Spatial and temporal aspects of cell signalling

As new techniques are developed to measure intracellular messengers it becomes increasingly apparent that there is a remarkable spatial and temporal organization of cell signalling. Cells possess a small discrete hormone-sensitive pool of inositol lipid. In some cells such as Xenopus oocytes and Limulus photoreceptors this phosphoinositide signalling system is highly concentrated in one region of the cell, so establishing localized calcium gradients. Another example is the hydrolysis of inositol lipids in eggs at the point of sperm entry resulting in a localized increase in Ins(1,4,5)P3 and calcium which spreads like a wave throughout the egg. In hamster eggs this burst of calcium at fertilization recurs at 1-3 min intervals for over 100 min, a particularly dramatic example of spontaneous activity. Spontaneous oscillations in intracellular calcium exist in many different cell types and are often induced by agonists that hydrolyse inositol lipids. We have made a distinction between oscillations that are approximately sinusoidal and occur at a higher frequency where free calcium is probably continuously involved in the oscillatory cycle and those where calcium falls to resting levels for many seconds between transients. In the former case, the oscillations are thought to be induced through a cytoplasmic oscillator based on the phenomenon of calcium-induced calcium release. Such oscillations can be induced in Xenopus oocytes after injection with Ins(1,4,5)P3. A receptor-controlled oscillator based on the periodic formation of Ins(1,4,5)P3 is probably responsible for the generation of the widely spaced calcium transients. The function of such calcium oscillations is currently unknown. They may be a reflection of the feedback interactions that operate to control intracellular calcium. Another possibility emerged from observations that in some cells the frequency of calcium oscillations varied with agonist concentration, suggesting that cells might employ these oscillations as a way of encoding information. One advantage of using such a frequency-dependent mechanism may lie in an increase in fidelity, especially at low agonist concentrations. Whatever these functions might be, it is clear that uncovering the mechanisms responsible for such oscillatory activity will greatly enhance our understanding of the relation between the phosphoinositides and calcium signalling.     

Control design for sustained oscillation in a two-gene regulatory network

Control strategies for gene regulatory networks have begun to be explored, both experimentally and theoretically, with implications for control of disease as well as for synthetic biology. Recent work has focussed on controls designed to achieve desired stationary states. Another useful objective, however, is the initiation of sustained oscillations in systems where oscillations are normally damped, or even not present. Alternatively, it may be desired to suppress (by damping) oscillations that naturally occur in an uncontrolled network. Here we address these questions in the context of piecewise-affine models of gene regulatory networks with affine controls that match the qualitative nature of the model. In the case of two genes with a single relevant protein concentration threshold per gene, we find that control of production terms (constant control) is effective in generating or suppressing sustained oscillations, while control of decay terms (linear control) is not effective. We derive an easily calculated condition to determine an effective constant control. As an example, we apply our analysis to a model of the carbon response network in Escherichia coli, reduced to the two genes that are essential in understanding its behavior.     

Electrifying rhythms in plant cells

Physiological oscillations (or rhythms) pervade all spatiotemporal scales of biological organization, either because they perform critical functions or simply because they can arise spontaneously and may be difficult to prevent. Regardless of the case, they reflect regulatory relationships between control points of a given system and offer insights as read-outs of the concerted regulation of a myriad of biological processes. Here we review recent advances in understanding ultradian oscillations (period < 24h) in plant cells, with a special focus on single-cell oscillations. Ion channels are at the center stage due to their involvement in electrical/excitabile phenomena associated with oscillations and cell-cell communication. We highlight the importance of quantitative approaches to measure oscillations in appropriate physiological conditions, which are essential strategies to deal with the complexity of biological rhythms. Future development of optogenetics techniques in plants will further boost research on the role of membrane potential in oscillations and waves across multiple cell types.     

Synergistic control of oscillations in the NF-kappaB signalling pathway

In previous work, we studied the behaviour of a model of part of the NF-kappaB signalling pathway. The model displayed oscillations that varied both in number, amplitude and frequency when its parameters were varied. Sensitivity analysis showed that just nine of the 64 reaction parameters were mainly responsible for the control of the oscillations when these parameters were varied individually. However, the control of the properties of any complex system is distributed, and, as many of these reactions are highly non-linear, we expect that their interactions will be too. Pairwise modulation of these nine parameters gives a search space some 50 times smaller (81 against 4096) than that required for the pairwise modulation of all 64 reactions, and this permitted their study (which would otherwise have been effectively intractable). Strikingly synergistic effects were observed, in which the effect of one of the parameters was strongly (and even qualitatively) dependent on the values of another parameter. Regions of parameter space could be found in which the amplitude, but not the frequency (timing), of oscillations varied, and vice versa. Such modelling will permit the design and performance of experiments aimed at disentangling the role of the dynamics of oscillations, rather than simply their amplitude, in determining cell fate. Overall, the analyses reveal a level of complexity in these dynamic models that is not apparent from study of their individual parameters alone and point to the value of manipulating multiple elements of complex networks to achieve desired physiological effects.     

Oscillations in calcium-cyclic AMP control loops form the basis of pacemaker activity and other high frequency biological rhythms.

In this paper theoretical and experimental evidence is presented which indicates that oscillations in internal calcium and cyclic AMP concentrations due to an instability in their common control loops are possible and indeed may be widespread. Further, it is demonstrated that fluctuations in various cellular properties, in particular membrane potential, are a direct consequence of these second messenger oscillations. Given the central importance of calcium and cyclic AMP to the regulation of metabolism, these oscillations would influence most metabolic processes especially rhythmic behaviour. We propose that these oscillations form the basis of several biological rhythms including, potential oscillations in cardiac pacemaker cells, neurones and insulin secreting β-cells, the minute rhythm in smooth muscle, cyclic AMP pulses in Dictyostelium, rhythmical cytoplasmic streaming in Physarum and transepitheliel potential oscillations in Calliphora salivary gland. This model makes possible an explanation of the frequency and amplitude effects of hormones.     

Oscillations in plant membrane transport: model predictions, experimental validation, and physiological implications

Although oscillations in membrane-transport activity are ubiquitous in plants, the ionic mechanisms of ultradian oscillations in plant cells remain largely unknown, despite much phenomenological data. The physiological role of such oscillations is also the subject of much speculation. Over the last decade, much experimental evidence showing oscillations in net ion fluxes across the plasma membrane of plant cells has been accumulated using the non-invasive MIFE technique. In this study, a recently proposed feedback-controlled oscillatory model was used. The model adequately describes the observed ion flux oscillations within the minute range of periods and predicts: (i) strong dependence of the period of oscillations on the rate constants for the H+ pump; (ii) a substantial phase shift between oscillations in net H+ and K+ fluxes; (iii) cessation of oscillations when H+ pump activity is suppressed; (iv) the existence of some 'window' of external temperatures and ionic concentrations, where non-damped oscillations are observed: outside this range, even small changes in external parameters lead to progressive damping and aperiodic behaviour; (v) frequency encoding of environmental information by oscillatory patterns; and (vi) strong dependence of oscillatory characteristics on cell size. All these predictions were successfully confirmed by direct experimental observations, when net ion fluxes were measured from root and leaf tissues of various plant species, or from single cells. Because oscillatory behaviour is inherent in feedback control systems having phase shifts, it is argued from this model that suitable conditions will allow oscillations in any cell or tissue. The possible physiological role of such oscillations is discussed in the context of plant adaptive responses to salinity, temperature, osmotic, hypoxia, and pH stresses.     

Modeling of Glucose-Induced cAMP Oscillations in Pancreatic β Cells: cAMP Rocks when Metabolism Rolls

Recent advances in imaging technology have revealed oscillations of cyclic adenosine monophosphate (cAMP) in insulin-secreting cells. These oscillations may be in phase with cytosolic calcium oscillations or out of phase. cAMP oscillations have previously been modeled as driven by oscillations in calcium, based on the known dependence of the enzymes that generate cAMP (adenylyl cyclase) and degrade it (phosphodiesterase). However, cAMP oscillations have also been reported to occur in the absence of calcium oscillations. Motivated by similarities between the properties of cAMP and metabolic oscillations in pancreatic β cells, we propose here that in addition to direct control by calcium, cAMP is controlled by metabolism. Specifically, we hypothesize that AMP inhibits adenylyl cyclase. We incorporate this hypothesis into the dual oscillator model for β cells, in which metabolic (glycolytic) oscillations cooperate with modulation of ion channels and metabolism by calcium. We show that the combination of oscillations in AMP and calcium in the dual oscillator model can account for the diverse oscillatory patterns that have been observed, as well as for experimental perturbations of those patterns. Predictions to further test the model are provided.     

Oscillation of the electric potential of frog skin under the effect of Li+: Experimental approach

Summary When a frog skin is used to separate two compartments, and lithium is added to the external medium, transmembrane electric potential oscillations frequently occur. When no external current is imposed, sustained oscillations, with a period of about 10 min, are maintained for several hours. An oscillation of the Na⁺ influx accompanies the electric oscillation, though the two oscillations are out of phase to a greater or less extent.Theophyllin promotes a significant decrease in the mean electric potential of the skin, but it does not affect very much the characteristics of the oscillation. Important factors influencing the oscillation are temperature, permeability of the external membrane to lithium, and potassium concentration in the internal medium. No correlation can be detected between oscilation characteristics and skin area. This suggests that the oscillation is of a local nature, possibly originating at the cellular level. Occurrence of macroscopic oscillations implies coupling between local oscillators. Coupling between two epithelia has been studied under diverse conditions. The coupling is of an electrical nature: by varying the value of the coupling resistance, it is possible to control synchronization of the oscillations.     

Tremor and other oscillations in neuromuscular systems

A model has been analyzed which is based on recent experimental evidence concerning the properties of muscles and the sensory feedback pathways from muscles. Damped oscillations can arise in the absence of sensory feedback due to the interaction of a muscle with inertial loads. These mechanical oscillations can have a wide range of frequencies depending on the inertial and elastic loads that are attached to the muscle. Small amounts of sensory feedback will tend to reduce deviations from a steady muscle length, but larger amounts of feedback can produce oscillations. The frequency of these reflex oscillations is determined by the properties of the muscle and feedback pathway, and is rather independent of load. If the strength of the sensory feedback is sufficient, either the mechanical oscillations or the reflex oscillations or both can grow, rather than decay, with time. The growth of these oscillations is limited by saturation non-linearities in the muscle receptors and the muscle itself, so that the oscillations approach a steady amplitude and frequency. Using typical properties of muscles and spinal reflex pathways, the frequency of reflex oscillations will be within the range 8–12 Hz found for physiological tremor. With the longer latency found for supraspinal reflexes, oscillations will occur in the range 4–6 Hz which is characteristic of Parkinson's and cerebellar diseases. The role of longer latency reflexes in the generation of these tremors is discussed.     

A Model of Oscillatory Blood Cell Counts in Chronic Myelogenous Leukaemia

In certain blood diseases, oscillations are found in blood cell counts. Particularly, such oscillations are sometimes found in chronic myelogenous leukaemia, and then occur in all the derived blood cell types: red blood cells, white blood cells, and platelets. It has been suggested that such oscillations arise because of an instability in the pluri-potential stem cell population, associated with its regulatory control system. In this paper, we consider how such oscillations can arise in a model of competition between normal (S) and genetically altered abnormal (A) stem cells, as the latter population grows at the expense of the former. We use an analytic model of long period oscillations to describe regions of oscillatory behaviour in the S–A phase plane, and give parametric criteria to describe when such oscillations will occur. We also describe a mechanism which can explain dynamically how the transformation from chronic phase to acute phase and blast crisis can occur.     

Divergent effect of mammalian PLCζ in generating Ca²⁺ oscillations in somatic cells compared with eggs

Sperm PLCζ (phospholipase Cζ) is a distinct phosphoinositide-specific PLC isoform that is proposed to be the physiological trigger of egg activation and embryo development at mammalian fertilization. Recombinant PLCζ has the ability to trigger Ca2? oscillations when expressed in eggs, but it is not known how PLCζ activity is regulated in sperm or eggs. In the present study, we have transfected CHO (Chinese-hamster ovary) cells with PLCζ fused with either YFP (yellow fluorescent protein) or luciferase and found that PLCζ-transfected cells did not display cytoplasmic Ca2? oscillations any differently from control cells. PLCζ expression was not associated with changes in CHO cell resting Ca2? levels, nor with a significantly changed Ca2? response to extracellular ATP compared with control cells transfected with either YFP alone, a catalytically inactive PLCζ or luciferase alone. Sperm extracts containing PLCζ also failed to cause Ca2? oscillations in CHO cells. Despite these findings, PLCζ-transfected CHO cell extracts exhibited high recombinant protein expression and PLC activity. Furthermore, either PLCζ-transfected CHO cells or derived cell extracts could specifically cause cytoplasmic Ca2? oscillations when microinjected into mouse eggs. These data suggest that PLCζ-mediated Ca2? oscillations may require specific factors that are only present within the egg cytoplasm or be inhibited by factors present only in somatic cell lines.     

Pattern formation,contrast control,and oscillations in the short term memory of shunting on-center off-surround networks

The transformation of spatial patterns and their storage in short term memory by shunting neural networks are studied herein. Various mechanisms are described for real-time regulation of the amount of contrast with which a pattern will be stored. Parametric studies are described for the amount of contrast in the network responses to patterns presented at variable background or overall activity levels. Mechanisms for removing spurious peak splits and other disinhibitory responses are described. Furman's (1965) results on processing of patterns by shunting networks are generalized and reanalysed. Periodic responses (stable and unstable) corresponding to the time scale of slow cortical waves can be generated if a tonic input is set between two threshold activity levels. Their frequency as a function of tonic input size is unimodal. Order-preserving limit cycles are never found in STM; hence sustained slow oscillations as a mechanism for storing a pattern in STM are ruled out in favor of steady states (i.e., fast oscillations) with spatially graded activity levels. Such slow oscillations can, nonetheless, continuously retune the network's responsiveness to the patterns that perturb it.     

Vasomotion: the case for chaos

Fluctuations in vascular calibre, a phenomenon known as vasomotion, are ubiquitous in the microcirculation and represent emergent behaviour that involves synchronisation of Ca²⁺ oscillations in individual vascular cells. Ideally, coordinated interactions between locally generated vasomotion and neuro-humoral control mechanisms will allow optimal sensing of flow and pressure within vascular networks and thereby facilitate synergistic readjustments in local vascular conductance and flow under conditions of dynamically changing metabolic demand. Indeed, many studies have reported that vasomotion becomes more prominent under pathophysiological conditions, suggesting that it may serve as an adaptive homeodynamic response that maintains or re-establishes flow when perfusion is compromised. We here summarise evidence that the apparent irregular nature of vasomotion reflects deterministic interactions between a small number of dominant control variables, rather than random events, and may therefore be formally classified as chaotic. We also discuss the potential physiological benefits of chaos in the microcirculation and the key roles of signalling via gap junctions and nitric oxide.     

Effect of rapid changes of the oxygenation state and other external parameters on the long-term behavior of the energy metabolism in the erythrocyte]

The red blood cell when transported through the circulatory system is exposed to a steady (approximately periodical) change of environmental conditions causing a permanent fluctuation of its important metabolic parameters. In a simple theoretical model it is demonstrated that a rapid oscillation of such parameters may stabilize a metabolic state which will collapse when this oscillation breaks off. The hypothesis is advanced that parameter oscillations caused by the physiological function of the red blood cell may be of importance for the maintenance of its energy metabolism and that the break-off of these oscillations may be a potential cause for the metabolic collapse, e.g. in stored blood.     

Yeast glycolytic oscillations that are not controlled by a single oscillophore: a new definition of oscillophore strength

Biochemical oscillations, such as glycolytic oscillations, are often believed to be caused by a single so-called ‘oscillophore’. The main characteristics of yeast glycolytic oscillations, such as frequency and amplitude, are however controlled by several enzymes. In this paper, we develop a method to quantify to which extent any enzyme determines the occurrence of oscillations. Principles extrapolated from metabolic control analysis are applied to calculate the control exerted by individual enzymes on the real and imaginary parts of the eigenvalues of the Jacobian matrix. We propose that the control exerted by an enzyme on the real part of the smallest eigenvalue, in terms of absolute value, quantifies to which extent that enzyme contributes to the emergence of instability. Likewise the control exerted by an enzyme on the imaginary part of complex eigenvalues may serve to quantify the extent to which that enzyme contributes to the tendency of the system to oscillate. The method was applied both to a core model and to a realistic model of yeast glycolytic oscillations. Both the control over stability and the control over oscillatory tendency were distributed among several enzymes, of which glucose transport, pyruvate decarboxylase and ATP utilization were the most important. The distributions of control were different for stability and oscillatory tendency, showing that control of instability does not imply control of oscillatory tendency nor vice versa. The control coefficients summed up to 1, suggesting the existence of a new summation theorem. These results constitute proof that glycolytic oscillations in yeast are not caused by a single oscillophore and provide a new, subtle, definition for the oscillophore strength of an enzyme.     

An oscillatory mode for microtubule assembly.

Depending upon the conditions under which polymerization takes place, pure tubulin can assemble into microtubules following either the usual monotonic kinetics or a more complex oscillatory mechanism. When present, these oscillations involve large cyclic changes in the extent of polymer formed before a steady-state is reached. Analysis of the microtubules formed at different times shows that these oscillations involve marked redistribution in both the length and number of microtubules. No significant difference is found between two populations of microtubules corresponding to the same level of assembly, one for which the extent of polymerization will remain stable with time and one for which it will decrease by as much as 90% in the next oscillation. The amplitude of these oscillations is sensitive to changes in the concentrations of protein, nucleotide (GTP, GDP or GMPpNp), magnesium ion or GTP regenerating system. A complete shift from an oscillatory to a monotonic polymerization can be induced by a minor increase in the concentration of free nucleotide, GTP or GDP.     

Collective oscillations in developing cells: insights from simple systems

From hormonal secretion to gene expression, multicellular dynamics are rich in oscillatory regulation. When organized in space and time, periodic cell-cell signaling can give rise to long-range coordination of gene expression and cell movement in tissues. Lack of synchrony of the oscillations on the other hand can serve as a source of initial divergence of cell fate in stem cells. How properties of individual cells can account for collective rhythmic behaviors at the tissue level remains elusive in most cases. Recently, studies in chemical reactions, synthetic gene circuits, yeast and social amoeba Dictyostelium have greatly enhanced our view of collective oscillations in cell populations. From these relatively simple systems, a unified view of how excitable and oscillatory regulations could be tuned and coupled to give rise to tissue-level oscillations is emerging. The review focuses on recent progress in cyclic adenosine monophosphate oscillations in Dictyostelium and highlights similarities and differences with other systems. We will see that the autonomy of single-cell level oscillations and different ways in which cells are coupled influence how group-level information can be encoded in collective oscillations.     

Oscillatory interactions between sensorimotor cortex and the periphery

Field potential recordings from motor cortex show oscillations in the beta-band (approximately 20 Hz), which are coherent with similar oscillations in the activity of contralateral contracting muscles. Recent findings have revised concepts of how this activity might be generated in the cortex, suggesting it could achieve useful computation. Other evidence shows that these oscillations engage not just motor structures, but also return from muscle to the central nervous system via feedback afferent pathways. Somatosensory cortex has strong beta-band oscillations, which are synchronised with those in motor cortex, allowing oscillatory sensory reafference to be interpreted in the context of the oscillatory motor command which produced it.     

Calcium oscillations in endothelial cells

Several different types of endothelial cells are now known to respond to agonist stimulation with oscillations of cytosolic free [Ca2+] ([Ca2+]i). The oscillations can be repetitive [Ca2+]i spikes or sinusoidal-like oscillations according to the type of endothelial cell. Several properties of these oscillations are described including the effect of removal of extracellular Ca2+ and of changes in membrane potential, and the spatial heterogeneity of the oscillations. Results obtained with human umbilical vein endothelial cells are assessed in relation to a model for [Ca2+]i oscillations that involves Ca(2+)-induced Ca2+ release. In some preparations the oscillations are synchronized in neighbouring cells, whereas in other preparations they are not. The degree of synchrony may have functional implications and this is discussed with respect to control of blood flow and transmural permeability. A third functional implication of oscillations, their possible effect on desensitization, is also discussed.     

Oscillations in an Intra-host Model of <Emphasis Type="Italic">Plasmodium Falciparum</Emphasis> Malaria Due to Cross-reactive Immune Response

We consider an intra-host model of malaria that allows for antigenic variation within a single species. More specifically, the host’s immune response is compartmentalized into reactions to major and minor epitopes. We investigate the conditions that lead to transient oscillations, which correspond to recurrent clinical episodes of the diseases, and how a small delay in the activation of the immune response can lead to persistent oscillations. We find that the efficacies of the immune responses to the major and minor epitopes, defined in terms of rate constants, play a crucial role in determining when there will be transient oscillations. The delay necessary to excite persistent oscillations, the time duration between disease episodes and their severity are also expressed in terms of the immune response efficacies. In addition, we describe how the severity and duration of the oscillations depend upon the parasite propagation rates and the immune response efficacies.