Role of substrate unbinding in Michaelis-Menten enzymatic reactions.
ABSTRACT: The Michaelis-Menten equation provides a hundred-year-old prediction by which any increase in the rate of substrate unbinding will decrease the rate of enzymatic turnover. Surprisingly, this prediction was never tested experimentally nor was it scrutinized using modern theoretical tools. Here we show that unbinding may also speed up enzymatic turnover--turning a spotlight to the fact that its actual role in enzymatic catalysis remains to be determined experimentally. Analytically constructing the unbinding phase space, we identify four distinct categories of unbinding: inhibitory, excitatory, superexcitatory, and restorative. A transition in which the effect of unbinding changes from inhibitory to excitatory as substrate concentrations increase, and an overlooked tradeoff between the speed and efficiency of enzymatic reactions, are naturally unveiled as a result. The theory presented herein motivates, and allows the interpretation of, groundbreaking experiments in which existing single-molecule manipulation techniques will be adapted for the purpose of measuring enzymatic turnover under a controlled variation of unbinding rates. As we hereby show, these experiments will not only shed first light on the role of unbinding but will also allow one to determine the time distribution required for the completion of the catalytic step in isolation from the rest of the enzymatic turnover cycle.
Project description:Most biological processes are controlled by complex systems of enzymatic chemical reactions. Although the majority of enzymatic networks have very elaborate structures, there are many experimental observations indicating that some turnover rates still follow a simple Michaelis-Menten relation with a hyperbolic dependence on a substrate concentration. The original Michaelis-Menten mechanism has been derived as a steady-state approximation for a single-pathway enzymatic chain. The validity of this mechanism for many complex enzymatic systems is surprising. To determine general conditions when this relation might be observed in experiments, enzymatic networks consisting of coupled parallel pathways are investigated theoretically. It is found that the Michaelis-Menten equation is satisfied for specific relations between chemical rates, and it also corresponds to a situation with no fluxes between parallel pathways. Our results are illustrated for a simple model. The importance of the Michaelis-Menten relationship and derived criteria for single-molecule experimental studies of enzymatic processes are discussed.
Project description:Understanding differentiation, a biological process from a multipotent stem or progenitor state to a mature cell is critically important. We developed a theoretical framework to quantify the underlying potential landscape and pathways for cell development and differentiation. We proposed a new mechanism of differentiation and found the differentiated states can emerge from the slow binding/unbinding of regulatory proteins to gene promoters. With slow promoter binding/unbinding, we found multiple meta-stable differentiated states, which can explain the origin of multiple states observed in recent experiments. The kinetic time for the differentiation and reprogramming strongly depends on the time scale of the promoter binding/unbinding processes. We discovered an optimal speed for differentiation for certain promoter binding/unbinding rates. Future experiments might be able to tell if cells differentiate at that optimal speed. We also quantified irreversible kinetic pathways for the differentiation and reprogramming, which captures the non-equilibrium dynamics in multipotent stem or progenitor cells.
Project description:Receptor-ligand interactions are essential for biological function and their binding strength is commonly explained in terms of static lock-and-key models based on molecular complementarity. However, detailed information on the full unbinding pathway is often lacking due, in part, to the static nature of atomic structures and ensemble averaging inherent to bulk biophysics approaches. Here we combine molecular dynamics and high-speed force spectroscopy on the streptavidin-biotin complex to determine the binding strength and unbinding pathways over the widest dynamic range. Experiment and simulation show excellent agreement at overlapping velocities and provided evidence of the unbinding mechanisms. During unbinding, biotin crosses multiple energy barriers and visits various intermediate states far from the binding pocket, while streptavidin undergoes transient induced fits, all varying with loading rate. This multistate process slows down the transition to the unbound state and favors rebinding, thus explaining the long lifetime of the complex. We provide an atomistic, dynamic picture of the unbinding process, replacing a simple two-state picture with one that involves many routes to the lock and rate-dependent induced-fit motions for intermediates, which might be relevant for other receptor-ligand bonds.
Project description:Recent work has demonstrated concentration-dependent unbinding rates of proteins from DNA, using fluorescence visualization of the bacterial nucleoid protein Fis [Graham et al. (2011) (Concentration-dependent exchange accelerates turnover of proteins bound to double-stranded DNA. Nucleic Acids Res., 39:2249)]. The physical origin of this concentration-dependence is unexplained. We use a combination of coarse-grained simulation and theory to demonstrate that this behavior can be explained by taking into account the dimeric nature of the protein, which permits partial dissociation and exchange with other proteins in solution. Concentration-dependent unbinding is generated by this simple model, quantitatively explaining experimental data. This effect is likely to play a major role in determining binding lifetimes of proteins in vivo where there are very high concentrations of solvated molecules.
Project description:Forced unbinding of complementary macromolecules such as ligand-receptor complexes can reveal energetic and kinetic details governing physiological processes ranging from cellular adhesion to drug metabolism. Although molecular-level experiments have enabled sampling of individual ligand-receptor complex dissociation events, disparities in measured unbinding force F(R) among these methods lead to marked variation in inferred binding energetics and kinetics at equilibrium. These discrepancies are documented for even the ubiquitous ligand-receptor pair, biotin-streptavidin. We investigated these disparities and examined atomic-level unbinding trajectories via steered molecular dynamics simulations, as well as via molecular force spectroscopy experiments on biotin-streptavidin. In addition to the well-known loading rate dependence of F(R) predicted by Bell's model, we find that experimentally accessible parameters such as the effective stiffness of the force transducer k can significantly perturb the energy landscape and the apparent unbinding force of the complex for sufficiently stiff force transducers. Additionally, at least 20% variation in unbinding force can be attributed to minute differences in initial atomic positions among energetically and structurally comparable complexes. For force transducers typical of molecular force spectroscopy experiments and atomistic simulations, this energy barrier perturbation results in extrapolated energetic and kinetic parameters of the complex that depend strongly on k. We present a model that explicitly includes the effect of k on apparent unbinding force of the ligand-receptor complex, and demonstrate that this correction enables prediction of unbinding distances and dissociation rates that are decoupled from the stiffness of actual or simulated molecular linkers.
Project description:Unbinding of a spin-labeled dinitrophenyl (DNP) hapten from the monoclonal antibody AN02 F(ab) fragment has been studied by force probe molecular dynamics (FPMD) simulations. In our nanosecond simulations, unbinding was enforced by pulling the hapten molecule out of the binding pocket. Detailed inspection of the FPMD trajectories revealed a large heterogeneity of enforced unbinding pathways and a correspondingly large flexibility of the binding pocket region, which exhibited induced fit motions. Principal component analyses were used to estimate the resulting entropic contribution of approximately 6 kcal/mol to the AN02/DNP-hapten bond. This large contribution may explain the surprisingly large effect on binding kinetics found for mutation sites that are not directly involved in binding. We propose that such "entropic control" optimizes the binding kinetics of antibodies. Additional FPMD simulations of two point mutants in the light chain, Y33F and I96K, provided further support for a large flexibility of the binding pocket. Unbinding forces were found to be unchanged for these two mutants. Structural analysis of the FPMD simulations suggests that, in contrast to free energies of unbinding, the effect of mutations on unbinding forces is generally nonadditive.
Project description:This paper examines the benefits of Michaelis-Menten model reduction techniques in stochastic tau-leaping simulations. Results show that although the conditions for the validity of the reductions for tau-leaping remain the same as those for the stochastic simulation algorithm (SSA), the reductions result in a substantial speed-up for tau-leaping under a different range of conditions than they do for SSA. The reason of this discrepancy is that the time steps for SSA and for tau-leaping are determined by different properties of system dynamics.
Project description:An 1-ns unbinding trajectory of retinol from the bovine serum retinol-binding protein has been obtained from molecular dynamics simulations. The behavior of water during ligand unbinding has never been studied in detail. I described a new method for defining a binding site, located the water molecules involved in the binding site, and examined their movements during unbinding. I found that there were only small changes in the binding site. During unbinding, the number of water molecules inside the binding site decreased, with some water molecules exhibiting movements similar in magnitude to bulk water, and there were rearrangements of the hydrogen bonds. This work represents the first detailed study of the behavior of water during an unbinding process.
Project description:Pyrazinamide (PZA) is the only first-line antitubercular drug active against latent Mycobacterium tuberculosis (Mtb). It is activated to pyrazinoic acid by the pncA-encoded pyrazinamidase enzyme (PZase). Despite the emergence of PZA drug resistance, the underlying mechanisms of resistance remain unclear. This study investigated part of these mechanisms by modelling a PZA-bound wild type and 82 mutant PZase structures before applying molecular dynamics (MD) with an accurate Fe2+ cofactor coordination geometry. After observing nanosecond-scale PZA unbinding from several PZase mutants, an algorithm was developed to systematically detect ligand release via centre of mass distances (COM) and ligand average speed calculations, before applying the statistically guided network analysis (SGNA) method to investigate conserved protein motions associated with ligand unbinding. Ligand and cofactor perspectives were also investigated. A conserved pair of lid-destabilising motions was found. These consisted of (1) antiparallel lid and side flap motions; (2) the contractions of a flanking region within the same flap and residue 74 towards the core. Mutations affecting the hinge residues (H51 and H71), nearby residues or L19 were found to destabilise the lid. Additionally, other metal binding site (MBS) mutations delocalised the Fe2+ cofactor, also facilitating lid opening. In the early stages of unbinding, a wider variety of PZA poses were observed, suggesting multiple exit pathways. These findings provide insights into the late events preceding PZA unbinding, which we found to occur in some resistant PZase mutants. Further, the algorithm developed here to identify unbinding events coupled with SGNA can be applicable to other similar problems.
Project description:Models for chemical reaction kinetics typically assume well-mixed conditions, in which chemical compositions change in time but are uniform in space. In contrast, many biological and microfluidic systems of interest involve non-uniform flows where gradients in flow velocity dynamically alter the effective reaction volume. Here, we present a theoretical framework for characterizing multi-step reactions that occur when an enzyme or enzymatic substrate is released from a flat solid surface into a linear shear flow. Similarity solutions are developed for situations where the reactions are sufficiently slow compared to a convective time scale, allowing a regular perturbation approach to be employed. For the specific case of Michaelis-Menten reactions, we establish that the transversally averaged concentration of product scales with the distance x downstream as x(5/3). We generalize the analysis to n-step reactions, and we discuss the implications for designing new microfluidic kinetic assays to probe the effect of flow on biochemical processes.