Frequency encoded biochemical regulation is more accurate than amplitude dependent control

Nonlinear delay differential equations and their application to modeling biological network motifs

Biological regulatory systems, such as cell signaling networks, nervous systems and ecological webs, consist of complex dynamical interactions among many components. Network motif models focus on small sub-networks to provide quantitative insight into overall behavior. However, such models often overlook time delays either inherent to biological processes or associated with multi-step interactions. Here we systematically examine explicit-delay versions of the most common network motifs via delay differential equation (DDE) models, both analytically and numerically. We find many broadly applicable results, including parameter reduction versus canonical ordinary differential equation (ODE) models, analytical relations for converting between ODE and DDE models, criteria for when delays may be ignored, a complete phase space for autoregulation, universal behaviors of feedforward loops, a unified Hill-function logic framework, and conditions for oscillations and chaos. We conclude that explicit-delay modeling simplifies the phenomenology of many biological networks and may aid in discovering new functional motifs.

Network motif models focus on small sub-networks in biological systems to quantitatively describe overall behavior but they often overlook time delays. Here, the authors systematically examine the most common network motifs via delay differential equations (DDE), often leading to more concise descriptions.

Modeling-Based Investigation of the Effect of Noise in Cellular Systems

Noise is pervasive in cellular biology and inevitably affects the dynamics of cellular processes. Biological systems have developed regulatory mechanisms to ensure robustness with respect to noise or to take advantage of stochasticity. We review here, through a couple of selected examples, some insights on possible robustness factors and constructive roles of noise provided by computational modeling. In particular, we focus on (1) factors that likely contribute to the robustness of oscillatory processes such as the circadian clocks and the cell cycle, (2) how reliable coding/decoding of calcium-mediated signaling could be achieved in presence of noise and, in some cases, enhanced through stochastic resonance, and (3) how embryonic cell differentiation processes can exploit stochasticity to create heterogeneity in a population of identical cells.

Highly sensitive optical interferometric technique reveals stress-dependent instantaneous nanometric growth fluctuations of Chinese chive leaf under heavy metal stress

Plant growth apart from being a complex and highly dynamic is dependent on its immediate environment. Leaf expansion measurements using Statistical Interferometry Technique, a sensitive interferometric technique at nanometric accuracy and at sub-second levels revealed the presence of characteristic nanometric intrinsic fluctuations [Plant Biotechnology 31, 195 (2014)]. In this paper, we demonstrate that the nanometric intrinsic fluctuations are sensitive enough that they change under exposure of heavy metals, essential micronutrient zinc and non-essential element cadmium, at relatively low concentrations in the leaves of Chinese chive (Allium tuberosum). The nanometric intrinsic fluctuations of leaves were observed for 4h under three cadmium concentrations or two zinc concentrations. Results showed significant reduction of nanometric intrinsic fluctuations for all cadmium concentrations, and in contrast significant increase of nanometric intrinsic fluctuations for all zinc concentrations. There was significant reduction of nanometric intrinsic fluctuations for cadmium exposure of concentrations of 0.001mM for even an hour, and significant increment of nanometric intrinsic fluctuations under 0.75mM zinc from 1hr exposure. For comparison, antioxidative enzymes and metal uptake were also measured under 4hr exposure of cadmium or zinc. However, no significant changes could be seen in antioxidative enzymes within 4h under the smaller concentration of 0.001mM cadmium as seen for nanometric intrinsic fluctuations. The results imply that nanometric intrinsic fluctuations can be not only used as a measure for heavy metal stress but also it can be more sensitive to detect the toxic as well as positive effects of smaller amounts of heavy metal on plants at an early stage.

Accurate encoding and decoding by single cells: amplitude versus frequency modulation

Cells sense external concentrations and, via biochemical signaling, respond by regulating the expression of target proteins. Both in signaling networks and gene regulation there are two main mechanisms by which the concentration can be encoded internally: amplitude modulation (AM), where the absolute concentration of an internal signaling molecule encodes the stimulus, and frequency modulation (FM), where the period between successive bursts represents the stimulus. Although both mechanisms have been observed in biological systems, the question of when it is beneficial for cells to use either AM or FM is largely unanswered. Here, we first consider a simple model for a single receptor (or ion channel), which can either signal continuously whenever a ligand is bound, or produce a burst in signaling molecule upon receptor binding. We find that bursty signaling is more accurate than continuous signaling only for sufficiently fast dynamics. This suggests that modulation based on bursts may be more common in signaling networks than in gene regulation. We then extend our model to multiple receptors, where continuous and bursty signaling are equivalent to AM and FM respectively, finding that AM is always more accurate. This implies that the reason some cells use FM is related to factors other than accuracy, such as the ability to coordinate expression of multiple genes or to implement threshold crossing mechanisms.

Signals, and hence information, can generally be transmitted either by amplitude (AM) or frequency (FM) modulation, as used, for example, in the transmission of radio waves since the 1930s. Both types of modulation are known to play a role in biology with AM conventionally associated with signaling and gene expression, and FM used to reliably transmit electrical signals over large distances between neurons. Surprisingly, FM was recently also observed in gene regulation, making their roles less distinct than previously thought. Although the engineering advantages and disadvantages of AM and FM are well understood, the equivalent question in biological systems is still largely unsolved. Here, we propose a simple model of signaling by receptors (or ion channels) with subsequent gene regulation, thus implementing both AM and FM in different types of biological pathways. We then compare the accuracy in the production of target proteins. We find that FM can be more accurate than AM only for a single receptor with fast signaling, whereas AM is more accurate in slow gene regulation and with signaling by multiple receptors. Finally, we propose possible reasons that cells use FM despite the potential decrease in accuracy.

Limits on information transduction through amplitude and frequency regulation of transcription factor activity

Signaling pathways often transmit multiple signals through a single shared transcription factor (TF) and encode signal information by differentially regulating TF dynamics. However, signal information will be lost unless it can be reliably decoded by downstream genes. To understand the limits on dynamic information transduction, we apply information theory to quantify how much gene expression information the yeast TF Msn2 can transduce to target genes in the amplitude or frequency of its activation dynamics. We find that although the amount of information transmitted by Msn2 to single target genes is limited, information transduction can be increased by modulating promoter cis-elements or by integrating information from multiple genes. By correcting for extrinsic noise, we estimate an upper bound on information transduction. Overall, we find that information transduction through amplitude and frequency regulation of Msn2 is limited to error-free transduction of signal identity, but not signal intensity information.

Dynamic signal encoding--from cells to organisms

Encoding information at the level of signal dynamics is characterized by distinct features, such as robustness to noise and high information content. Currently, a growing number of studies are unravelling the functional importance of signalling dynamics at the single cell level. In addition, first insights are emerging into how the principles of dynamic signal encoding apply to a multicellular context, such as development. In this review, we will first discuss general concepts of information transmission via signalling dynamics and recent experimental examples focusing on underlying principles, including the role of intracellular network topologies. How multicellular organisms use temporal modulation of specific signalling pathways, such as signalling gradients or oscillations, to faithfully control cell fate decisions and pattern formation will also be addressed. Finally, we will consider how technical advancements in the detection and perturbation of signalling dynamics contribute to reshaping our understanding of dynamic signalling in developing organisms.

Multiplexing oscillatory biochemical signals

In recent years it has been increasingly recognized that biochemical signals are not necessarily constant in time and that the temporal dynamics of a signal can be the information carrier. Moreover, it is now well established that the protein signaling network of living cells has a bow-tie structure and that components are often shared between different signaling pathways. Here we show by mathematical modeling that living cells can multiplex a constant and an oscillatory signal: they can transmit these two signals simultaneously through a common signaling pathway, and yet respond to them specifically and reliably. We find that information transmission is reduced not only by noise arising from the intrinsic stochasticity of biochemical reactions, but also by crosstalk between the different channels. Yet, under biologically relevant conditions more than 2 bits of information can be transmitted per channel, even when the two signals are transmitted simultaneously. These observations suggest that oscillatory signals are ideal for multiplexing signals.

Burst BMP triggered receptor kinase activity drives Smad1 mediated long-term target gene oscillation in C2C12 cells

Bone Morphogenetic Proteins (BMPs) are important growth factors that regulate many cellular processes. During embryogenesis they act as morphogens and play a critical role during organ development. They influence cell fates via concentration-gradients in the embryos where cells transduce this extracellular information into gene expression profiles and cell fate decisions. How receiving cells decode and quantify BMP2/4 signals is hardly understood. There is little data on the quantitative relationships between signal input, transducing molecules, their states and location, and ultimately their ability to integrate graded systemic inputs and generate qualitative responses. Understanding this signaling network on a quantitative level should be considered a prerequisite for efficient pathway modulation, as the BMP pathway is a prime target for therapeutic invention. Hence, we quantified the spatial distribution of the main signal transducer of the BMP2/4 pathway in response to different types and levels of stimuli in c2c12 cells. We found that the subcellular localization of Smad1 is independent of ligand concentration. In contrast, Smad1 phosphorylation levels relate proportionally to BMP2 ligand concentrations and they are entirely located in the nucleus. Interestingly, we found that BMP2 stimulates target gene expression in non-linear, wave-like forms. Amplitudes showed a clear concentration-dependency, for sustained and transient stimulation. We found that even burst-stimulation triggers gene-expression wave-like modulations that are detectable for at least 30 h. Finally, we show here that target gene expression oscillations depend on receptor kinase activity, as the kinase drives further expression pulses without receptor reactivation and the target gene expression breaks off after inhibitor treatment in c2c12 cells.

Reliability of frequency and amplitude decoding in gene regulation

In biochemical signaling, information is often encoded in oscillatory signals. However, the advantages of such a coding strategy over an amplitude-encoding scheme of constant signals remain unclear. Here we study the dynamics of a simple model gene promoter in response to oscillating and constant transcription factor signals. We find that in biologically relevant parameter regimes an oscillating input can produce a more constant protein level than a constant input. Our results suggest that oscillating signals may be used to minimize noise in gene regulation.

Calcium efflux systems in stress signaling and adaptation in plants

Transient cytosolic calcium ([Ca(2+)](cyt)) elevation is an ubiquitous denominator of the signaling network when plants are exposed to literally every known abiotic and biotic stress. These stress-induced [Ca(2+)](cyt) elevations vary in magnitude, frequency, and shape, depending on the severity of the stress as well the type of stress experienced. This creates a unique stress-specific calcium "signature" that is then decoded by signal transduction networks. While most published papers have been focused predominantly on the role of Ca(2+) influx mechanisms to shaping [Ca(2+)](cyt) signatures, restoration of the basal [Ca(2+)](cyt) levels is impossible without both cytosolic Ca(2+) buffering and efficient Ca(2+) efflux mechanisms removing excess Ca(2+) from cytosol, to reload Ca(2+) stores and to terminate Ca(2+) signaling. This is the topic of the current review. The molecular identity of two major types of Ca(2+) efflux systems, Ca(2+)-ATPase pumps and Ca(2+)/H(+) exchangers, is described, and their regulatory modes are analyzed in detail. The spatial and temporal organization of calcium signaling networks is described, and the importance of existence of intracellular calcium microdomains is discussed. Experimental evidence for the role of Ca(2+) efflux systems in plant responses to a range of abiotic and biotic factors is summarized. Contribution of Ca(2+)-ATPase pumps and Ca(2+)/H(+) exchangers in shaping [Ca(2+)](cyt) signatures is then modeled by using a four-component model (plasma- and endo-membrane-based Ca(2+)-permeable channels and efflux systems) taking into account the cytosolic Ca(2+) buffering. It is concluded that physiologically relevant variations in the activity of Ca(2+)-ATPase pumps and Ca(2+)/H(+) exchangers are sufficient to fully describe all the reported experimental evidence and determine the shape of [Ca(2+)](cyt) signatures in response to environmental stimuli, emphasizing the crucial role these active efflux systems play in plant adaptive responses to environment.

Using Jensen's inequality to explain the role of regular calcium oscillations in protein activation

Oscillations of cytosolic Ca(2 +) are very important for cellular signalling in excitable and non-excitable cells. The information of various extracellular stimuli is encoded into oscillating patterns of Ca(2 +) that subsequently lead to the activation of different Ca(2 +)-sensitive target proteins in the cell. The question remains, however, why this information is transmitted by means of an oscillating rather than a constant signal. Here we show that, in fact, Ca(2 +) oscillations can achieve a better activation of target proteins than a comparable constant signal with the same amount of Ca(2 +) used. For this we use Jensen's inequality that describes the relation between the function value of the average of a set of argument values and the average of the function values of the arguments from that set. We analyse the role of the cooperativity of the binding of Ca(2 +) and of zero-order ultrasensitivity, which are two properties that are often observed in experiments on the activation of Ca(2 +)-sensitive target proteins. Our results apply to arbitrary oscillation shapes and a very general decoding model, thus generalizing the observations of several previous studies. We compare our results with data from experimental studies investigating the activation of nuclear factor of activated T cells (NFAT) and Ras by oscillatory and constant signals. Although we are restricted to specific approximations due to the lack of detailed kinetic data, we find good qualitative agreement with our theoretical predictions.

Cross-talk between signaling pathways can generate robust oscillations in calcium and cAMP

Background

To control and manipulate cellular signaling, we need to understand cellular strategies for information transfer, integration, and decision-making. A key feature of signal transduction is the generation of only a few intracellular messengers by many extracellular stimuli.

Methodology/Principal Findings

Here we model molecular cross-talk between two classic second messengers, cyclic AMP (cAMP) and calcium, and show that the dynamical complexity of the response of both messengers increases substantially through their interaction. In our model of a non-excitable cell, both cAMP and calcium concentrations can oscillate. If mutually inhibitory, cross-talk between the two second messengers can increase the range of agonist concentrations for which oscillations occur. If mutually activating, cross-talk decreases the oscillation range, but can generate ‘bursting’ oscillations of calcium and may enable better filtering of noise.

Conclusion

We postulate that this increased dynamical complexity allows the cell to encode more information, particularly if both second messengers encode signals. In their native environments, it is unlikely that cells are exposed to one stimulus at a time, and cross-talk may help generate sufficiently complex responses to allow the cell to discriminate between different combinations and concentrations of extracellular agonists.

Timing in cellular Ca2+ signaling

Calcium (Ca2+) signals are generated across a broad time range. Kinetic considerations impact how information is processed to encode and decode Ca2+ signals, the choreography of responses that ensure specific and efficient signaling and the overall temporal amplification such that ephemeral Ca2+ signals have lasting physiological value. The reciprocal importance of timing for Ca2+ signaling, and Ca2+ signaling for timing is exemplified by the altered kinetic profiles of Ca2+ signals in certain diseases and the likely role of basal Ca2+ fluctuations in the perception of time itself.

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.

Modulation of tyramine signaling by osmolality in an insect secretory epithelium

The control of water balance in multicellular organisms depends on absorptive and secretory processes across epithelia. This study concerns the effects of osmolality on the function of the Malpighian tubules (MTs), a major component of the insect excretory system. Previous work has shown that the biogenic amine tyramine increases transepithelial chloride conductance and urine secretion in Drosophila MTs. This study demonstrates that the response of MTs to tyramine, as measured by the depolarization of the transepithelial potential (TEP), is modulated by the osmolality of the surrounding medium. An increase in osmolality caused decreased tyramine sensitivity, whereas a decrease in osmolality resulted in increased tyramine sensitivity; changes in osmolality of +/-20% resulted in a nearly 10-fold modulation of the response to 10 nM tyramine. The activity of another diuretic agent, leucokinin, was similarly sensitive to osmolality, suggesting that the modulation occurs downstream of the tyramine receptor. In response to continuous tyramine signaling, as likely occurs in vivo, the TEP oscillates, and an increase in osmolality lengthened the period of these oscillations. Increased osmolality also caused a decrease in the rate of urine production; this decrease was attenuated by the tyraminergic antagonist yohimbine. A model is proposed in which this modulation of tyramine signaling enhances the conservation of body water during dehydration stress. The modulation of ligand signaling is a novel effect of osmolality and may be a widespread mechanism through which epithelia respond to changes in their environment.

Egg activation events are regulated by the duration of a sustained [Ca2+]cyt signal in the mouse

Although the dynamics of oscillations of cytosolic Ca2+ concentration ([Ca2+]cyt) play important roles in early mammalian development, the impact of the duration when [Ca2+]cyt is elevated is not known. To determine the sensitivity of fertilization-associated responses [i.e., cortical granule exocytosis, resumption of the cell cycle, Ca2+/calmodulin-dependent protein kinase II (CaMKII) activity, recruitment of maternal mRNAs] and developmental competence of the parthenotes to the duration of a [Ca2+]cyt transient, unfertilized mouse eggs were subjected to a prolonged [Ca2+]cyt change for 15, 25, or 50 min by means of repetitive Ca2+ electropermeabilization at 2-min intervals. The initiation and completion of fertilization-associated responses are correlated with the duration of time in which the [Ca2+]cyt is elevated, with the exception that autonomous CaMKII activity is down-regulated with prolonged elevated [Ca2+]cyt. Activated eggs from 25- or 50-min treatments readily develop to the blastocyst stage with no sign of apoptosis or necrosis and some implant. Ca2+ influx into unfertilized eggs causes neither Ca2+ release from intracellular stores nor rapid removal of cytosolic Ca2+. Thus, the total Ca2+ signal input appears to be an important regulatory parameter that ensures completion of fertilization-associated events and oocytes have a surprising degree of tolerance for a prolonged change in [Ca2+]cyt.

Signal processing times in neutrophil activation: dependence on ligand concentration and the relative phase of metabolic oscillations

Intracellular NAD(P)H oscillations exhibited by polarized neutrophils display congruent with 20 s periods, which are halved to congruent with 10 s upon stimulation with chemotactic peptides such as FNLPNTL (N-formyl-nle-leu-phe-nle-tyr-lys). By monitoring this frequency change, we have measured accurately the time interval between stimulus and metabolic frequency changes. A microscope flow chamber was designed to allow rapid delivery of FNLPNTL to adherent cells. Using fluorescein as a marker, we found delivery to be complete and stable throughout the chamber within approximately 400 ms. Peptides were injected into the chamber at concentrations ranging from 10(-6) to 10(-9) M. Injections also varied with respect to the relative phase of a cell's NAD(P)H oscillations. The time interval between injection of 10(-6) M FNLPNTL and the acquisition of congruent with 10 s period metabolic oscillations was found to be 12.2+/-3.3 s when injections occurred at the NAD(P)H oscillation peak whereas the lag time was 22.5+/-4.8 s when coinciding with a trough. At 10(-8) M FNLPNTL, lag times were found to be 26.1+/-5.2 and 30.5+/-7.3 s for injections at NAD(P)H peaks and troughs, respectively. FNLPNTL at 10(-9) M had no effect on metabolic oscillations, consistent with previous studies. Our experiments show that the kinetics of transmembrane signal processing, in contrast to a simple transmembrane chemical reaction, can depend upon both ligand dose and its temporal relationship with intracellular metabolic oscillations.

Modelling of simple and complex calcium oscillations. From single-cell responses to intercellular signalling

This review provides a comparative overview of recent developments in the modelling of cellular calcium oscillations. A large variety of mathematical models have been developed for this wide-spread phenomenon in intra- and intercellular signalling. From these, a general model is extracted that involves six types of concentration variables: inositol 1,4,5-trisphosphate (IP3), cytoplasmic, endoplasmic reticulum and mitochondrial calcium, the occupied binding sites of calcium buffers, and the fraction of active IP3 receptor calcium release channels. Using this framework, the models of calcium oscillations can be classified into 'minimal' models containing two variables and 'extended' models of three and more variables. Three types of minimal models are identified that are all based on calcium-induced calcium release (CICR), but differ with respect to the mechanisms limiting CICR. Extended models include IP3--calcium cross-coupling, calcium sequestration by mitochondria, the detailed gating kinetics of the IP3 receptor, and the dynamics of G-protein activation. In addition to generating regular oscillations, such models can describe bursting and chaotic calcium dynamics. The earlier hypothesis that information in calcium oscillations is encoded mainly by their frequency is nowadays modified in that some effect is attributed to amplitude encoding or temporal encoding. This point is discussed with reference to the analysis of the local and global bifurcations by which calcium oscillations can arise. Moreover, the question of how calcium binding proteins can sense and transform oscillatory signals is addressed. Recently, potential mechanisms leading to the coordination of oscillations in coupled cells have been investigated by mathematical modelling. For this, the general modelling framework is extended to include cytoplasmic and gap-junctional diffusion of IP3 and calcium, and specific models are compared. Various suggestions concerning the physiological significance of oscillatory behaviour in intra- and intercellular signalling are discussed. The article is concluded with a discussion of obstacles and prospects.

Establishment of order in the flow of genetic information in cells

The activities related to the flow of genetic information encoded in DNA in a cell are very orderly. This order, in a living cell, is achieved through specific, but noncovalent, interactions of varieties of structurally dynamic macromolecules under constantly changing physiological conditions. Hence, it is expected that there should be some force that can stabilize the multicomponent reaction processes and establish (or maintain) order in genetic regulatory functions under far-from-equilibrium conditions. The genetic regulatory functions in a cell, however, are believed to be energetically coupled. Expression of genes in a cell is often modulated under changing environmental conditions, raising the possibility of a state controlled nature of the genetic regulatory functions. Adenosine triphosphate (ATP) is the major free-energy contributor for these energy-consuming cellular activities. Enzymatic transfer of high-energy phosphate group from ATP to other reactive components is considered to be the chief mode of energy-transduction in a cell for various biosynthetic processes, as well as other activities related to the flow of information. In an effort to find a solution of the paradox, we assessed the contribution of physiological state of a cell in the process of maintaining order in genetic regulatory functions. As an approach, we systematically perturbed the normal energy flow of a cellular system (bovine aortic endothelial [BAE] cell) by a protein kinase inhibitor (staurosporine), and then followed the expression patterns of several constitutively-expressed protein-encoding genes to measure the effects. Staurosporine, as a function of its concentration, disintegrated the membrane structure of these cells, and eventually caused their death. These secondary consequences of staurosporine treatment offered two additional grossly altered physiological states of the cell to study. Under all of these dramatically altered energy states of the system, an extreme degree of functional coherence prevailed at every level of genetic regulatory function. Integrity at the level of gene transcription remained unaffected. Degradation rate of specific mRNA remained unaltered. Translational activities involving varieties of mRNA species continued in an well-ordered manner. Other state changes, resulting from nutrient and metabolic starvation, or inhibition of oxidative phosphorylation, in addition to the staurosporine treatments, also failed to disintegrate these ordered activities. The steady-state levels of specific mRNA underwent certain changes in these conditions, however, without maintaining any proportional relationships with the staurosporine concentrations applied or the ATP levels in the cell. These results thus led us to propose that the internal energy or a certain intrinsic property of the participating components, rather than the physiological state of the cell, acts as the dominant force in maintaining order and stability of genetic regulatory functions in a cell. Kinetic analyses under different energy states of the cell also supported the hypothesis, and further demonstrated the autoregulatory nature of the genetic order establishment. All of these results suggest a process of molecular self-organization as the fundamental principle for genetic regulation in a cellular system.

Cellular memory: neutrophil orientation reverses during temporally decreasing chemoattractant concentrations

Cell directional orientation or shape polarization is the first cellular step in neutrophil locomotion. To better understand how chemoattractants interact with cells, we studied neutrophil polarization (or shape changes) during exposure to a temporally decreasing chemoattractant signal of N-formyl-methionyl-leucyl-phenylalanine (FMLP) in the absence of a spatial concentration gradient. To accomplish this objective, we used a manifold of differing FMLP concentrations attached to a stopped-flow microscope chamber. Spatial gradients of a fluorescent chemotactic peptide could not be detected in the chamber by using microfluorometry. When FMLP was injected at continually increasing concentrations at 10-s intervals, the shape and relative direction of the neutrophil persisted. However, when temporally decreasing FMLP concentrations were injected, approximately 80% of the cells changed their direction with 44% of the total cells swinging about to 180 degrees +/- 15 degrees. Most of these directional changes involved dissolution of both the lamellipodium and uropod and reformation of these structures 180 degrees from their original positions. This research suggests that neutrophils reverse their morphological polarity when exposed to temporally decreasing ligand concentrations by "remembering" their ligand exposure history and relative direction.

Pulsatile adrenocorticotropic hormone: an overview

Adrenocorticotropic hormone (ACTH) is secreted by corticotrophic cells in pulsatile bursts. This paper reviews the extant literature on the phenomenon of pulsatile ACTH after addressing basic issues of hormone pulsatility in neuroendocrine systems. The following themes emerged from reviewing 51 studies measuring plasma ACTH at intervals of 20 min or less: marked inter-individual variability in the pattern of ACTH, the dependence of pulse identification on sampling frequency, the similarity in ACTH pulse amplitude and frequency across species, and the predominance of amplitude over frequency changes in ACTH pulses in altered physiological states. As the hypothalamic-pituitary-adrenocortical (HPA) axis plays a critical role in orchestrating adaptation and survival, the ability to modulate the shape of ACTH signals may prove to be an important means of transmitting complex information to ACTH responsive cells. The clinical and neurobiological significance of temporal alterations in ACTH secretion represents an area for future investigation.

Activation-dependent and biphasic electromagnetic field effects: model based on cooperative enzyme kinetics in cellular signaling

Experiments on filed exposure effects of extremely-low-frequency electric and magnetic fields (EMFs) on biological systems have shown that, in many cases, the biological-functional status is of fundamental importance for an effective interaction. For example, studies of calcium uptake regulation in cells of the immune system, particularly in T lymphocytes, have revealed that, depending on the degree of cellular activation, either stimulatory, inhibitory, or no field exposure effects are observed for identical field parameters. A brief summary of the experimental findings is given, and a theoretical approach is presented that accounts in a qualitative manner for EMF exposure effects 1) that depend on the degree of cellular activation and 2) that exhibit a biphasic response behavior (stimulation/ inhibition). In the model, biochemical stimulation of the cell results in activation of specific signaling pathways that regulate calcium dynamics in the cell (calcium release from intracellular calcium stores and capacitative calcium entry). We assume that, controlled by these pathways, a specific EMF-sensitive enzyme system becomes activated. The activated enzyme, in turn, exhibits a feedback control on the signal processes, thus leading to a modulation of calcium entry. This modulation may affect other cellular processes that are calcium dependent (e.g., DNA synthesis). Magnetic field exposure is assumed to alter the kinetics of a specific step within the enzyme-reaction cycle in accord with the radical-pair mechanism, although the formulism is not restricted to this specific example. Results show that inclusion of cooperative steps within the enzyme-reaction cycle provides a theoretical basis that enables a simple description of a biphasic response behavior to EMF exposure.

A class of parametrically excited calcium oscillation detectors

Intracellular Ca2+ oscillations are often a response to external signals such as hormones. Changes in the external signal can alter the frequency, amplitude, or form of the oscillations suggesting that information is encoded in the pattern of Ca2+ oscillations. How might a cell decode this signal? We show that an excitable system whose kinetic parameters are modulated by the Ca2+ concentration can function as a Ca2+ oscillation detector. Such systems have the following properties: (1) They are more sensitive to an oscillatory than to a steady Ca2+ signal. (2) Their response is largely independent of the signal amplitude. (3) They can extract information from a noisy signal. (4) Unlike other frequency sensitive detectors, they have a flat frequency response. These properties make a Ca(2+)-sensitive excitable system nearly ideal for detecting and decoding Ca2+ oscillations. We suggest that Ca2+ oscillations, in concert with these detectors, can act as cellular timekeepers to coordinate related biochemical reactions and enhance their overall efficiency.

Repetitive calcium stimuli drive meiotic resumption and pronuclear development during mouse oocyte activation

Freshly ovulated (12 hr post hCG) F1 (C57BL/6 x CBA) hybrid mouse oocytes were parthenogenetically activated by repetitive elevation of Ca2+ induced by carefully controlled electrical pulses. Different patterns of stimulation were employed to examine the role of repetitive calcium changes on meiotic resumption and pronuclear development. In the first series of experiments oocytes received 33 electrical pulses of 1.8 kV/cm delivered every 4 min. The pulse duration decreased according to a negative exponential equation from a 900-microseconds first pulse to give a total pulse duration of 18.721 msec. The strength of calcium stimuli was varied by changing the concentration of CaCl2 in the medium. Ninety-eight percent of the oocytes stimulated with 12 microM calcium extruded the second polar body by the end of treatment and 92% completed pronuclear formation between 3.5 and 8 hr after the first pulse. For higher or lower Ca2+ concentrations the proportion of oocytes developing pronuclei decreased; the timing of pronuclear formation was retarded and the majority of oocytes failed to form a pronucleus after extrusion of the second polar body. In the second series of experiments, the strength of the calcium stimuli was modulated by changing the duration of the 33 electrical pulses given in the presence of 12 microM calcium. By increasing the total pulse duration to 33.958 msec, 100% of the oocytes activated and completed pronuclear formation between 3 and 5 hr after the first electric pulse. Stimulation protocols of lower total pulse duration (less than 18.721 msec) gave rise to high rates of partial activation (up to 95%). Examination of these partially activated oocytes showed metaphases with haploid sets of chromatids characteristic of third meiotic metaphase arrest. The results indicate that repetitive calcium stimuli can regulate the rate and extent of meiotic resumption and the time course of pronuclear formation during mouse oocyte activation. They suggest that meiotic resumption in mammalian oocytes is regulated by the amplitude and frequency of cytosolic calcium oscillations induced by the activating stimulus.

Protein phosphorylation driven by intracellular calcium oscillations: a kinetic analysis

Given the ubiquitous nature of signal-induced Ca2+ oscillations, the question arises as to how cellular responses are affected by repetitive Ca2+ spikes. Among these responses, we focus on those involving protein phosphorylation. We examine, by numerical simulations of a theoretical model, the situation where a protein is phosphorylated by a Ca(2+)-activated kinase and dephosphorylated by a phosphatase. This reversible phosphorylation system is coupled to a mechanism generating cytosolic Ca2+ oscillations; for definiteness, this oscillatory mechanism is based on the process of Ca(2+)-induced Ca2+ release. The analysis shows that the average fraction of phosphorylated protein increases with the frequency of repetitive Ca2+ spikes; the latter frequency generally rises with the extent of external stimulation. Protein phosphorylation therefore provides a mechanism for the encoding of the external stimulation in terms of the frequency of signal-induced Ca2+ oscillations. Such a frequency encoding requires precise kinetic conditions on the Michaelis-Menten constants of the kinase and phosphatase, their maximal rates, and the degree of cooperativity in kinase activation by Ca2+. In particular, the most efficient encoding of Ca2+ oscillations based on protein phosphorylation occurs in conditions of zero-order ultrasensitivity, when the kinase and phosphatase are saturated by their protein substrate. The kinetic analysis uncovers a wide variety of temporal patterns of phosphorylation that could be driven by signal-induced Ca2+ oscillations.

Pulsatile signaling in intercellular communication. Periodic stimuli are more efficient than random or chaotic signals in a model based on receptor desensitization

The efficiency of various patterns of pulsatile stimulation is determined in a model in which a receptor becomes desensitized in the presence of its stimulatory ligand. The effect of stochastic or chaotic changes in the duration and/or interval between successive pulses in a series of square-wave stimuli is investigated. Before addressing the effect of random variations in the pulsatile signal, we first extend the results of a previous analysis (Li, Y.X., and A. Goldbeter. 1989. Biophys. J. 55:125-145) by demonstrating the existence of an optimal periodic signal that maximizes target cell responsiveness whatever the magnitude of stimulation. As to the effect of stochastic or chaotic variations in the pulsatile stimulus, three kinds of random distributions are used, namely, a Gaussian and a white-noise distribution, and a chaotic time series generated by the logistic map. All these random distributions are symmetrically centered around the reference value of the duration or interval that characterizes the optimal periodic stimulus yielding maximal responsiveness in target cells. Stochastically or chaotically varying pulses are less effective than the periodic signal that corresponds to the optimal pattern of pulsatile stimulation. The response of the receptor system is most sensitive to changes in the time interval that separates successive stimuli. Similar conclusions hold when stochastic or chaotic signals are compared to a reference periodic stimulus differing from the optimal one, although the effect of random variations is then reduced. The decreased efficiency of stochastic pulses accounts for the observed superiority of periodic versus stochastic pulses of cyclic AMP (cAMP) in Dictyostelium amoebae. The results are also discussed with respect to the efficiency of periodic versus stochastic or chaotic patterns of hormone secretion.

The occurrence and functions of ultradian rhythms

Ultradian oscillations with periods between 5 min and 4 h have been described in cell-free extracts, single-celled eukaryotes, cultured cells and embryos. Whereas some of these potentially oscillatory systems (e.g. glycolysis) may only exhibit this type of behaviour rarely if at all in vivo, other ultradian oscillators in lower eukaryotes are rhythms and probably have timekeeping functions. Rhythms with ultradian periods of 10 min to 20 h in oxygen consumption and carbon dioxide production have also been studied in endotherm animals: these rhythms may be modified by variations of environmental parameters and by circadian and infradian synchronizers. Interspecies and interstrain differences strongly suggest that these rhythms are endogenous and have a genetic origin. We suggest that the temporal organization of biochemical and physiological processes facilitates optimization of thermodynamic maintenance of the organism within the random fluctuations of its physicochemical environment and contributes to genetic selection.

Structure and function of inositol trisphosphate receptors

Inositol 1,4,5-trisphosphate (Ins(1,4,5)P3) is a soluble intracellular messenger formed rapidly after activation of a variety of cell-surface receptors that stimulate phosphoinositidase C activity. The initial response to Ins(1,4,5)P3 is a rapid Ca2+ efflux from nonmitochondrial intracellular stores which are probably specialized subcompartments of the endoplasmic reticulum, although their exact identities remain unknown. This initial response is followed by more complex Ca2+ signals: regenerative Ca2+ waves propagate across the cell, repetitive Ca2+ spikes occur, and stimulated Ca2+ entry across the plasma membrane contributes to the sustained Ca2+ signal. The mechanisms underlying these complex Ca2+ signals are unknown, although Ins(1,4,5)P3 is clearly involved. The intracellular receptor that mediates Ins(1,4,5)P3-stimulated Ca2+ mobilization has been purified and functionally reconstituted, and its amino acid sequence deduced from its cDNA sequence. These studies demonstrate that the Ins(1,4,5)P3 receptor has an integral Ca2+ channel separated from the Ins(1,4,5)P3 binding site by a long stretch of residues some of which form binding sites for allosteric regulators, and some of which are substrates for phosphorylation. In this review, we discuss the ligand recognition characteristics of Ins(1,4,5)P3 receptors, and their functional properties in their native environment and after purification, and we relate these properties to what is known of the structure of the receptor. In addition to regulation by Ins(1,4,5)P3, the Ins(1,4,5)P3 receptor is subject to many additional regulatory influences which include Ca2+, adenine nucleotides, pH and phosphorylation by protein kinases. Many of the functional and structural characteristics of the Ins(1,4,5)P3 receptor show striking similarities to another intracellular Ca2+ channel, the ryanodine receptor. These properties of the Ins(1,4,5)P3 are discussed, and their possible roles in contributing to the complex Ca2+ signals evoked by extracellular stimuli are considered.

Frequency encoding of pulsatile signals of cAMP based on receptor desensitization in Dictyostelium cells

Dictyostelium discoideum amoebae represent a prototype for the study of periodic signaling in intercellular communication. These cells synthesize cAMP in response to cAMP pulses. Cell responsiveness in Dictyostelium can be characterized by the capability to generate a large number of significant responses to cAMP signals in a given amount of time. The existence of a frequency of pulsatile cAMP signals yielding maximum responsiveness is demonstrated by analysis of a realistic model for cAMP synthesis, based on receptor desensitization. The optimal frequency of stimulation closely depends on the kinetics of receptor desensitization and resensitization in target cells. Synthesis of cAMP is determined both in conditions where cells are not excitable and in conditions where they relay suprathreshold pulses of cAMP. Moreover, the effect of the stimulus waveform is investigated, and several measures of cell responsiveness are compared. The results provide an explanation for the effectiveness of cAMP pulses delivered at 5 min intervals, and for the failure of pulses delivered at 2 min intervals, in inducing slime mold development. Besides applying to intercellular communication in Dictyostelium, the present analysis bears on patterns of pulsatile signaling observed for hormones and growth factors. In all these cases, it appears that pulsatile signals can be encoded in terms of their frequency on the basis of desensitization in target cells.

Minimal model for signal-induced Ca2+ oscillations and for their frequency encoding through protein phosphorylation

In a variety of cells, hormonal or neurotransmitter signals elicit a train of intracellular Ca2+ spikes. The analysis of a minimal model based on Ca2(+)-induced Ca2+ release from intracellular stores shows how sustained oscillations of cytosolic Ca2+ may develop as a result of a rise in inositol 1,4,5-trisphosphate (InsP3) triggered by external stimulation. This rise elicits the release of a certain amount of Ca2+ from an InsP3-sensitive intracellular store. The subsequent rise in cytosolic Ca2+ in turn triggers the release of Ca2+ from a second store insensitive to InsP3. In contrast to the model proposed by Meyer and Stryer [Meyer, T. & Stryer, L. (1988) Proc. Natl. Acad. Sci. USA 85, 5051-5055], the present model, which contains only two variables, predicts the occurrence of periodic Ca2+ spikes in the absence of InsP3 oscillations. Such results indicate that repetitive Ca2+ spikes evoked by external stimuli do not necessarily require the concomitant, periodic variation of InsP3. The model is closely related to that proposed by Kuba and Takeshita [Kuba, K. & Takeshita, S. (1981) J. Theor. Biol. 93, 1009-1031] for Ca2+ oscillations in sympathetic neurones, based on Ca2(+)-induced Ca2+ release. We extend their results by showing the minimal conditions in which the latter process gives rise to periodic behavior and take into account the role of the rise in InsP3 caused by external stimulation. The analysis further shows how signal-induced Ca2+ oscillations might be effectively encoded in terms of their frequency through the phosphorylation of a cellular substrate by a protein kinase activated by cytosolic Ca2+.

The liver as a self-organizing system. I. Theoretics of its representation

The liver is described as a composite system consisting of a set of operative creodic microunits open to a continuous flow of matter, energy and informations. Its dynamics depend on two interactive and interrelated subsystems with actions described as homopoiesis and homeorhesis, making it an autoisodiasostic system. The system's emergent (equifinal) or emergence states, operative potential, diffusion and reaction phenomena and compensation states are also formally described. For readers not familiar with the language of general system theory, of system dynamics and of categorical analysis, a glossary of some terms is provided.

Impaired pulsatile secretion of insulin in relatives of patients with non-insulin-dependent diabetes

In fasting nondiabetic subjects, insulin is secreted in regular pulses every 12 to 15 minutes, but patients with non-insulin-dependent diabetes lack regular oscillatory insulin secretion. To investigate whether abnormal insulin oscillations are an early feature of diabetes, we studied 10 minimally glucose-intolerant first-degree relatives of patients with non-insulin-dependent diabetes and 10 controls matched for age and obesity. We performed a time-series analysis of fasting plasma insulin levels in blood samples obtained at 1-minute intervals for 150 minutes. Fasting plasma glucose levels were higher in the relatives than in the controls (mean +/- SD, 5.4 +/- 0.7 vs. 4.4 +/- 0.3 mmol per liter). Autocorrelation of pooled data showed no regular oscillatory activity in the relatives but a 13-minute cycle in the controls (r = 0.23, P less than 0.001). Similarly, Fourier transform analysis showed no significant peak in the relatives but the expected significant peak at 13 to 14 minutes in the controls (P less than 0.05). First-phase (0 to 10 minutes) insulin secretory responses to glucose administered intravenously were not significantly impaired in the relatives (geometric mean, 188 pmol per liter [26.2 mU per liter]; range of SD, +103 to -67 pmol per liter [+14.4 to -9.3 mU per liter]), as compared with the controls (geometric mean, 231 pmol per liter [32.2 mU per liter]; range of SD, +131 to -83 pmol per liter [+18.2 to -11.6 mU per liter]). We conclude that abnormal oscillatory insulin secretion may be an early phenomenon in the development of non-insulin-dependent diabetes.

Why are so many biological systems periodic?

The ubiquity of oscillations in biological systems is well established. Oscillations are observed in all types of organisms from the simplest to the most complex. Periods can range from fractions of a second to months or years. From time to time, it has been suggested that many biological oscillations are the result of the breakdown of effective self-regulation. The opposite view is defended here. It is argued that most periodic behavior is not pathological but rather constitutes the normal operation for these systems. They are present because they confer positive functional advantages for the organism. The advantages fall into five general categories: temporal organization, spatial organization, prediction of repetitive events, efficiency and precision of control.