Mathematical modelling of dynamics and control in metabolic networks. V. Static bifurcations in single biochemical control loops

Here we expand an earlier study of feedback activation in simple linear reaction sequences by searching the parameter space of biologically realistic rate laws for multiple stable steady states. The impetus for this work is to seek the origin of decision making strategies at the metabolic level, with particular emphasis on the switching between the operating conditions needed to meet changing substrate availability and organism requirements. The control loop considered herein is a linear reaction chain in which the end product of the reaction sequence feedback activates the first reaction in the sequence to produce feedback control. It has been found that the criteria for the existence of multiple steady state solutions in such loops involve only the kinetics of the regulatory enzyme controlling the first reaction and that of end product removal. The effects of these kinetics are examined here using two representative models for the regulatory enzyme: the lumped controller, based on Hill-type kinetics, and the symmetry model. The behavior of these two models is qualitatively similar, and both show the characteristics needed for switching between low and high substrate utilization. The removal rate is assumed to be of the Michaelis-Menten type. Judicious scaling of the governing equations permits separation of genetically determined kinetic parameters from concentration dependent ones. This allows us to conclude that, for a fixed set of kinetic parameters, the steady state flux through the loop can be switched between stable steady states by merely varying metabolite or enzyme concentrations. In particular, when the initial substrate exceeds a certain critical level, the loop can be "switched on" (by a discontinuous increase in the flux through the chain), and similarly, when it falls below a critical level, the pathway is shut down. Similar effects can be realized by varying the ratios of enzyme concentrations. It is proposed that by identifying these critical points one can gain significant insight into the objectives of decision making at the metabolic level.     

All Together Now: The Need for a Combined Empirical and Modeling Approach When Studying Primate Group Coordination

Studies of collective decision making attempt to explain the simultaneous behaviors of many individuals and how these contribute to the behavior observed at a collective level. However, this can be problematic to achieve given the general constraints of field or experimental data. This is particularly the case for primates, and results in limited reproducibility of events and it is difficult to separate the effects of different variables. Advocates of theoretical models have proposed that simple rules of interaction successfully reproduce different phases of group movement and the transitions between them, and greatly contribute to our knowledge of complex phenomena. Models can simulate practically any situation and tell us what response would emerge from it, including complex situations such as group decision making. The general heuristic value of these models has been universally recognized. However, the modeling approach tends to oversimplify real situations, and very few biological validations yet exist. I here suggest that it is essential to confront theoretical results with real data and that the combination of the 2 approaches will substantially improve our comprehension of collective decision making.     

The quantitative analysis of chromosome pairing and chiasma formation based on the relative frequencies of MI configurations. V. Interchange trisomics

Information obtained previously and presently on chromosome pairing and chiasma formation in trisomics and in interchange heterozygotes has been applied in newly constructed models for calculating expected MI configuration frequencies in interchange trisomics. Good fit betwen calculated and observed frequencies in some and poor fit in other cases confirmed the expectation of genetic variation in the crossing-over potentials of some or all chromosome regions. If conclusions in respect of chromosome pairing pattern are to be based on relative frequencies of MI configurations, valid values for crossing-over potentials are required. These can only be obtained from genetically comparable material. A few more disturbing factors are recognised. Environmental effects are one of these factors but may have a relatively simple character. Good agreement between expected and observed frequencies of configurations was taken to indicate the validity of the assumption that homologous chromosome end segments have equal probability of being involved in pairing, irrespective of the length of the segment. This conclusion was confirmed by the segregation of chromosomal types in the progenies of interchange trisomics: the excess chromosome was combined as frequently with the interchange set and with the normal set respectively, as expected on basis of the same models, assuming 60–80% viability of trisomes compared to diploids.     

Presenting Scientific Theories Within Risk Assessments

We propose a structure for presenting risk assessments with the purpose of enhancing the transparency of the selection process of scientific theories and models derived from them. The structure has two stages, with 7 steps, where the stages involve two types of theories: core and auxiliary, which need to be identified in order to explain and evaluate observations and predictions. Core theories are those that are “fundamental” to the phenomena being observed, whereas auxiliary theories are those that describe or explain the actual observation process of the phenomena. The formulation of a scientific theory involves three constitutive components or types of judgments: explanative, evaluative, and regulative or aesthetic, driven by reason. Two perspectives guided us in developing the proposed structure: (1) In a risk assessment explanations based on notions of causality can be used as a tool for developing models and predictions of possible events outside the range of direct experience. The use of causality for development of models is based on judgments, reflecting regulative or aesthetic conceptualizations of different phenomena and how they (should) fit together in the world. (2) Weight of evidence evaluation should be based on falsification principles for excluding models, rather than validation or justification principles that select the best or nearly best-fitting models. Falsification entails discussion that identifies challenges to proposed models, and reconciles apparent inconsistencies between models and data. Based on the discussion of these perspectives the 7 steps of the structure are: the first stage for core theories, (A) scientific concepts, (B) causality network, and (C) mathematical model; and the second stage for auxiliary theories, (D) data interpretation, (E) statistical model, (F) evaluation (weight of evidence), and (G) reconciliation, which includes the actual decision formulation.     

Covariate-adjusted varying coefficient models

Covariate-adjusted regression was recently proposed for situations where both predictors and response in a regression model are not directly observed, but are observed after being contaminated by unknown functions of a common observable covariate. The method has been appealing because of its flexibility in targeting the regression coefficients under different forms of distortion. We extend this methodology proposed for regression into the framework of varying coefficient models, where the goal is to target the covariate-adjusted relationship between longitudinal variables. The proposed method of covariate-adjusted varying coefficient model (CAVCM) is illustrated with an analysis of a longitudinal data set containing calcium absorbtion and intake measurements on 188 subjects. We estimate the age-dependent relationship between these two variables adjusted for the covariate body surface area. Simulation studies demonstrate the flexibility of CAVCM in handling different forms of distortion in the longitudinal setting.     

Quantal calcium release and calcium entry in the pancreatic acinar cell.

In the past decade, there have been remarkable advances in our understanding of the calcium messenger system that mediates the effects of various agonists. The purpose of the present article is to describe two areas of current interest in the calcium signaling field--quantal calcium release and calcium entry into the cell--using the pancreatic acinar cell as a model. Proposed mechanisms describing these phenomena and the role they play in the kinetics of calcium movements in the cell are discussed.     

What we talk about when we talk about access deficits

Semantic impairments have been divided into storage deficits, in which the semantic representations themselves are damaged, and access deficits, in which the representations are intact but access to them is impaired. The behavioural phenomena that have been associated with access deficits include sensitivity to cueing, sensitivity to presentation rate, performance inconsistency, negative serial position effects, sensitivity to number and strength of competitors, semantic blocking effects, disordered selection between strong and weak competitors, correlation between semantic deficits and executive function deficits and reduced word frequency effects. Four general accounts have been proposed for different subsets of these phenomena: abnormal refractoriness, too much activation, impaired competitive selection and deficits of semantic control. A combination of abnormal refractoriness and impaired competitive selection can account for most of the behavioural phenomena, but there remain several open questions. In particular, it remains unclear whether access deficits represent a single syndrome, a syndrome with multiple subtypes or a variable collection of phenomena, whether the underlying deficit is domain-general or domain-specific, whether it is owing to disorders of inhibition, activation or selection, and the nature of the connection (if any) between access phenomena in aphasia and in neurologically intact controls. Computational models offer a promising approach to answering these questions.     

Bayesian model averaging for evaluation of candidate gene effects

Statistical assessment of candidate gene effects can be viewed as a problem of variable selection and model comparison. Given a certain number of genes to be considered, many possible models may fit to the data well, each including a specific set of gene effects and possibly their interactions. The question arises as to which of these models is most plausible. Inference about candidate gene effects based on a specific model ignores uncertainty about model choice. Here, a Bayesian model averaging approach is proposed for evaluation of candidate gene effects. The method is implemented through simultaneous sampling of multiple models. By averaging over a set of competing models, the Bayesian model averaging approach incorporates model uncertainty into inferences about candidate gene effects. Features of the method are demonstrated using a simulated data set with ten candidate genes under consideration.     

From temporal processing to developmental language disorders: mind the gap

The ‘rapid temporal processing’ and the ‘temporal sampling framework’ hypotheses have been proposed to account for the deficits in language and literacy development seen in specific language impairment and dyslexia. This paper reviews these hypotheses and concludes that the proposed causal chains between the presumed auditory processing deficits and the observed behavioural manifestation of the disorders are vague and not well established empirically. Several problems and limitations are identified. Most data concern correlations between distantly related tasks, and there is considerable heterogeneity and variability in performance as well as concerns about reliability and validity. Little attention is paid to the distinction between ostensibly perceptual and metalinguistic tasks or between implicit and explicit modes of performance, yet measures are assumed to be pure indicators of underlying processes or representations. The possibility that diagnostic categories do not refer to causally and behaviourally homogeneous groups needs to be taken seriously, taking into account genetic and neurodevelopmental studies to construct multiple-risk models. To make progress in the field, cognitive models of each task must be specified, including performance domains that are predicted to be deficient versus intact, testing multiple indicators of latent constructs and demonstrating construct reliability and validity.     

Phase model-based neuron stabilization into arbitrary clusters

Deep brain stimulation (DBS) is a common method of combating pathological conditions associated with Parkinson’s disease, Tourette syndrome, essential tremor, and other disorders, but whose mechanisms are not fully understood. One hypothesis, supported experimentally, is that some symptoms of these disorders are associated with pathological synchronization of neurons in the basal ganglia and thalamus. For this reason, there has been interest in recent years in finding efficient ways to desynchronize neurons that are both fast-acting and low-power. Recent results on coordinated reset and periodically forced oscillators suggest that forming distinct clusters of neurons may prove to be more effective than achieving complete desynchronization, in particular by promoting plasticity effects that might persist after stimulation is turned off. Current proposed methods for achieving clustering frequently require either multiple input sources or precomputing the control signal. We propose here a control strategy for clustering, based on an analysis of the reduced phase model for a set of identical neurons, that allows for real-time, single-input control of a population of neurons with low-amplitude, low total energy signals. After demonstrating its effectiveness on phase models, we apply it to full state models to demonstrate its validity. We also discuss the effects of coupling on the efficacy of the strategy proposed and demonstrate that the clustering can still be accomplished in the presence of weak to moderate electrotonic coupling.     

Comparative kinetic analysis reveals that inducer-specific ion release precedes the mitochondrial permeability transition

Relationships among the multiple events that precede the mitochondrial membrane permeability transition (MPT) are not yet clearly understood. A combination of newly developed instrumental and computational approaches to this problem is described. The instrumental innovation is a high-resolution digital apparatus for the simultaneous, real-time measurement of four mitochondrial parameters as indicators of the respiration rate, membrane potential, calcium ion transport, and mitochondrial swelling. A computational approach is introduced that tracks the fraction of mitochondria that has undergone pore opening. This approach allows multiple comparisons on a single time scale. The validity of the computational approach for studying complex mitochondrial phenomena was evaluated with mitochondria undergoing an MPT induced by Ca(2+), phenylarsine oxide or alamethicin. Selective ion leaks were observed that precede the permeability transition and that are inducer specific. These results illustrate the occurrence of inducer-specific sequential changes associated with the induction of the permeability transition. Analysis of the temporal relationship among the multiple mitochondrial parameters of isolated mitochondria should provide insights into the mechanisms underlying these responses.     

Comparative kinetic analysis reveals that inducer-specific ion release precedes the mitochondrial permeability transition

Relationships among the multiple events that precede the mitochondrial membrane permeability transition (MPT) are not yet clearly understood. A combination of newly developed instrumental and computational approaches to this problem is described. The instrumental innovation is a high-resolution digital apparatus for the simultaneous, real-time measurement of four mitochondrial parameters as indicators of the respiration rate, membrane potential, calcium ion transport, and mitochondrial swelling. A computational approach is introduced that tracks the fraction of mitochondria that has undergone pore opening. This approach allows multiple comparisons on a single time scale. The validity of the computational approach for studying complex mitochondrial phenomena was evaluated with mitochondria undergoing an MPT induced by Ca²⁺, phenylarsine oxide or alamethicin. Selective ion leaks were observed that precede the permeability transition and that are inducer specific. These results illustrate the occurrence of inducer-specific sequential changes associated with the induction of the permeability transition. Analysis of the temporal relationship among the multiple mitochondrial parameters of isolated mitochondria should provide insights into the mechanisms underlying these responses.     

A multicriteria decision making approach for estimating the number of clusters in a data set

Determining the number of clusters in a data set is an essential yet difficult step in cluster analysis. Since this task involves more than one criterion, it can be modeled as a multiple criteria decision making (MCDM) problem. This paper proposes a multiple criteria decision making (MCDM)-based approach to estimate the number of clusters for a given data set. In this approach, MCDM methods consider different numbers of clusters as alternatives and the outputs of any clustering algorithm on validity measures as criteria. The proposed method is examined by an experimental study using three MCDM methods, the well-known clustering algorithm-k-means, ten relative measures, and fifteen public-domain UCI machine learning data sets. The results show that MCDM methods work fairly well in estimating the number of clusters in the data and outperform the ten relative measures considered in the study.     

Critical analysis of methods for analysing human calcium kinetics

A comparison has been made between several different compartmental and non-compartmental methods for analyzing human calcium kinetics. Using data from studies in six normal subjects, plus a computer-generated set of “error-free” data, the bone accretion rate and the exchangeable calcium pool size have been calculated by each method, along with their corresponding uncertainties. The effects of selective deletions of data have also been determined for the various methods.The results are highly dependent upon the model employed and the parameter investigated. In general, the non-compartmental models provide accretion rates which are less sensitive to measurement errors, and have less stringent requirements as to the necessary duration of an experimental study. Among compartmental models, a three-compartment model based on data collected from two hours to twenty days after isotopic calcium injection gives estimates of skeletal accretion rate and exchangeable pool size very similar to those resulting from a four-compartment model that includes additional earlier data.The relative advantages of various compartmental and non-compartmental methods of analysis are discussed in relation to these results, and practical recommendations offered to the clinical investigator.     

Signal transduction of eicosanoid CB1 receptor ligands.

The eicosanoid ligand, arachidonylethanolamide (anandamide), interacts with the CB1 cannabinoid receptor in the brain to signal its response. Pharmacophoric points of interaction between this agonist and the receptor have been proposed based upon structure-activity relationship studies of ligand binding to the receptor. Three dimensional quantitative structure-activity relationship (3D-QSAR) models have been constructed based upon the corresponding pharmacophoric points predicted for cannabinoid ligands delta9-tetrahydrocannabinol and 9-nor-9beta-hydroxyhexa-hydrocannabinol. A novel data set has been used to test the statistical validity of these models. Once the ligand interacts with the CB1 receptor, signal transduction occurs via G-proteins of the Gi/o family which are shown to be associated with the receptor. Evidence suggests that the juxtamembrane region of the C-terminal of the CB1 receptor is critical for activation of these G-proteins.     

A mixture theory model of fluid and solute transport in the microvasculature of normal and malignant tissues. I. Theory

In order to better understand the mechanisms governing transport of drugs, nanoparticle-based treatments, and therapeutic biomolecules, and the role of the various physiological parameters, a number of mathematical models have previously been proposed. The limitations of the existing transport models indicate the need for a comprehensive model that includes transport in the vessel lumen, the vessel wall, and the interstitial space and considers the effects of the solute concentration on fluid flow. In this study, a general model to describe the transient distribution of fluid and multiple solutes at the microvascular level was developed using mixture theory. The model captures the experimentally observed dependence of the hydraulic permeability coefficient of the capillary wall on the concentration of solutes present in the capillary wall and the surrounding tissue. Additionally, the model demonstrates that transport phenomena across the capillary wall and in the interstitium are related to the solute concentration as well as the hydrostatic pressure. The model is used in a companion paper to examine fluid and solute transport for the simplified case of an axisymmetric geometry with no solid deformation or interconversion of mass.     

A role for calcium release-activated current (CRAC) in cholinergic modulation of electrical activity in pancreatic beta-cells.

S. Bordin and colleagues have proposed that the depolarizing effects of acetylcholine and other muscarinic agonists on pancreatic beta-cells are mediated by a calcium release-activated current (CRAC). We support this hypothesis with additional data, and present a theoretical model which accounts for most known data on muscarinic effects. Additional phenomena, such as the biphasic responses of beta-cells to changes in glucose concentration and the depolarizing effects of the sarco-endoplasmic reticulum calcium ATPase pump poison thapsigargin, are also accounted for by our model. The ability of this single hypothesis, that CRAC is present in beta-cells, to explain so many phenomena motivates a more complete characterization of this current.     

Modelling receptor-controlled intracellular calcium oscillators.

This paper presents mathematical models for the hepatocyte calcium oscillator which follow the concepts in a class of informal models developed to account for the striking dependence on the receptor type of several features of the calcium oscillations, in particular the shape and duration of the free calcium transients. The essence of these models is that the transients should be timed by a build-up of activated GTP-binding proteins, which, combined with positive feedback processes and perhaps with cooperative effects, leads to a sudden activation of phospholipase C (PLC), followed by negative feedback processes which switch off the calcium rise and lead to a fall in free calcium back to resting levels. These models predict pulsatile oscillations in inositol (1,4,5)P3 as well as in free calcium. We show that receptor-controlled intracellular calcium oscillators involving an unknown positive feedback pathway onto PLC and negative feedback from protein kinase C (PKC) onto G-proteins and receptors, or negative feedback by stimulation of GTPase activity can simulate many of the features of observed intracellular calcium oscillations. These oscillators exhibit a dependence of frequency on agonist concentration and a dependence of transient duration on receptor and G-protein type. We also show that a PLC-dependent GTPase activating factor (GAF) could provide explanations for some otherwise puzzling features of intracellular calcium oscillations.     

Ecological validity of social interaction tests in rats and mice

Different rat and mouse models are used in studies of social interactions. Simple behavioral measures, which are commonly used in the laboratory, allow to perform relatively short experiments and to use multiple brain manipulation techniques. However, too much focus on the simplest behavioral models generates a serious risk of reducing ecological validity or even studying phenomena which would never happen outside of the laboratory. In this review, we discuss the suitability of mice and rats as model organisms for studying social behaviors, with focus on social transmission of fear paradigms. First, we briefly introduce the concept of domestication and what impact it had on laboratory rodents. Then, we present two aspects of social behaviors, sociability and dominance, which are crucial for social organization in these species. Finally, we present experimental models used for studying how animals transmit information about danger between each other, and how these models may reflect what happens in the natural environment. We discuss the difficulties that arise from our limited knowledge of rat and mouse ecology, especially their social life. We also explore the subject of balancing ecological validity and controllability in rodent models of social behaviors, the latter being particularly important for studying brain activity. Although it is very challenging, an efficient program for social neuroscience research should, in our opinion, aim at bridging the gap between laboratory and field studies.