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PubMed2004

Graded and binary responses in stochastic gene expression.

Recently, several theoretical and experimental studies have been undertaken to probe the effect of stochasticity on gene expression (GE). In experiments, the GE response to an inducing signal in a cell, measured by the amount of mRNAs/proteins synthesized, is found to be either graded or binary. The latter type of response gives rise to a bimodal distribution in protein levels in an ensemble of cells. One possible origin of binary response is cellular bistability achieved through positive feedback or autoregulation. In this paper, we study a simple, stochastic model of GE and show that the origin of binary response lies exclusively in stochasticity. The transitions between the active and inactive states of the gene are random in nature. Graded and binary responses occur in the model depending on the relative stability of the activated and deactivated gene states with respect to that of mRNAs/proteins. The theoretical results on binary response provide a good description of the 'all-or-none' phenomenon observed in an eukaryotic system.

Gene Expression↗

PubMed2003

Analysis of noise in quorum sensing.

Noise may play a pivotal role in gene circuit functionality, as demonstrated for the genetic switch in the bacterial phage lambda. Like the lambda switch, bacterial quorum sensing (QS) systems operate within a population and contain a bistable switching element, making it likely that noise plays a functional role in QS circuit operation. Therefore, a detailed analysis of the noise behavior of QS systems is needed. We have developed a set of tools generally applicable to the analysis of gene circuits, with an emphasis on investigations in the frequency domain (FD), that we apply here to the QS system in the marine bacterium Vibrio fischeri. We demonstrate that a tight coupling between exact stochastic simulation and FD analysis provides insights into the structure/function relationships in the QS circuit. Furthermore, we argue that a noise analysis is incomplete without consideration of the power spectral densities (PSDs) of the important molecular output signals. As an example we consider reversible reactions in the QS circuit, and show through analysis and exact stochastic simulation that these circuits make significant and dynamic modifications to the noise spectra. In particular, we demonstrate a "whitening" effect, which occurs as the noise is processed through these reversible reactions.

Calibration↗

PubMed2002

Testing a mathematical model of the yeast cell cycle.

We derived novel, testable predictions from a mathematical model of the budding yeast cell cycle. A key qualitative prediction of bistability was confirmed in a strain simultaneously lacking cdc14 and G1 cyclins. The model correctly predicted quantitative dependence of cell size on gene dosage of the G1 cyclin CLN3, but it incorrectly predicted strong genetic interactions between G1 cyclins and the anaphase-promoting complex specificity factor Cdh1. To provide constraints on model generation, we determined accurate concentrations for the abundance of all nine cyclins as well as the inhibitor Sic1 and the catalytic subunit Cdc28. For many of these we determined abundance throughout the cell cycle by centrifugal elutriation, in the presence or absence of Cdh1. In addition, perturbations to the Clb-kinase oscillator were introduced, and the effects on cyclin and Sic1 levels were compared between model and experiment. Reasonable agreement was obtained in many of these experiments, but significant experimental discrepancies from the model predictions were also observed. Thus, the model is a strong but incomplete attempt at a realistic representation of cell cycle control. Constraints of the sort developed here will be important in development of a truly predictive model.

CDC28 Protein Kinase, S cerevisiae↗

PubMed2005

Bifurcation discovery tool.

MOTIVATION: Biochemical networks often yield interesting behavior such as switching, oscillation and chaotic dynamics. This article describes a tool that is capable of searching for bifurcation points in arbitrary ODE-based reaction networks by directing the user to regions in the parameter space, where such interesting dynamical behavior can be observed. RESULTS: We have implemented a genetic algorithm that searches for Hopf bifurcations, turning points and bistable switches. The software is implemented as a Systems Biology Workbench (SBW) enabled module and accepts the standard SBML model format. The interface permits a user to choose the parameters to be searched, admissible parameter ranges, and the nature of the bifurcation to be sought. The tool will return the parameter values for the model for which the particular behavior is observed. AVAILABILITY: The software, tutorial manual and test models are available for download at the following website: http:/www.sys-bio.org/ under the bifurcation link. The software is an open source and licensed under BSD.

Algorithms↗

PubMed1976

A fluidically controlled ventilator for bronchoscopy.

A simple time-cycled device uses an oscillating, fluidic, bistable element to control the high-pressure oxygen, supply to the ejector of a ventilating bronchoscope. Both manual and automatic modes of function are available, and inflation pressure and respiratory rate are controlled. Its construction is simple, the cost is low and the number of components is small.

Bronchoscopes↗

PubMed1994

Post-tetanic excitability changes and ectopic discharges in a human motor axon.

Post-tetanic ectopic discharges were studied in an identifiable human motor axon that could be stimulated non-invasively with high selectivity. This axon was tetanized at 300/s, for periods of 1-30 min, with 0.1 ms current pulses applied at the wrist. Repetitive discharges could be evoked by stimulation after tetani of 10 min or longer, and occurred spontaneously after tetani of 15 min or more. After a 20 min tetanus, bursts of up to 20 impulses at intervals of about 7 ms could be evoked for more than 30 min. Immediately after tetani of short duration, the threshold current required to excite the unit was increased, and it subsequently recovered monotonically. After tetani of 15 min or more, the threshold rose, then fell rapidly to below resting threshold, where it stayed for about as long as the stimuli evoked repetitive firing, before rising slowly to a second, broader maximum. The final recovery phase followed a stereotyped time course, whether starting immediately after a 3 min tetanus, or 2 h after a 30 min tetanus. When excitability was tested at defined intervals after the last impulse, abrupt transitions from low to high threshold were recorded, indicating that the axon could stay depolarized for at least 4 s after an impulse before rapidly hyperpolarizing. Repetitive discharges were evoked both when the threshold was low and when it was high, but the latency between the direct response and the start of the burst was different in the two cases. Only the short latency bursts, occurring at high threshold, were affected by polarizing currents applied at the stimulation site. The bursts at long latency (up to 200 ms) were presumed to originate elsewhere. Spontaneous bursts, occurring at intervals of 4-20 s, resembled the bursts which could be evoked by stimulation at about the same time. Our observations suggest that these post-tetanic ectopic discharges, like post-ischaemic motor discharges, occur on transitions from a hyperpolarized to a depolarized state. The transitions may occur spontaneously, but are readily triggered by an action potential, giving rise to a prolonged supernormal period. The bistability of the membrane potential probably occurs because accumulation of potassium ions under the myelin makes the currents through internodal potassium channels regenerative.

Action Potentials↗

PubMed2003

300-Hz subthalamic oscillations in Parkinson's disease.

Despite several studies and models, much remains unclear about how the human basal ganglia operate. Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is an effective treatment for complicated Parkinson's disease, but how DBS acts also remains unknown. The clinical benefit of DBS at frequencies >100 Hz suggests the possible importance of neural rhythms operating at frequencies higher than the range normally considered for basal ganglia processing (<100 Hz). The electrodes implanted for DBS also offer the opportunity to record neural activity from the human basal ganglia. This study aimed to assess whether oscillations at frequencies >100 Hz operate in the human STN. While recording local field potentials from the STN of nine patients with Parkinson's disease through DBS electrodes, we found a dopamine- and movement-dependent 300-Hz rhythm. At rest, and in the absence of dopaminergic medication, in most cases (eight out of 11 nuclei) the 100-1000 Hz band showed no consistent rhythm. Levodopa administration elicited (or markedly increased) a 300-Hz rhythm at rest [(mean +/- SD) central frequency: 319 +/- 33 Hz; bandwidth: 72 +/- 21 Hz; power increase (after medication - before medication)/before medication: 1.30 +/- 1.25; n = 11, P = 0.00098]. The 300-Hz rhythm was also increased by apomorphine, but not by orphenadrine. The 300-Hz rhythm was modulated by voluntary movement. Before levodopa administration, movement-related power increase in the 300-Hz rhythm was variably present in different subjects, whereas after levodopa it became a robust phenomenon [before 0.014 +/- 0.014 arbitrary units (AU), after 0.178 +/- 0.339 AU; n = 8, P = 0.0078]. The dopamine-dependent 300-Hz rhythm probably reflects a bistable compound nuclear activity and supports high-resolution information processing in the basal ganglia circuit. An absent 300-Hz subthalamic rhythm could be a pathophysiological clue in Parkinson's disease. The 300-Hz rhythm also provides the rationale for an excitatory--and not only inhibitory--interpretation of DBS mechanism of action in humans.

Adult↗

PubMed2003

Dynamics and plasticity of stimulus-selective persistent activity in cortical network models.

Persistent neuronal activity is widespread in many areas of the cerebral cortex of monkeys performing cognitive tasks with a working memory component. Modeling studies have helped understanding of the conditions under which persistent activity can be sustained in cortical circuits. Here, we first review several basic models of persistent activity, including bistable models with excitation only and multistable models for working memory of a discrete set of pictures or objects with structured excitation and global inhibition. In many experiments, persistent activity has been shown to be subject to changes due to associative learning. In cortical network models, Hebbian learning shapes the synaptic structure and, in turn, the properties of persistent activity when pictures are associated together in the course of a task. It is shown how the theoretical models can reproduce basic experimental findings of neurophysiological recordings from inferior temporal and perirhinal cortices obtained using the following experimental protocols: (i) the pair-associate task; (ii) the pair-associate task with color switch; and (iii) the delay match to sample task with a fixed sequence of samples.

Animals↗

PubMed1987

Nucleo-cytoplasmic interaction during macronuclear differentiation in ciliate protists: genetic basis for cytoplasmic control of SerH expression during macronuclear development in Tetrahymena thermophila.

A novel class of mutations affecting the developmental expression of SerH cell surface antigen genes of Tetrahymena thermophila is described. Unlike previous categories of mutation, the four independently isolated mutations of this class act through the cytoplasm to affect SerH genes during macronuclear development. That is, macronuclei which develop under the influence of mutant cytoplasm do not subsequently express H, most likely because the developmental processing of SerH genes is affected. The cytoplasmic effect is specific for the SerH locus and is independent of which SerH allele is present. In place of H, hitherto unknown antigens are expressed. Expression of SerH can be rescued during development either by wild-type cytoplasm exchanged between conjugants or by the homozygous wild-type genotype. The mutations segregate independently of the SerH genes and identify one, possibly two, bistable genes. Possible models to explain these results are discussed.

Alleles↗

PubMed2003

A theoretical model for the regulation of Sex-lethal, a gene that controls sex determination and dosage compensation in Drosophila melanogaster.

Cell fate commitment relies upon making a choice between different developmental pathways and subsequently remembering that choice. Experimental studies have thoroughly investigated this central theme in biology for sex determination. In the somatic cells of Drosophila melanogaster, Sex-lethal (Sxl) is the master regulatory gene that specifies sexual identity. We have developed a theoretical model for the initial sex-specific regulation of Sxl expression. The model is based on the well-documented molecular details of the system and uses a stochastic formulation of transcription. Numerical simulations allow quantitative assessment of the role of different regulatory mechanisms in achieving a robust switch. We establish on a formal basis that the autoregulatory loop involved in the alternative splicing of Sxl primary transcripts generates an all-or-none bistable behavior and constitutes an efficient stabilization and memorization device. The model indicates that production of a small amount of early Sxl proteins leaves the autoregulatory loop in its off state. Numerical simulations of mutant genotypes enable us to reproduce and explain the phenotypic effects of perturbations induced in the dosage of genes whose products participate in the early Sxl promoter activation.

Animals↗

PubMed1996

A model for antigen-induced T cell unresponsiveness based on autophosphorylative protein tyrosine kinase activity.

Helper T cell signaling is initiated by the aggregation of TCR with the induction of tyrosine kinase activity as one of the earliest consequences. Here, a theoretical model for antigen-induced unresponsiveness is presented that relies on a cascade of tyrosine phosphorylation-dephosphorylation cycles. A mechanism is described for both desensitization in the presence of antigen and persistent lowering of cell responsiveness after stimulus removal. An important component of the model, leading to bistability, is the presence of autophosphorylating protein tyrosine kinases in the early steps of TCR signaling. One of its predictions is that, following stimulation, the net phosphorylative activity of these receptor-associated tyrosine kinases will remain above background level after removal of the antigen. It is proposed that this residual tyrosine kinase activity is linked to a deficient signal transduction capacity of the TCR system that leads to a state of prolonged unresponsiveness. In addition, the present analysis defines the notion of a signaling threshold for hyporesponsiveness induction, associated with a durable switch and amplification of the net tyrosine kinase activity. This approach emphasizes the role of tyrosine kinases in the down-regulation of cellular competence.

Antigen Presentation↗

PubMed2006

Encoding folding paths of RNA switches.

RNA co-transcriptional folding has long been suspected to play an active role in helping proper native folding of ribozymes and structured regulatory motifs in mRNA untranslated regions (UTRs). Yet, the underlying mechanisms and coding requirements for efficient co-transcriptional folding remain unclear. Traditional approaches have intrinsic limitations to dissect RNA folding paths, as they rely on sequence mutations or circular permutations that typically perturb both RNA folding paths and equilibrium structures. Here, we show that exploiting sequence symmetries instead of mutations can circumvent this problem by essentially decoupling folding paths from equilibrium structures of designed RNA sequences. Using bistable RNA switches with symmetrical helices conserved under sequence reversal, we demonstrate experimentally that native and transiently formed helices can guide efficient co-transcriptional folding into either long-lived structure of these RNA switches. Their folding path is controlled by the order of helix nucleations and subsequent exchanges during transcription, and may also be redirected by transient antisense interactions. Hence, transient intra- and inter-molecular base pair interactions can effectively regulate the folding of nascent RNA molecules into different native structures, provided limited coding requirements, as discussed from an information theory perspective. This constitutive coupling between RNA synthesis and RNA folding regulation may have enabled the early emergence of autonomous RNA-based regulation networks.

Base Sequence↗

PubMed2006

Perception of causality in schizophrenia spectrum disorder.

Patients with schizophrenia spectrum disorders often maintain deviating views on cause-effect relationships, especially when positive and disorganization symptoms are manifest. Altered perceived causality is prominent in delusional ideation, in ideas of reference, and in the mentalizing ability (theory of mind [ToM]) of patients. Perceiving causal relationships may be understood either as higher order cognitive reasoning or as low-level information processing. In the present study, perception of causality was investigated as a low-level, preattentional capability similar to gestalt-like perceptual organization. Thirty-one patients (24 men and 7 women with mean age 27.7 years) and the same number of healthy control subjects matched to patients with respect to age and sex were tested. A visual paradigm was used in which 2 identical discs move, from opposite sides of a monitor, steadily toward and then past one another. Their coincidence generates an ambiguous, bistable percept (discs either "stream through" or "bounce off" one another). The bouncing perception, ie, perceived causality, is enhanced when auditory stimuli are presented at the time of coincidence. Psychopathology was measured using the Positive and Negative Syndrome Scale. It was found that positive symptoms were strongly associated with increased perceived causality and disorganization with attenuated perceived causality. Patients in general were not significantly different from controls, but symptom subgroups showed specifically altered perceived causality. Perceived causality as a basic preattentional process may contribute to higher order cognitive alterations and ToM deficiencies. It is suggested that cognitive remediation therapy should address both increased and reduced perception of causality.

Adult↗

PubMed1999

Analysis of cytokine dynamics in corneal allograft rejection.

Motivated by the discovery of oscillations in tumour necrosis factor-alpha (TNF-alpha) concentration in the aqueous humour of rabbits undergoing corneal allograft rejection, a simple mathematical model is developed for the regulation of TNF-alpha, which incorporates both negative feedback and amplification pathways. Mathematical analysis reveals a surprisingly rich behavioural repertoire for this simple cytokine pathway, including excitability, threshold behaviour, hysteresis, oscillations and bistability. This suggests new possibilities for experimental demonstration, and reveals the potential contributions of nonlinear dynamics to understanding cytokine regulation.

Animals↗

PubMed2003

Imperfect vaccination: some epidemiological and evolutionary consequences.

An aim of some vaccination programmes is to reduce the prevalence of an infectious disease and ultimately to eradicate it. We show that eradication success depends on the type of vaccine as well as on the vaccination coverage. Vaccines that reduce the parasite within-host growth rate select for higher parasite virulence and this evolution may both increase the prevalence of the disease and prevent disease eradication. By contrast, vaccines that reduce the probability of infection select against virulence and may lead more easily to eradication. In some cases, epidemiological feedback on parasite evolution yields an evolutionary bistable situation where, for intermediate vaccination coverage, parasites can evolve towards either high or low virulence, depending on the initial conditions. These results have practical implications for the design and use of imperfect vaccines in public- and animal-health programmes.

Animals↗

PubMed2004

Population dynamic theory of size-dependent cannibalism.

Cannibalism is characterized by four aspects: killing victims, gaining energy from victims, size-dependent interactions and intraspecific competition. In this review of mathematical models of cannibalistic populations, we relate the predicted population dynamic consequences of cannibalism to its four defining aspects. We distinguish five classes of effects of cannibalism: (i) regulation of population size; (ii) destabilization resulting in population cycles or chaos; (iii) stabilization by damping population cycles caused by other interactions; (iv) bistability such that, depending on the initial conditions, the population converges to one of two possible stable states; and (v) modification of the population size structure. The same effects of cannibalism may be caused by different combinations of aspects of cannibalism. By contrast, the same combination of aspects may lead to different effects. For particular cannibalistic species, the consequences of cannibalism will depend on the presence and details of the four defining aspects. Empirical evidence for the emerged theory of cannibalism is discussed briefly. The implications of the described dynamic effects of cannibalism are discussed in the context of community structure, making a comparison with the community effects of intraguild predation.

Animals↗

PubMed2004

Obtaining multiple separate food sources: behavioural intelligence in the Physarum plasmodium.

To evaluate performance in a complex survival task, we studied the morphology of the Physarum plasmodium transportation network when presented with multiple separate food sources. The plasmodium comprises a network of tubular elements through which chemical nutrient, intracellular signals and the viscous body are transported and circulated. When three separate food sources were presented, located at the vertices of a triangle, the tubular network connected them via a short pathway, which was often analogous to the mathematically shortest route known as Steiner's minimum tree (SMT). The other common network shape had high fault tolerance against accidental disconnection of the tubes and was known as cycle (CYC). Pattern selection appeared to be a bistable system involving SMT and CYC. When more than three food sources were presented, the network pattern tended to be a patchwork of SMT and CYC. We therefore concluded that the plasmodium tube network is a well designed and intelligent system.

Animals↗

PubMed2006

Disparate maturation adaptations to size-dependent mortality.

Body size is an important determinant of resource use, fecundity and mortality risk. Evolution of maturation size in response to size-dependent selection is thus a fundamental part of life-history theory. Increased mortality among small individuals has previously been predicted to cause larger maturation size, whereas increased mortality among large individuals is expected to have the opposite effect. Here we use a continuously size-structured model to demonstrate that, contrary to these widespread expectations, increased mortality among small individuals can have three alternative effects: maturation size may increase, decrease or become evolutionarily bistable. We show that such complex responses must be reckoned with whenever mortality is size-dependent, growth is indeterminate, reproduction impairs growth and fecundity increases with size. Predicting adaptive responses to altered size-dependent mortality is thus inherently difficult, since, as demonstrated here, such mortality cannot only reverse the direction of adaptation, but also cause abrupt shifts in evolutionarily stable maturation sizes.

Adaptation, Biological↗