23,770 research outputs found
Parallel versus off-pathway Michaelis-Menten mechanism for single-enzyme kinetics of a fluctuating enzyme
Recent fluorescence spectroscopy measurements of the turnover time
distribution of single-enzyme turnover kinetics of -galactosidase
provide evidence of Michaelis-Menten kinetics at low substrate concentration.
However, at high substrate concentrations, the dimensionless variance of the
turnover time distribution shows systematic deviations from the
Michaelis-Menten prediction. This difference is attributed to conformational
fluctuations in both the enzyme and the enzyme-substrate complex and to the
possibility of both parallel and off-pathway kinetics. Here, we use the
chemical master equation to model the kinetics of a single fluctuating enzyme
that can yield a product through either parallel or off-pathway mechanisms. An
exact expression is obtained for the turnover time distribution from which the
mean turnover time and randomness parameters are calculated. The parallel and
off-pathway mechanisms yield strikingly different dependences of the mean
turnover time and the randomness parameter on the substrate concentration. In
the parallel mechanism, the distinct contributions of enzyme and
enzyme-substrate fluctuations are clearly discerned from the variation of the
randomness parameter with substrate concentration. From these general results
we conclude that an off-pathway mechanism, with substantial enzyme-substrate
fluctuations, is needed to rationalize the experimental findings of
single-enzyme turnover kinetics of -galactosidase.Comment: 27 pages, 5 figure
Enzyme kinetics for a two-step enzymic reaction with comparable initial enzyme-substrate ratios
We extend the validity of the quasi-steady state assumption for a model double intermediate enzyme-substrate reaction to include the case where the ratio of initial enzyme to substrate concentration is not necessarily small. Simple analytical solutions are obtained when the reaction rates and the initial substrate concentration satisfy a certain condition. These analytical solutions compare favourably with numerical solutions of the full system of differential equations describing the reaction. Experimental methods are suggested which might permit the application of the quasi-steady state assumption to reactions where it may not have been obviously applicable before
Enzyme kinetics far from the standard quasi-steady-state and equilibrium approximations
Analytic approximations of the time-evolution of the single enzyme-substrate reaction are valid for all but a small region of parameter space in the positive initial enzyme-initial substrate concentration plane. We find velocity equations for the substrate decomposition and product formation with the aid of the total quasi-steady-state approximation and an aggregation technique for cases where neither the more normally employed standard nor reverse quasi-steady-state approximations are valid. Applications to determining reaction kinetic parameters are discussed
Spatio-temporal correlations can drastically change the response of a MAPK pathway
Multisite covalent modification of proteins is omnipresent in eukaryotic
cells. A well-known example is the mitogen-activated protein kinase (MAPK)
cascade, where in each layer of the cascade a protein is phosphorylated at two
sites. It has long been known that the response of a MAPK pathway strongly
depends on whether the enzymes that modify the protein act processively or
distributively: distributive mechanism, in which the enzyme molecules have to
release the substrate molecules in between the modification of the two sites,
can generate an ultrasensitive response and lead to hysteresis and bistability.
We study by Green's Function Reaction Dynamics, a stochastic scheme that makes
it possible to simulate biochemical networks at the particle level and in time
and space, a dual phosphorylation cycle in which the enzymes act according to a
distributive mechanism. We find that the response of this network can differ
dramatically from that predicted by a mean-field analysis based on the chemical
rate equations. In particular, rapid rebindings of the enzyme molecules to the
substrate molecules after modification of the first site can markedly speed up
the response, and lead to loss of ultrasensitivity and bistability. In essence,
rapid enzyme-substrate rebindings can turn a distributive mechanism into a
processive mechanism. We argue that slow ADP release by the enzymes can protect
the system against these rapid rebindings, thus enabling ultrasensitivity and
bistability
Iterative Approximate Solutions of Kinetic Equations for Reversible Enzyme Reactions
We study kinetic models of reversible enzyme reactions and compare two
techniques for analytic approximate solutions of the model. Analytic
approximate solutions of non-linear reaction equations for reversible enzyme
reactions are calculated using the Homotopy Perturbation Method (HPM) and the
Simple Iteration Method (SIM). The results of the approximations are similar.
The Matlab programs are included in appendices.Comment: 28 pages, 22 figure
Cloning, preparation and preliminary crystallographic studies of penicillin V acylase autoproteolytic processing mutants
The crystallization of three catalytically inactive mutants of penicillin Vacylase (PVA) from Bacillus sphaericus in precursor and processed forms is reported. The mutant proteins crystallize in different primitive monoclinic space groups that are distinct from the crystal forms for the native enzyme. Directed mutants and clone constructs were designed to study the post-translational autoproteolytic processing of PVA. The catalytically inactive mutants will provide threedimensional structures of precursor PVA forms, plus open a route to the study of enzyme-substrate complexes for this industrially important enzyme
Rule-based Modelling and Tunable Resolution
We investigate the use of an extension of rule-based modelling for cellular
signalling to create a structured space of model variants. This enables the
incremental development of rule sets that start from simple mechanisms and
which, by a gradual increase in agent and rule resolution, evolve into more
detailed descriptions
- …