants and processive ability for the GHs. Previously, a positive correlation has been observed between substrate binding affinity and processive ability. SmChiA with highest processive ability of the three GHs bind with a k_on of 11.5 ± 0.2 μM⁻¹s⁻¹, which is five-fold and 130-fold faster than SmChiB (less processive) and SmChiC (nonprocessive), respectively.     

Modeling the activity burst in the initial phase of cellulose hydrolysis by the processive cellobiohydrolase Cel7A

The hydrolysis of cellulose by processive cellulases, such as exocellulase TrCel7A from Trichoderma reesei, is typically characterized by an initial burst of high activity followed by a slowdown, often leading to incomplete hydrolysis of the substrate. The origins of these limitations to cellulose hydrolysis are not yet fully understood. Here, we propose a new model for the initial phase of cellulose hydrolysis by processive cellulases, incorporating a bound but inactive enzyme state. The model, based on ordinary differential equations, accurately reproduces the activity burst and the subsequent slowdown of the cellulose hydrolysis and describes the experimental data equally well or better than the previously suggested model. We also derive steady-state expressions that can be used to describe the pseudo-steady state reached after the initial activity burst. Importantly, we show that the new model predicts the existence of an optimal enzyme-substrate affinity at which the pseudo-steady state hydrolysis rate is maximized. The model further allows the calculation of glucose production rate from the first cut in the processive run and reproduces the second activity burst commonly observed upon new enzyme addition. These results are expected to be applicable also to other processive enzymes.     

A possible mechanism of processive nucleotide and repeat additions by the telomerase

Telomerase is a specialized cellular ribonucleoprotein complex that can synthesize long stretches of a DNA primer by using an intrinsic RNA template sequence. This requires that the telomerase must be able to carry out both nucleotide and repeat additions. Here, based on available structures and experimental data, a model is presented to describe these two addition activities. In the model, the forward movement of the polymerase active site along the template during the processive nucleotide addition is rectified through the incorporation of a matched base, via the Brownian ratchet mechanism. The unpairing of the DNA:RNA hybrid and then repositioning of product 3′-end after each round of repeat synthesis, which are prerequisites for the processive repeat addition, are caused by a force acting on the primer. The force results from the conformational transition of the stem III pseudoknot, which is mechanically induced by the rotation of TERT fingers together with stem IV loop towards the polymerase active site upon a nucleotide binding. Based on the model, the dynamics of processive nucleotide and repeat additions by recombinant Tetrahymena telomerase is studied analytically, which gives good quantitative explanations to the previous experimental results. Moreover, some predicted results are presented. In particular, it is shown that the repeat addition processivity is mainly determined by the difference between the free-energy change required to disrupt the DNA:RNA hybrid and that required to unfold the stem III pseudoknot. A large difference in free energy corresponds to a low repeat addition processivity while a small difference in free energy corresponds to a high repeat addition processivity.     

Mammalian Kinesin-3 Motors Are Dimeric In Vivo and Move by Processive Motility upon Release of Autoinhibition

Kinesin-3 motors drive the transport of synaptic vesicles and other membrane-bound organelles in neuronal cells. In the absence of cargo, kinesin motors are kept inactive to prevent motility and ATP hydrolysis. Current models state that the Kinesin-3 motor KIF1A is monomeric in the inactive state and that activation results from concentration-driven dimerization on the cargo membrane. To test this model, we have examined the activity and dimerization state of KIF1A. Unexpectedly, we found that both native and expressed proteins are dimeric in the inactive state. Thus, KIF1A motors are not activated by cargo-induced dimerization. Rather, we show that KIF1A motors are autoinhibited by two distinct inhibitory mechanisms, suggesting a simple model for activation of dimeric KIF1A motors by cargo binding. Successive truncations result in monomeric and dimeric motors that can undergo one-dimensional diffusion along the microtubule lattice. However, only dimeric motors undergo ATP-dependent processive motility. Thus, KIF1A may be uniquely suited to use both diffuse and processive motility to drive long-distance transport in neuronal cells.     

Kinetic models of translocation, head-on collision, and DNA cleavage by type I restriction endonucleases

Digestion of linear DNA by type I restriction endonucleases is generally activated following the head-on collision of two translocating enzymes. However, the resulting distributions of cleavage loci along the DNA vary with different enzymes; in some cases, cleavage is located in a discrete region midway between a pair of recognition sites while in other cases cleavage is broadly distributed and occurs at nearly every intervening locus. Statistical models for DNA translocation, collision, and cleavage are described that can account for these observations and that are generally applicable to other DNA-based motor proteins. If translocation is processive (stepping forward is significantly more likely than DNA dissociation), then the linear distribution of an ensemble of proteins can be described simply using a Poisson relationship. The pattern of cleavage sites resulting from collision between two processive type I enzymes over a distance d can then be described by a binomial distribution with a standard deviation 0.5 x d1/2. Alternatively, if translocation is nonprocessive (stepping forward or dissociating become equally likely events), the linear distribution is described by a continuum of populated states and is thus extended. Comparisons of model data to the kinetics of DNA translocation and cleavage discount the nonprocessive model. Instead, the observed differences between enzymes are due to asynchronous events that occur upon collision. Therefore, type I restriction enzymes can be described as having processive DNA translocation but, in some cases, nonprocessive DNA cleavage.     

Effects of substitutions of arginine residues on the basic surface of herpes simplex virus UL42 support a role for DNA binding in processive DNA synthesis

The way that UL42, the processivity subunit of the herpes simplex virus DNA polymerase, interacts with DNA and promotes processivity remains unclear. A positively charged face of UL42 has been proposed to participate in electrostatic interactions with DNA that would tether the polymerase to a template without preventing its translocation via DNA sliding. An alternative model proposes that DNA binding by UL42 is not important for processivity. To investigate these issues, we substituted alanine for each of four conserved arginine residues on the positively charged surface. Each single substitution decreased the DNA binding affinity of UL42, with 14- to 30-fold increases in apparent dissociation constants. The mutant proteins exhibited no meaningful change in affinity for binding to the C terminus of the catalytic subunit of the polymerase, indicating that the substitutions exert a specific effect on DNA binding. The substitutions decreased UL42-mediated long-chain DNA synthesis by the polymerase in the same rank order in which they affected DNA binding, consistent with a role for DNA binding in polymerase processivity. Combining these substitutions decreased DNA binding further and impaired the complementation of a UL42 null virus in transfected cells. Additionally, using a revised mathematical model to analyze rates of dissociation of UL42 from DNAs of various lengths, we found that dissociation from internal sites, which would be the most important for tethering the polymerase, was relatively slow, even at ionic strengths that permit processive DNA synthesis by the holoenzyme. These data provide evidence that the basic surface of UL42 interacts with DNA and support a model in which DNA binding by UL42 is important for processive DNA synthesis.     

On the processivity of DNA replication

In this paper we describe the nature and importance of processive enzymatic reactions in biological processes. A model is set up to describe the processive synthetic process in DNA replication, and experiments are presented to define and test the model, using the components of the T4 phage-coded five-protein (in vitro) DNA replication system of Alberts. Nossal and coworkers. These experiments are performed either with a homogeneous oligo dT-poly dA primer-template system, or with a natural primer-template system using phage M13 DNA. The results are used to define some molecular aspects of the microscopic "processivity cycle".     

Actin polymerization upon processive capping by formin: a model for slowing and acceleration

Formin family proteins act as processive cappers of actin filaments, and determine the dynamics of a number of intracellular processes that are based on actin polymerization. The rate of filament growth upon processive capping varies within a broad range depending on the formin type and presence of profilin. While FH2 domains of various formins slow down polymerization by different extents, the FH1-FH2 domains in conjunction with profilin accelerate the reaction. Study of the physical mechanism of processive capping is vital for understanding the intracellular actin dynamics. We propose a model predicting that variation of a single physical parameter—the effective elastic energy of the formin-capped barbed end—results in the observed diversity of the polymerization rates. The model accounts for the whole range of the experimental results including the drastic slowing down of polymerization by FH2 of Cdc12 formin and the 4.5-fold acceleration of the reaction by FH1-FH2 of mDai1 formin in the presence of profilin. Fitting the theoretical predictions to the experimental curves provides the values of the effective elastic energies of different formin-barbed end complexes.     

A flexible domain is essential for the large step size and processivity of myosin VI

Myosin VI moves processively along actin with a larger step size than expected from the size of the motor. Here, we show that the proximal tail (the approximately 80-residue segment following the IQ domain) is not a rigid structure but, rather, a flexible domain that permits the heads to separate. With a GCN4 coiled coil inserted in the proximal tail, the heads are closer together in electron microscopy (EM) images, and the motor takes shorter processive steps. Single-headed myosin VI S1 constructs take nonprocessive 12 nm steps, suggesting that most of the processive step is covered by a diffusive search for an actin binding site. Based on these results, we present a mechanical model that describes stepping under an applied load.     

A model of myosin V processivity

Cytoplasmic transport is mediated by a group of molecular motors that typically work in isolation, under conditions where they must move their cargos long distances without dissociating from their tracks. This processive behavior requires specific adaptations of motor enzymology to meet these unique physiologic demands. One of these involves the ability of the two heads of a processive motor to communicate their structural states to each other. In this study, we examine a processive motor from the myosin superfamily myosin V. We have measured the kinetics of nucleotide release, of phosphate release, and of the weak-to-strong transition, as this motor interacts with actin, and we have used these studies to develop a model of how myosin V functions as a transport motor. Surprisingly, both heads release phosphate rapidly upon the initial encounter with an actin filament, suggesting that there is little or no intramolecular strain associated with this step. However, ADP release can be affected by both forward and rearward strain, and under steady-state conditions it is essentially prevented in the lead head until the rear head detaches. Many of these features are remarkably like those underlying the processive movement of kinesin on microtubules, supporting our hypothesis that different molecular motors satisfy the requirement for processive movement in similar ways, regardless of their particular family of origin.     

Kinetic Analysis of the Three-step Steroid Aromatase Reaction of Human Cytochrome P450 19A1

Cytochrome P450 19A1 (P450 19A1), the aromatase, catalyzes the conversion of androgens to estrogens through a sequential three-step reaction, generating 19-hydroxy and 19-aldehyde intermediates en route to the product estrogen. A procedure for the heterologous expression and purification of P450 19A1 in Escherichia coli was developed (k_cat of 0.06 s⁻¹ for the conversion of androstenedione to estrone). Binding of the substrate and intermediates show low micromolar dissociation constants and are at least two-step processes. Rates of reduction of the iron were fast in the presence of substrate, either intermediate, or product. P450 19A1 is a distributive rather than a processive enzyme, with the sequential reaction allowing free dissociation of the intermediates as revealed by pulse-chase experiments. Conversion of androstenedione to estrone (under single turnover conditions) generated a progress curve showing changes in the concentrations of the substrate, intermediates, and product. A minimal kinetic model containing the individual rate constants for the steps in P450 19A1 catalysis was developed to globally fit the time course of the overall reaction, the dissociation constants, the two-step ligand binding, the distributive character, the iron-reduction rates, and the steady-state conversion of the 19-hydroxy androstenedione and 19-aldehyde androstenedione intermediates to estrone.     

Emergent Systems Energy Laws for Predicting Myosin Ensemble Processivity

In complex systems with stochastic components, systems laws often emerge that describe higher level behavior regardless of lower level component configurations. In this paper, emergent laws for describing mechanochemical systems are investigated for processive myosin-actin motility systems. On the basis of prior experimental evidence that longer processive lifetimes are enabled by larger myosin ensembles, it is hypothesized that emergent scaling laws could coincide with myosin-actin contact probability or system energy consumption. Because processivity is difficult to predict analytically and measure experimentally, agent-based computational techniques are developed to simulate processive myosin ensembles and produce novel processive lifetime measurements. It is demonstrated that only systems energy relationships hold regardless of isoform configurations or ensemble size, and a unified expression for predicting processive lifetime is revealed. The finding of such laws provides insight for how patterns emerge in stochastic mechanochemical systems, while also informing understanding and engineering of complex biological systems.     

Uridylate-containing RNA sequences determine specificity for binding and polyadenylation by the catalytic subunit of vaccinia virus poly(A) polymerase.

VP55, the catalytic subunit of vaccinia virus poly(A) polymerase, has the remarkable property of adding 30-35 adenylates to RNA 3' ends in a rapid processive burst before an abrupt transition to slow, non-processive adenylate addition. Here, we demonstrate that this property results from the affinity of the enzyme for uridylate residues within the 3' 31-40 nt of the RNA primer. At physiological salt concentrations, both polyadenylation and stable VP55 binding required the presence of multiple uridylates within a 31-40 nt length of RNA, though specific RNA sequences were not necessary. Even DNA in which the deoxythymidylate residues were replaced with ribouridylates, could be polyadenylated in a processive manner. Both the unmethylated pyrimidine ring and a 2'-OH on the associated sugar are features of ribouridylates that are important for priming. The abrupt termination of processive polyadenylation was attributed to translocation of VP55 along the nascent poly(A) tail, which lacks uridylates for stable binding. As evidence for translocation and interaction with newly synthesized RNA, other homopolymer tails were synthesized by VP55 in the presence of Mn2+, which relaxes its donor nucleotide specificity. Only during poly(U) tail synthesis did processive nucleotide addition fail to terminate.     

A kinetic model describing the processivity of myosin-V

The precise details of how myosin-V coordinates the biochemical reactions and mechanical motions of its two head elements to engineer effective processive molecular motion along actin filaments remain unresolved. We compare a quantitative kinetic model of the myosin-V walk, consisting of five basic states augmented by two further states to allow for futile hydrolysis and detachments, with experimental results for run lengths, velocities, and dwell times and their dependence on bulk nucleotide concentrations and external loads in both directions. The model reveals how myosin-V can use the internal strain in the molecule to synchronize the motion of the head elements. Estimates for the rate constants in the reaction cycle and the internal strain energy are obtained by a computational comparison scheme involving an extensive exploration of the large parameter space. This scheme exploits the fact that we have obtained analytic results for our reaction network, e.g., for the velocity but also the run length, diffusion constant, and fraction of backward steps. The agreement with experiment is often reasonable but some open problems are highlighted, in particular the inability of such a general model to reproduce the reported dependence of run length on ADP concentration. The novel way that our approach explores parameter space means that any confirmed discrepancies should give new insights into the reaction network model.     

A peptide model system for processive phosphorylation by Src family kinases

The Src homology 2 (SH2) and Src homology 3 (SH3) domains of Src family kinases are involved in substrate recognition in vivo. Many cellular substrates of Src kinases contain a large number of potential phosphorylation sites, and the SH2 and SH3 domains of Src are known to be required for phosphorylation of these substrates. In principle, Src could phosphorylate these substrates by either a processive mechanism, in which the enzyme remains bound to the peptide substrate during multiple phosphorylation events, or a nonprocessive (distributive) mechanism, where each phosphorylation requires a separate binding interaction between enzyme and substrate. Here we use a synthetic peptide system to demonstrate that Hck, a Src family kinase, can phosphorylate substrates containing an SH2 domain ligand by a processive mechanism. Hck catalyzes the phosphorylation of these sites in a defined order. Furthermore, we show that addition of an SH3 domain to a peptide can enhance its phosphorylation both by activating Hck and by increasing the affinity of the substrate. On the basis of our observations on the role of the SH2 and SH3 domains in substrate recognition, we present a model for substrate targeting in vivo.