Large-angle stimulated Raman scattering of short laser pulses in plasma

The features of the large-angle stimulated Raman scattering of short laser pulses in a homogeneous underdense plasma are studied analytically. It is found that, for scattering angles that are not too close to zero, a steady-state regime of the convective amplification of unstable waves is established in the frame of reference comoving with the laser pulse. The problem of convective amplification in a two-dimensional region is solved in both weak-and strong-coupling regimes. It is shown that the steady-state envelopes of the scattered radiation and scattering plasma waves are two-dimensional in nature. It is found that, for a given scattering angle, the maximum possible spatial amplification at the trailing edge of the pulse is achieved if the ratio of the transverse to longitudinal size of the pulse is larger than the cotangent of one-half of the scattering angle.     

Stability of Ensemble Models Predicts Productivity of Enzymatic Systems

Stability in a metabolic system may not be obtained if incorrect amounts of enzymes are used. Without stability, some metabolites may accumulate or deplete leading to the irreversible loss of the desired operating point. Even if initial enzyme amounts achieve a stable steady state, changes in enzyme amount due to stochastic variations or environmental changes may move the system to the unstable region and lose the steady-state or quasi-steady-state flux. This situation is distinct from the phenomenon characterized by typical sensitivity analysis, which focuses on the smooth change before loss of stability. Here we show that metabolic networks differ significantly in their intrinsic ability to attain stability due to the network structure and kinetic forms, and that after achieving stability, some enzymes are prone to cause instability upon changes in enzyme amounts. We use Ensemble Modelling for Robustness Analysis (EMRA) to analyze stability in four cell-free enzymatic systems when enzyme amounts are changed. Loss of stability in continuous systems can lead to lower production even when the system is tested experimentally in batch experiments. The predictions of instability by EMRA are supported by the lower productivity in batch experimental tests. The EMRA method incorporates properties of network structure, including stoichiometry and kinetic form, but does not require specific parameter values of the enzymes.     

Simple Biochemical Pathways far from Steady State Can Provide Switchlike and Integrated Responses

Covalent modification cycles (systems in which the activity of a substrate is regulated by the action of two opposing enzymes) and ligand/receptor interactions are ubiquitous in signaling systems and their steady-state properties are well understood. However, the behavior of such systems far from steady state remains unclear. Here, we analyze the properties of covalent modification cycles and ligand/receptor interactions driven by the accumulation of the activating enzyme and the ligand, respectively. We show that for a large range of parameters both systems produce sharp switchlike response and yet allow for temporal integration of the signal, two desirable signaling properties. Ultrasensitivity is observed also in a region of parameters where the steady-state response is hyperbolic. The temporal integration properties are tunable by regulating the levels of the deactivating enzyme and receptor, as well as by adjusting the rate of accumulation of the activating enzyme and ligand. We propose that this tunability is used to generate precise responses in signaling systems.     

Enhanced intracellular stability of sFv-Fc fusion intrabodies

The ability of intracellular antibodies (intrabodies) to block the function of a target protein can be dependent on the stability of the single-chain antibody (sFv) when expressed in the intracellular environment. Low-affinity sFvs capable of reaching high steady-state levels can be more effective modulators of target proteins than high-affinity, unstable sFvs. In an effort to enhance the intracellular stability of sFvs when expressed as intrabodies, we have generated novel sFv-Fc fusion intrabodies. Fusion of the native sFv sequence with the entire heavy chain constant region fragment of IgG results in decreased turnover of the intrabody and enhanced steady-state accumulation of sFv-Fc protein, while maintaining the ability to target intrabody expression to sub-cellular compartments. Here, we describe the rationale and design for this strategy using two anti-cyclin E sFvs constructed for use as intrabodies.     

Simple Biochemical Pathways far from Steady State Can Provide Switchlike and Integrated Responses

Covalent modification cycles (systems in which the activity of a substrate is regulated by the action of two opposing enzymes) and ligand/receptor interactions are ubiquitous in signaling systems and their steady-state properties are well understood. However, the behavior of such systems far from steady state remains unclear. Here, we analyze the properties of covalent modification cycles and ligand/receptor interactions driven by the accumulation of the activating enzyme and the ligand, respectively. We show that for a large range of parameters both systems produce sharp switchlike response and yet allow for temporal integration of the signal, two desirable signaling properties. Ultrasensitivity is observed also in a region of parameters where the steady-state response is hyperbolic. The temporal integration properties are tunable by regulating the levels of the deactivating enzyme and receptor, as well as by adjusting the rate of accumulation of the activating enzyme and ligand. We propose that this tunability is used to generate precise responses in signaling systems.     

Absolute stability and dynamical stabilisation in predator-prey systems

Many ecological systems exhibit multi-year cycles. In such systems, invasions have a complicated spatiotemporal structure. In particular, it is common for unstable steady states to exist as long-term transients behind the invasion front, a phenomenon known as dynamical stabilisation. We combine absolute stability theory and computation to predict how the width of the stabilised region depends on parameter values. We develop our calculations in the context of a model for a cyclic predator-prey system, in which the invasion front and spatiotemporal oscillations of predators and prey are separated by a region in which the coexistence steady state is dynamically stabilised.     

Diffusion and simultaneous chemical reactions: I. A method for solving the equations of some systems in which a fixed concentration exists at a boundary

Many solutions are available to the differential equations for systems consisting of a space region with a boundary at which the concentration is fixed, diffusion occurring across this boundary. A method is described for readily transforming these solutions into results for similar systems in which the diffusing substance is removed by a first-order reaction and also removed or produced at a rate which is expressible as a polynomial in the time variable. Subsidiary transformations and steady-state conditions are also discussed. An indication is given of biological applications of the results made available by this method.     

Effects of cell motility and chemotaxis on microbial population growth.

A mathematical model is developed to elucidate the effects of biophysical transport processes (nutrient diffusion, cell motility, and chemotaxis) along with biochemical reaction processes (cell growth and death, nutrient uptake) upon steady-state bacterial population growth in a finite one-dimensional region. The particular situation considered is that of growth limitation by a nutrient diffusing from an adjacent phase not accessible to the bacteria. It is demonstrated that the cell motility and chemotaxis properties can have great influence on steady-state population size. In fact, motility effects can be as significant as growth kinetic effects, in a manner analogous to diffusion- and reaction-limited regimes in chemically reacting systems. In particular, the following conclusions can be drawn from our analysis for bacterial populations growing at steady-state in a confined, unmixed region: (a) Random motility may lead to decreased population density; (b) chemotaxis can allow increased population density if the chemotactic response is large enough; (c) a species with superior motility properties can outgrow a species with superior growth kinetic properties; (d) motility effects become greater as the size of the confined growth region increases; and (e) motility effects are diminished by significant mass-transfer limitation of the nutrient from the adjacent source phase. The relationships of these results for populations to previous conclusions for individual cells is discussed, and implications for microbial competition are suggested.     

Periodic operation of well mixed enzyme reactors with steady state multiplicities using relay feedback

Periodic operation of a well mixed enzyme reactor with input and output multiplicities is theoretically analyzed. The system is an isothermal continuously stirred tank enzyme reactor with a non ideal mixing represented by a Cholettes’ model and a reaction kinetics given by k ₁ c/(k ₁ c+1)². The system exhibits input multiplicities and output multiplicities. Some of the input steady-states correspond to unstable steady-states. The periodic operation in the inlet feed concentration cannot be done by open loop oscillation method. Relay feedback method is essential for the periodic operation of such systems. The improvement in the average conversion is calculated for the two unstable input steady-states. Higher average conversion is obtained at the largest value of the feed concentration. The limitation of relay feedback method for the stable input steady-state is also brought out.     

Equality of average and steady-state levels in some nonlinear models of biological oscillations

Nonlinear oscillatory systems, playing a major role in biology, do not exhibit harmonic oscillations. Therefore, one might assume that the average value of any of their oscillating variables is unequal to the steady-state value. For a number of mathematical models of calcium oscillations (e.g. the Somogyi–Stucki model and several models developed by Goldbeter and co-workers), the average value of the cytosolic calcium concentration (not, however, of the concentration in the intracellular store) does equal its value at the corresponding unstable steady state at the same parameter values. The average value for parameter values in the unstable region is even equal to the level at the stable steady state for other parameter values, which allow stability. This holds for all parameters except those involved in the net flux across the cell membrane. We compare these properties with a similar property of the Higgins–Selkov model of glycolytic oscillations and two-dimensional Lotka–Volterra equations. Here, we show that this equality property is critically dependent on the following conditions: There must exist a net flux across the model boundaries that is linearly dependent on the concentration variable for which the equality property holds plus an additive constant, while being independent of all others. A number of models satisfy these conditions or can be transformed such that they do so. We discuss our results in view of the question which advantages oscillations may have in biology. For example, the implications of the findings for the decoding of calcium oscillations are outlined. Moreover, we elucidate interrelations with metabolic control analysis. This paper is dedicated to the memory of the late Reinhart Heinrich, who was the academic teacher of S.S. and, to a great extent, also of M.M.     

Stabilization of the cloning vector pACYC184 by insertion of F plasmid leading region sequences

The leading region of the F plasmid is, by definition, the first part of the plasmid DNA to be transferred to the recipient cell during conjugation. Restriction fragments of the leading region, when cloned into the plasmid vector pACYC184, extended the maintenance of the normally unstable p15A-derived vector replicon in rec+ Escherichia coli K-12 cells. Mutations in the host's general recombination systems were found to influence the maintenance of these hybrid plasmids.     

New insights into the genetic instability of streptomyces

Abstract The high level of genetic instability in Streptomyces ambofaciens is related to large scale DNA rearrangements (deletions and DNA amplifications) which occur within a 2 Mb chromosomal region. The genome of several Streptomyces species is linear and the unstable region is present at the chromosomal extremities. This has raised the questions of the role of the unstable region (which is dispensable under laboratory conditions), the functions of the genes present in this area, and the relationships between instability and chromosomal linearity. The unstable region of Streptomyces and the replication termini of several other microorganisms, including Escherichia coli , share numerous common traits. This suggests that the unstable region of Streptomyces includes the replication terminus, and that chromosomal instability is related to the termination process.     

Bifurcation diagram of a model chemical reaction—I. Stability changes of time-periodic solutions

The stability properties of the first two time-periodic solutions bifurcating from an unstable uniform steady-state are analyzed for a model chemical system subject to zero fluxes at the boundaries. The existence of new (secondary) bifurcation points is investigated on the small amplitude solutions and calculated analytically in the limit of small diffusion coefficients.     

Exact solutions to the continuous-quality equation for soil organic matter turnover

All living systems depend on transformations of elements between different states. In particular, the transformation of dead organic matter in the soil (SOM) by decomposers (microbes) releases elements incorporated in SOM and makes the elements available anew to plants. A major problem in analysing and describing this process is that SOM, as the result of the decomposer activity, is a mixture of a very large number of molecules with widely differing chemical and physical properties. The continuous-quality equation (CQE) is a general equation describing this complexity by assigning a continuous-quality variable to each carbon atom in SOM. The use of CQE has been impeded by its complicated mathematics. Here, we show by deriving exact solutions that, at least for some specific cases, there exist solutions to CQE. These exact solutions show that previous approximations have overestimated the rate by which litter decomposes and as a consequence underestimated steady state SOM amounts. The exact and approximate solutions also differ with respect to the parameter space in which they yield finite steady-state SOM amounts. The latter point is important because temperature is one of the parameters and climatic change may move the solution from a region of the parameter space with infinite steady-state SOM to a region of finite steady-state SOM, with potentially large changes in soil carbon stores. We also show that the solution satisfies the Chapman-Kolmogorov theorem. The importance of this is that it provides efficient algorithms for numerical solutions.     

A generalized theoretical treatment of the kinetics of an enzyme-catalysed reaction in the presence of an unstable irreversible modifier

A generalized theoretical treatment of the kinetics of an enzyme-catalysed reaction in the presence of an unstable irreversible inhibitor (or activator) is presented. Analytical expressions describing the time-dependence of product formation have been derived in coefficient form amenable to non-linear regression analysis for two operationally distinct types of reaction mechanism dependent on whether the reaction of the unstable modifier (X) with either or both the free enzyme (E) and enzyme-substrate complex (ES) occurs as a simple bimolecular process, or proceeds through the intermediacy of either or both adsorptive enzyme-modifier (EX) and enzyme-modifier-substrate (EXS) complexes in what may be considered as an extension of the Botts-Morales general modifier mechanism for (stable) reversible enzyme inhibitors and activators. Special cases of both models are classified in an analogous way to the traditional naming of reversible enzyme modifications, and guidelines concerning tests of mechanism and determination of kinetic parameters are given. In particular, it has been shown that kinetic constants describing enzyme inactivation by an unstable site-specific inhibitor forming a reversible EX complex prior to covalent modification step may be determined from a single progress curve. Kinetic analysis of the extended Botts-Morales mechanism describing irreversible enzyme inactivation has demonstrated that analytical expressions describing the time-course of product formation may be derived for a stable modifier by retaining the usual steady-state assumptions regarding the fluxes around ES and EXS provided quasi-equilibrium modifier binding to E and ES is assumed, but for unstable modifiers all of the binding steps must be assumed to be at quasi-equilibrium in the steady-state, except under restrictive circumstances.     

Fluxes,first passage times,and the reduction of Hill diagrams

The steady-state flux resulting from the coupling of two multistate systems is considered. The dynamics of these systems are described (a) as diffusion along a continuous one-dimensional free-energy profile specified by a conformational coordinate or (b) in terms of transitions between a discrete but arbitrary number of substates. If these multistate systems are connected in a simple way, it is shown that the steady-state flux can be obtained analytically. For both the continuous and discrete cases, the exact flux is shown to be identical to that calculated from a simple kinetic scheme involving only four states, if the effective rate constants of this reduced scheme are appropriately defined in terms of the mean first passage times for moving between various points along the multistate cycles. These results clarify and quantify the manner in which the internal conformational dynamics of two multistate systems influences the steady-state flux.     

Myotonic dystrophy: An unstable CTG repeat in a protein kinase gene

Myotonic dystrophy (DM) is caused by the amplification of CTG repeats in the 3′ untranslated region of a gene encoding a protein homologous to serine/threonine protein kinases. In DM patients the CTG repeats are extremely unstable, varying in length from patient to patient and generally increasing in length in successive generations. There is a strong correlation between the size of the repeats and the age of onset and severity of the disease. The molecular basis of the effect of the CTG expansion on the development of the DM phenotype continues to be investigated. The first working hypothesis of the molecular mechanism of DM was a reduction in steady-state myotonin-protein kinase (Mt-PK) mRNA and protein levels. However, although the consensus finding is that the Mt PK mRNA and protein levels are decreased in DM patients, it is still not clear if this reduction leads directly to the DM phenotype. In this short review we discuss the molecular aspects of CTG instability and the expression of the myotonin-protein kinase gene in normal and DM populations.