Bayesian inference of biochemical kinetic parameters using the linear noise approximation

Background  

Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.     

The stochastic nature of biochemical networks

Cell behaviour and the cellular environment are stochastic. Phenotypes vary across isogenic populations and in individual cells over time. Here we will argue that to understand the abilities of cells we need to understand their stochastic nature. New experimental techniques allow gene expression to be followed in single cells over time and reveal stochastic bursts of both mRNA and protein synthesis in many different types of organisms. Stochasticity has been shown to be exploited by bacteria and viruses to decide between different behaviours. In fluctuating environments, cells that respond stochastically can out-compete those that sense environmental changes, and stochasticity may even have contributed to chromosomal gene order. We will focus on advances in modelling stochasticity, in understanding its effects on evolution and cellular design, and on means by which it may be exploited in biotechnology and medicine.     

The temperature factor and magnetic noise under the conditions of stochastic resonance of magnetosomes

The influence of magnetic noise on the dynamics of magnetic nanoparticles under the conditions of stochastic resonance is considered. The effect of the magnetic noise is shown to be equivalent to the growth of the effective thermostat temperature for the particles at the permanent actual temperature of the medium. This regularity may be used for testing the hypothesis on the involvement of magnetic nanoparticles in the formation of biological effects of weak magnetic fields.     

Temperature factor and magnetic noise under conditions of stochastic resonance of magnetosomes

The influence of magnetic noise on the dynamics of magnetic nanoparticles under stochastic resonance conditions is considered. The effect of magnetic noise on the nanoparticles at a fixed actual ambient temperature is equivalent to an increase in the effective temperature of the thermostat. This observation may be used to test whether magnetic nanoparticles are involved in the biological effects of weak magnetic fields.     

Simple, fast and accurate implementation of the diffusion approximation algorithm for stochastic ion channels with multiple states

BACKGROUND: The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled gating particles, while the DA was modeled using uncoupled gating particles. Implementations of DA with coupled particles, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. MAIN CONTRIBUTIONS: We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable--allowing an easy, transparent and efficient DA implementation, avoiding unnecessary approximations. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods, except when short time steps or low channel numbers were used.     

Activated dynamics and timescale separation within the landscape paradigm: signature of complexity, diversity and glassiness

The landscape paradigm has become a widespread picture within the realm of complex systems. Complex systems include a great variety of systems, ranging from glasses to biopolymers, which display a common dynamical behavior. Within this framework, the dynamics of a such a system can be envisioned as the search it performs on its (potential energy) landscape. This approach rests on the belief that the relaxation behavior depends only on generic features, irrespective of specific details and lies on the validity of a timescale separation scenario computationally corroborated but not properly validated yet form first principles. In this work we shall show that the prevalence of activated dynamics over other kinds of mechanisms determines the emergence of complex dynamical behavior. Thus, complexity and diversity are not intrinsic properties of a system but depend on the kind of exploration of the landscape. We shall focus mainly on an ample generic context (complex hierarchical systems which have been used as models of glasses, spin glasses and biopolymers) and a specific one (model glass formers). For the last case we shall be able to reveal (in mechanistic terms) the microscopic rationale for the occurrence of timescale separation. Furthermore, we shall explore the connections between these two up to now mostly unrelated contexts and the relation to a variational principle, and we shall reveal the conditions for the applicability of the landscape approach.     

The logical analysis of continuous, non-linear biochemical control networks

We propose a mapping to study the qualitative properties of continuous biochemical control networks which are invariant to the parameters used to describe the networks but depend only on the logical structure of the networks. For the networks, we are able to place a lower limit on the number of steady states and strong restrictions on the phase relations between components on cycles and transients. The logical structure and the dynamical behavior for a number of simple systems of biological interest, the feedback (predator-prey) oscillator, the bistable switch, the phase dependent switch, are discussed. We discuss the possibility that these techniques may be extended to study the dynamics of large many component systems.     

Mathematical descriptions of biochemical networks: stability, stochasticity, evolution

In this paper, we review some fundamental aspects, as well as some new developments, in the emerging field of network biology. The focus of attention is placed on mathematical approaches to conceptual modeling of biomolecular networks with special emphasis on dynamic stability, stochasticity and evolution.     

The linear theory of neuron networks: The dynamic problem

The development of a general theory of neuron-networks is here extended to cases of non-steady state activity. Conditions for stability and neutrality of an equilibrium point are set up, and the possible functions representing the variation of excitation over time are enumerated. The inverse network problem is considered—which is, given a preassigned pattern of activity over time, to construct when possible a neuron-network having this pattern. Finally, a canonical form for neuron networks is derived, in the sense of a network of a certain special topological structure which is equivalent in activity characteristics to any given network.     

The linear theory of neuron networks: The static problem

The construction of a theory of activity in neuron networks of arbitrary topological structure is commenced under the linear excitation hypothesis: we consider conditions for possible steady-state equilibria, deferring a dynamical treatment to the sequel.     

The presence of both stochastic and deterministic dynamics in electroretinograms measured under identical experimental conditions

We have studied whether living things investigated under the same measuring conditions can generate signals with different types of dynamics. We also wanted to detect the possible effects of low-intensity microwaves using parameters of deterministic chaos. For this purpose, two sets of electroretinograms were analysed by methods aimed at recognizing different types of dynamics. Both sets included the time series recorded from objects exposed to low-intensity microwaves and those that were not exposed. The analytical methods are based on nonlinear forecasting and a “surrogate data” technique. Although the experimental conditions were identical for the two sets, we have shown that both have time series with deterministic and stochastic dynamics. We also found that the use of parameters of deterministic dynamics is insufficient to distinguish between the sets. Received: 18 January 1994 / Accepted: 13 June 1997     

The prebiotic source influences the growth, biochemical features and survival under simulated gastrointestinal conditions of the probiotic Lactobacillus acidophilus

The viability of the probiotic strain Lactobacillus acidophilus DSM 20079, after its passage through the simulated gastric and pancreatic juices, was evaluated as function of its pre-growth in a medium containing the known prebiotics pectin or inulin, and was compared to glucose used as control. The presence of pectin or inulin did not affect the growth (12.11(log10) colony forming units/mL and 12.08(log10) colony forming units/mL for pectin and inulin respectively versus 12.22(log10) colony forming units/mL obtained for glucose). Pectin and inulin, in contrast to glucose, induced cell stress resistance against gastrointestinal juices (Δ(log10) 1 and 2 colony forming units/mL respectively, versus Δ(log10) 4.5 for glucose). The data were confirmed by the analysis of the protein pattern following stress treatments which, in the case of microbial cells grown with glucose, revealed a relevant protein degradation after the double passage through simulated gastric and intestinal juices. An impressive metabolic change, as function of the growth conditions, was demonstrated by analyzing the proteomic profile with a μ-2DE system, used herein for the first time as evaluation tool of prebiotic-probiotic interactions. The analysis revealed a different pH protein distribution that was mostly acidic in the presence of pectin and neutral-alkaline in the presence of inulin. Both prebiotics stimulated the production of butyrate, a relevant healthy bio-molecule not detectable in the presence of glucose, that was measured by HPLC analysis to be 14.5 fold higher after growth in the presence of inulin, as compared to pectin. Three specific proteins were detected at pH 6 after growth in the presence of pectin or inulin. They could be correlated to the stress resistance and/or to the production of butyrate, the common phenotypic characteristics induced in the bacterial strain by the two prebiotics.     

The growth of cereals under soil conditions characteristic of an unstable tilth

Summary In a series of experiments with winter cereals growing in pots, mechanical compaction of moist soil over wheat seed severely inhibited germination — no plants emerged from a compacted sandy loam soil. Conversely, the destruction of the surface tilth by falling water drops had no effect on the rate of emergence of either wheat or oats.Tillered wheat plants, growing at winter temperatures, survived prolonged adverse conditions of soil aeration.     

Effect of pH on Rhodomonas salina growth,biochemical composition,and taste,produced in semi-large scale under sunlight conditions

Journal of Applied Phycology - Rhodomonas salina is a microalgal species, belonging to the cryptophytes, and is widely used as aquaculture feed because of its high nutritional profile and...