A predictive model for the spontaneous synchronization of Saccharomyces cerevisiae grown in continuous culture. I. Concept

A structured segregated model was developed for studying spontaneous oscillations of S. cerevisiae in continuous culture. The model is based on cells of a simple metabolic structure and assumptions about the modification of this structure during the cell cycle. The most important features of the model cells are the ability to grow on ethanol and glucose simultaneously in continuous culture, the accumulation of intracellular storage carbohydrates during the single cell phase and their mobilization during the budding phase. The model predicts oscillations of considerable similarity to those observed in experiments.     

On Ohta's hypothesis: Most amino acid substitutions are deleterious

Ohta's hypothesis that most amino acid substitutions are deleterious grew out of a class of population-genetics models called shift models. Recently, shift models have been shown to be biologically unreasonable and have been replaced by a more plausible house-of-cards model. In this paper, the simplest form of the house-of-cards models is shown to be incompatible with most of the major features of protein evolution. Moreover, this model is shown to not be a model of exclusively deleterious-allele evolution, but rather to be a model with an equal mix of deleterious and advantageous substitutions.     

Bayesian latent trait modeling of migraine symptom data

Definition of disease phenotype is a necessary preliminary to research into genetic causes of a complex disease. Clinical diagnosis of migraine is currently based on diagnostic criteria developed by the International Headache Society. Previously, we examined the natural clustering of these diagnostic symptoms using latent class analysis (LCA) and found that a four-class model was preferred. However, the classes can be ordered such that all symptoms progressively intensify, suggesting that a single continuous variable representing disease severity may provide a better model. Here, we compare two models: item response theory and LCA, each constructed within a Bayesian context. A deviance information criterion is used to assess model fit. We phenotyped our population sample using these models, estimated heritability and conducted genome-wide linkage analysis using Merlin-qtl. LCA with four classes was again preferred. After transformation, phenotypic trait values derived from both models are highly correlated (correlation = 0.99) and consequently results from subsequent genetic analyses were similar. Heritability was estimated at 0.37, while multipoint linkage analysis produced genome-wide significant linkage to chromosome 7q31-q33 and suggestive linkage to chromosomes 1 and 2. We argue that such continuous measures are a powerful tool for identifying genes contributing to migraine susceptibility.     

Instabilities in multiserotype disease models with antibody-dependent enhancement

This paper investigates the complex dynamics induced by antibody-dependent enhancement (ADE) in multiserotype disease models. ADE is the increase in viral growth rate in the presence of immunity due to a previous infection of a different serotype. The increased viral growth rate is thought to increase the infectivity of the secondary infectious class. In our models, ADE induces the onset of oscillations without external forcing. The oscillations in the infectious classes represent outbreaks of the disease. In this paper, we derive approximations of the ADE parameter needed to induce oscillations and analyze the associated bifurcations that separate the types of oscillations. We then investigate the stability of these dynamics by adding stochastic perturbations to the model. We also present a preliminary analysis of the effect of a single serotype vaccination in the model.     

Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays

In the glucose-insulin regulatory system, ultradian insulin secretory oscillations are observed to have a period of 50-150 min. After pioneering work traced back to the 1960s, several mathematical models have been proposed during the last decade to model these ultradian oscillations as well as the metabolic system producing them. These currently existing models still lack some of the key physiological aspects of the glucose-insulin system. Applying the mass conservation law, we introduce two explicit time delays and propose a more robust alternative model for better understanding the glucose-insulin endocrine metabolic regulatory system and the ultradian insulin secretory oscillations for the cases of continuous enteral nutrition and constant glucose infusion. We compare the simulation profiles obtained from this two time delay model with those from the other existing models. As a result, we notice many unique features of this two delay model. Based on our intensive simulations, we suspect that one of the possibly many causes of ultradian insulin secretion oscillations is the time delay of the insulin secretion stimulated by the elevated glucose concentration.     

Experimental testing of dynamic energy budget models

1. Dynamic energy budget (DEB) models describing the allocation of assimilate to the competing processes of growth, reproduction and maintenance in individual organisms have been applied to a variety of species with some success. There are two contrasting model formulations based on dynamic allocation rules that have been widely used (net production and net assimilation formulations). However, the predictions of these two classes of DEB models are not easily distinguished on the basis of simple growth and fecundity data.
2. It is shown that different assumptions incorporated in the rules determining allocation to growth and reproduction in two classes of commonly applied DEB models predict qualitatively distinct patterns for an easily measured variable, cumulative reproduction by the time an individual reaches an arbitrary size.
3. A comparison with experimental data from Daphnia pulex reveals that, in their simplest form, neither model predicts the observed qualitative pattern of reproduction, despite the fact that both formulations capture basic growth features.
4. An examination of more elaborate versions of the two models, in which the allocation rules are modified to account for brief periods of starvation experienced in the laboratory cultures, reveals that a version of the net production model can predict the qualitative pattern seen for cumulative eggs as a function of mass in D. pulex . The analysis leads to new predictions which can be easily tested with further laboratory experiments.     

Heterogeneity of Methicillin-Resistant <Emphasis Type="Italic">Staphylococcus aureus</Emphasis> Strains (MRSA) Characterized by Flow Cytometry

We used fluorescent penicillin Bocillin FL for characterization of control methicillin-resistant Staphylococcus aureus (MRSA) strains belonging to one of four heterogenic classes and comparing them with clinical MRSA isolates. Significant differences in percentage of fluorescent cells and reduction of Bocillin FL binding after incubation with methicillin between control strains from classes I and IV were observed, whereas the strains from classes II and III were differed after incubation with methicillin. According to this criteria, 55.8% of the clinical isolates population were similar to the strain of class IV or homogenic resistant, 11.8% was found as I, and 32.3% were categorized as class II or III. However, continuous diversity of measured features was also discussed.     

The effect of intracortical competition on the formation of topographic maps in models of Hebbian learning

Correlation-based learning (CBL) models and self-organizing maps (SOM) are two classes of Hebbian models that have both been proposed to explain the activity-driven formation of cortical maps. Both models differ significantly in the way lateral cortical interactions are treated, leading to different predictions for the formation of receptive fields. The linear CBL models predict that receptive field profiles are determined by the average values and the spatial correlations of the second order of the afferent activity patterns, wheras SOM models map stimulus features. Here, we investigate a class of models which are characterized by a variable degree of lateral competition and which have the CBL and SOM models as limit cases. We show that there exists a critical value for intracortical competition below which the model exhibits CBL properties and above which feature mapping sets in. The class of models is then analyzed with respect to the formation of topographic maps between two layers of neurons. For Gaussian input stimuli we find that localized receptive fields and topographic maps emerge above the critical value for intracortical competition, and we calculate this value as a function of the size of the input stimuli and the range of the lateral interaction function. Additionally, we show that the learning rule can be derived via the optimization of a global cost function in a framework of probabilistic output neurons which represent a set of input stimuli by a sparse code. Received: 23 June 1999 / Accepted in revised form: 05 November 1999     

Transforming between discrete and continuous angle distribution models: application to protein χ1 torsions

Two commonly employed angular-mobility models for describing amino-acid side-chain χ(1) torsion conformation, the staggered-rotamer jump and the normal probability density, are discussed and performance differences in applications to scalar-coupling data interpretation highlighted. Both models differ in their distinct statistical concepts, representing discrete and continuous angle distributions, respectively. Circular statistics, introduced for describing torsion-angle distributions by using a universal circular order parameter central to all models, suggest another distribution of the continuous class, here referred to as the elliptic model. Characteristic of the elliptic model is that order parameter and circular variance form complementary moduli. Transformations between the parameter sets that describe the probability density functions underlying the different models are provided. Numerical aspects of parameter optimization are considered. The issues are typified by using a set of χ(1) related (3) J coupling constants available for FK506-binding protein. The discrete staggered-rotamer model is found generally to produce lower order parameters, implying elevated rotatory variability in the amino-acid side chains, whereas continuous models tend to give higher order parameters that suggest comparatively less variation in angle conformations. The differences perceived regarding angular mobility are attributed to conceptually different features inherent to the models.     

Feedback identification of continuous microbial growth systems

The fundamental problem of dynamic modeling of continuous culture systems for process control and optimization is addressed. Forcing a system to bifurcation via feedback control is a very promising method for model discrimination and identification. Dynamic information is obtained by using this technique, the dynamic behavior of the chemostat as predicted by unstructured models, the model with delay, and a structured model has been analyzed. The method exposes significant differences in the nonlinear dynamic structure of the various models and can be implemented to discriminate between various possible models for a continuous culture system.     

Secondary structure-based assignment of the protein structural classes

Structural class categorizes proteins based on the amount and arrangement of the constituent secondary structures. The knowledge of structural classes is applied in numerous important predictive tasks that address structural and functional features of proteins. We propose novel structural class assignment methods that use one-dimensional (1D) secondary structure as the input. The methods are designed based on a large set of low-identity sequences for which secondary structure is predicted from their sequence (PSSA^sc model) or assigned based on their tertiary structure (SSA^sc). The secondary structure is encoded using a comprehensive set of features describing count, content, and size of secondary structure segments, which are fed into a small decision tree that uses ten features to perform the assignment. The proposed models were compared against seven secondary structure-based and ten sequence-based structural class predictors. Using the 1D secondary structure, SSA^sc and PSSA^sc can assign proteins to the four main structural classes, while the existing secondary structure-based assignment methods can predict only three classes. Empirical evaluation shows that the proposed models are quite promising. Using the structure-based assignment performed in SCOP (structural classification of proteins) as the golden standard, the accuracy of SSA^sc and PSSA^sc equals 76 and 75%, respectively. We show that the use of the secondary structure predicted from the sequence as an input does not have a detrimental effect on the quality of structural class assignment when compared with using secondary structure derived from tertiary structure. Therefore, PSSA^sc can be used to perform the automated assignment of structural classes based on the sequences.     

What makes biochemical networks tick?

In view of the increasing number of reported concentration oscillations in living cells, methods are needed that can identify the causes of these oscillations. These causes always derive from the influences that concentrations have on reaction rates. The influences reach over many molecular reaction steps and are defined by the detailed molecular topology of the network. So-called 'autoinfluence paths', which quantify the influence of one molecular species upon itself through a particular path through the network, can have positive or negative values. The former bring a tendency towards instability. In this molecular context a new graphical approach is presented that enables the classification of network topologies into oscillophoretic and nonoscillophoretic, i.e. into ones that can and ones that cannot induce concentration oscillations. The network topologies are formulated in terms of a set of uni-molecular and bi-molecular reactions, organized into branched cycles of directed reactions, and presented as graphs. Subgraphs of the network topologies are then classified as negative ones (which can) and positive ones (which cannot) give rise to oscillations. A subgraph is oscillophoretic (negative) when it contains more positive than negative autoinfluence paths. Whether the former generates oscillations depends on the values of the other subgraphs, which again depend on the kinetic parameters. An example shows how this can be established. By following the rules of our new approach, various oscillatory kinetic models can be constructed and analyzed, starting from the classified simplest topologies and then working towards desirable complications. Realistic biochemical examples are analyzed with the new method, illustrating two new main classes of oscillophore topologies.     

The Probability of Extinction of Infectious Salmon Anemia Virus in One and Two Patches

Single-type and multitype branching processes have been used to study the dynamics of a variety of stochastic birth–death type phenomena in biology and physics. Their use in epidemiology goes back to Whittle’s study of a susceptible–infected–recovered (SIR) model in the 1950s. In the case of an SIR model, the presence of only one infectious class allows for the use of single-type branching processes. Multitype branching processes allow for multiple infectious classes and have latterly been used to study metapopulation models of disease. In this article, we develop a continuous time Markov chain (CTMC) model of infectious salmon anemia virus in two patches, two CTMC models in one patch and companion multitype branching process (MTBP) models. The CTMC models are related to deterministic models which inform the choice of parameters. The probability of extinction is computed for the CTMC via numerical methods and approximated by the MTBP in the supercritical regime. The stochastic models are treated as toy models, and the parameter choices are made to highlight regions of the parameter space where CTMC and MTBP agree or disagree, without regard to biological significance. Partial extinction events are defined and their relevance discussed. A case is made for calculating the probability of such events, noting that MTBPs are not suitable for making these calculations.