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Biomedical subjects

Richard Bertram

Publications and source records attributed to Richard Bertram.

At least 19 recordsLinked to original sources
PubMed2007

Low dose of dopamine may stimulate prolactin secretion by increasing fast potassium currents.

Dopamine (DA) released from the hypothalamus tonically inhibits pituitary lactotrophs. DA (at micromolar concentration) opens potassium channels, hyperpolarizing the lactotrophs and thus preventing the calcium influx that triggers prolactin hormone release. Surprisingly, at concentrations approximately 1000 lower, DA can stimulate prolactin secretion. Here, we investigated whether an increase in a K+ current could mediate this stimulatory effect. We considered the fast K+ currents flowing through large-conductance BK channels and through A-type channels. We developed a minimal lactotroph model to investigate the effects of these two currents. Both IBK and IA could transform the electrical pattern of activity from spiking to bursting, but through distinct mechanisms. IBK always increased the intracellular Ca2+ concentration, while IA could either increase or decrease it. Thus, the stimulatory effects of DA could be mediated by a fast K+ conductance which converts tonically spiking cells to bursters. In addition, the study illustrates that

Animals↗
PubMed2006

Interaction of glycolysis and mitochondrial respiration in metabolic oscillations of pancreatic islets.

Insulin secretion from pancreatic beta-cells is oscillatory, with a typical period of 2-7 min, reflecting oscillations in membrane potential and the cytosolic Ca(2+) concentration. Our central hypothesis is that the slow 2-7 min oscillations are due to glycolytic oscillations, whereas faster oscillations that are superimposed are due to Ca(2+) feedback onto metabolism or ion channels. We extend a previous mathematical model based on this hypothesis to include a more detailed description of mitochondrial metabolism. We demonstrate that this model can account for typical oscillatory patterns of membrane potential and Ca(2+) concentration in islets. It also accounts for temporal data on oxygen consumption in islets. A recent challenge to the notion that glycolytic oscillations drive slow Ca(2+) oscillations in islets are data showing that oscillations in Ca(2+), mitochondrial oxygen consumption, and NAD(P)H levels are all terminated by membrane hyperpolarization. We demonstrate that these data are in fact compatible with a model in which glycolytic oscillations are the key player in rhythmic islet activity. Finally, we use the model to address the recent finding that the activity of islets from some mice is uniformly fast, whereas that from islets of other mice is slow. We propose a mechanism for this dichotomy.

Animals↗
PubMed2006

Residual bound Ca2+ can account for the effects of Ca2+ buffers on synaptic facilitation.

Facilitation is a transient stimulation-induced increase in synaptic response, a ubiquitous form of short-term synaptic plasticity that can regulate synaptic transmission on fast time scales. In their pioneering work, Katz and Miledi and Rahamimoff demonstrated the dependence of facilitation on presynaptic Ca(2+) influx and proposed that facilitation results from the accumulation of residual Ca(2+) bound to vesicle release triggers. However, this bound Ca(2+) hypothesis appears to contradict the evidence that facilitation is reduced by exogenous Ca(2+) buffers. This conclusion led to a widely held view that facilitation must depend solely on the accumulation of Ca(2+) in free form. Here we consider a more realistic implementation of the bound Ca(2+) mechanism, taking into account spatial diffusion of Ca(2+), and show that a model with slow Ca(2+) unbinding steps can retain sensitivity to free residual Ca(2+). We demonstrate that this model agrees with the facilitation accumulation time course and its biphasic decay exhibited by the crayfish inhibitor neuromuscular junction (NMJ) and relies on fewer assumptions than the most recent variants of the free residual Ca(2+) hypothesis. Further, we show that the bound Ca(2+) accumulation is consistent with Kamiya and Zucker's experimental results, which revealed that photolytic liberation of a fast Ca(2+) buffer decreases the synaptic response within milliseconds. We conclude that Ca(2+) binding processes with slow unbinding times (tens to hundreds of milliseconds) constitute a viable mechanism of synaptic facilitation at some synapses and discuss the experimental evidence for such a mechanism.

Action Potentials↗
PubMed2006

A simplified model for mitochondrial ATP production.

Most of the adenosine triphosphate (ATP) synthesized during glucose metabolism is produced in the mitochondria through oxidative phosphorylation. This is a complex reaction powered by the proton gradient across the mitochondrial inner membrane, which is generated by mitochondrial respiration. A detailed model of this reaction, which includes dynamic equations for the key mitochondrial variables, was developed earlier by Magnus and Keizer. However, this model is extraordinarily complicated. We develop a simpler model that captures the behavior of the original model but is easier to use and to understand. We then use it to investigate the mitochondrial responses to glycolytic and calcium input. We use the model to explain experimental observations of the opposite effects of raising cytosolic Ca(2+)in low and high glucose, and to predict the effects of a mutation in the mitochondrial enzyme nicotinamide nucleotide transhydrogenase (Nnt) in pancreatic beta-cells.

Adenosine Triphosphate↗
PubMed2006

Glucose modulates [Ca2+]i oscillations in pancreatic islets via ionic and glycolytic mechanisms.

Pancreatic islets of Langerhans display complex intracellular calcium changes in response to glucose that include fast (seconds), slow ( approximately 5 min), and mixed fast/slow oscillations; the slow and mixed oscillations are likely responsible for the pulses of plasma insulin observed in vivo. To better understand the mechanisms underlying these diverse patterns, we systematically analyzed the effects of glucose on period, amplitude, and plateau fraction (the fraction of time spent in the active phase) of the various regimes of calcium oscillations. We found that in both fast and slow islets, increasing glucose had limited effects on amplitude and period, but increased plateau fraction. In some islets, however, glucose caused a major shift in the amplitude and period of oscillations, which we attribute to a conversion between ionic and glycolytic modes (i.e., regime change). Raising glucose increased the plateau fraction equally in fast, slow, and regime-changing islets. A mathematical model of the pancreatic islet consisting of an ionic subsystem interacting with a slower metabolic oscillatory subsystem can account for these complex islet calcium oscillations by modifying the relative contributions of oscillatory metabolism and oscillatory ionic mechanisms to electrical activity, with coupling occurring via K(ATP) channels.

Adenine Nucleotides↗
PubMed2006

Diffusion of calcium and metabolites in pancreatic islets: killing oscillations with a pitchfork.

Cell coupling is important for the normal function of the beta-cells of the pancreatic islet of Langerhans, which secrete insulin in response to elevated plasma glucose. In the islets, electrical and metabolic communications are mediated by gap junctions. Although electrical coupling is believed to account for synchronization of the islets, the role and significance of diffusion of calcium and metabolites are not clear. To address these questions we analyze two different mathematical models of islet calcium and electrical dynamics. To study diffusion of calcium, we use a modified Morris-Lecar model. Based on our analysis, we conclude that intercellular diffusion of calcium is not necessary for islet synchronization, at most supplementing electrical coupling. Metabolic coupling is investigated with a recent mathematical model incorporating glycolytic oscillations. Bifurcation analysis of the coupled system reveals several modes of behavior, depending on the relative strength of electrical and metabolic coupling. We find that whereas electrical coupling always produces synchrony, metabolic coupling can abolish both oscillations and synchrony, explaining some puzzling experimental observations. We suggest that these modes are generic features of square-wave bursters and relaxation oscillators coupled through either the activation or recovery variable.

Animals↗
PubMed2006

Prolactin secretory rhythm of mated rats induced by a single injection of oxytocin.

Mating or vaginocervical stimulation [copulatory stimulus (CS)] induces two daily surges of the hormone prolactin (PRL) in rats. This unique secretory pattern of PRL surges is characteristic for the first half of pregnancy and is also present in ovariectomized (OVX) rats. Studies have shown that CS additionally provokes an acute release of the hormone oxytocin (OT). In this study, we tested whether a single injection of OT (iv) is sufficient to initiate the PRL secretion pattern of OVX/CS rats. Furthermore, we measured the 24-h profile of dopamine (DA) content in the anterior lobe of the pituitary gland, because DA is the major inhibitory factor of PRL secretion. The results indicated that a single injection of OT induces a PRL secretory rhythm and a DA release pattern similar to that initiated by CS. Immunocytochemical investigation showed that particular OTergic neurons in the hypothalamus express receptors for PRL, as well as for vasoactive intestinal polypeptide, which indicates an involvement in generating the PRL rhythm and entraining it to the ambient photoperiod. On the basis of this study, we suggest that the PRL-DA inhibitory feedback loop between lactotrophs and DAergic neurons plays a crucial role in generating the oscillatory PRL secretion pattern in CS rats. A timing signal, likely provided by the hypothalamic suprachiasmatic nucleus, entrains the autonomous PRL oscillation to a particular time of day. Mathematical modeling was used to illustrate the proposed network function. The experimental results further suggest an additional feedback mechanism in which certain hypothalamic OTergic neurons are influenced by PRL.

Animals↗
PubMed2006

A mathematical model for the mating-induced prolactin rhythm of female rats.

For the first 10 days of pregnancy and the first 12 days of pseudopregnancy, the secretion of prolactin (PRL) from pituitary lactotrophs is rhythmic, with two surges/day. This rhythm can also be triggered by bolus injection of oxytocin (OT). We describe a mathematical model for the initiation, maintenance, and termination of the OT-induced PRL rhythm. In our model, the mechanism for this circadian rhythm is mutual interaction between lactotrophs and neuroendocrine dopamine (DA) neurons. This rhythm is, under normal lighting conditions, entrained by the suprachiasmatic nucleus (SCN) but persists in the absence of input from the SCN. We postulate that OT injection triggers the rhythm by activating a population of bistable hypothalamic neurons that innervate and inhibit DA neurons. The bistable nature of these neurons allows them to act as a memory device, maintaining the rhythm long after OT has been cleared from the blood. The mechanism for this memory device and the arguments supporting it are detailed with computer simulations. Finally, we consider potential targets for a rhythm-terminating factor and make predictions that may be used to determine which mechanism is operational in terminating the OT- or mating-induced PRL rhythm.

Animals↗
PubMed2005

Intra- and inter-islet synchronization of metabolically driven insulin secretion.

Insulin secretion from pancreatic beta-cells is pulsatile with a period of 5-10 min and is believed to be responsible for plasma insulin oscillations with similar frequency. To observe an overall oscillatory insulin profile it is necessary that the insulin secretion from individual beta-cells is synchronized within islets, and that the population of islets is also synchronized. We have recently developed a model in which pulsatile insulin secretion is produced as a result of calcium-driven electrical oscillations in combination with oscillations in glycolysis. We use this model to investigate possible mechanisms for intra-islet and inter-islet synchronization. We show that electrical coupling is sufficient to synchronize both electrical bursting activity and metabolic oscillations. We also demonstrate that islets can synchronize by mutually entraining each other by their effects on a simple model "liver," which responds to the level of insulin secretion by adjusting the blood glucose concentration in an appropriate way. Since all islets are exposed to the blood, the distributed islet-liver system can synchronize the individual islet insulin oscillations. Thus, we demonstrate how intra-islet and inter-islet synchronization of insulin oscillations may be achieved.

Adenosine Diphosphate↗
PubMed2005

Individual mice can be distinguished by the period of their islet calcium oscillations: is there an intrinsic islet period that is imprinted in vivo?

Pulsatile insulin secretion in vivo is believed to be derived, in part, from the intrinsic glucose-dependent intracellular calcium concentration ([Ca2+]i) pulsatility of individual islets. In isolation, islets display fast, slow, or mixtures of fast and slow [Ca2+]i oscillations. We show that the period of islet [Ca2+]i oscillations is unique to each mouse, with the islets from an individual mouse demonstrating similar rhythms to one another. Based on their rhythmic period, mice were broadly classified as being either fast (0.65 +/- 0.1 min; n = 6 mice) or slow (4.7 +/- 0.2 min; n = 15 mice). To ensure this phenomenon was not an artifact of islet-to-islet communication, we confirmed that islets cultured in isolation (period: 2.9 +/- 0.1 min) were not statistically different from islets cultured together from the same mouse (3.1 +/- 0.1 min, P > 0.52, n = 5 mice). We also compared pulsatile insulin patterns measured in vivo with islet [Ca2+]i patterns measured in vitro from six mice. Mice with faster insulin pulse periods corresponded to faster islet [Ca2+]i patterns, whereas slower insulin patterns corresponded to slower [Ca2+]i patterns, suggesting that the insulin rhythm of each mouse is preserved to some degree by its islets in vitro. We propose that individual mice have characteristic oscillatory [Ca2+]i patterns, which are imprinted in vivo through an unknown mechanism.

Animals↗
PubMed2004

Filtering of calcium transients by the endoplasmic reticulum in pancreatic beta-cells.

Calcium handling in pancreatic beta-cells is important for intracellular signaling, the control of electrical activity, and insulin secretion. The endoplasmic reticulum (ER) is a key organelle involved in the storage and release of intracellular Ca2+. Using mathematical modeling, we analyze the filtering properties of the ER and clarify the dual role that it plays as both a Ca2+ source and a Ca2+ sink. We demonstrate that recent time-dependent data on the free Ca2+ concentration in pancreatic islets and beta-cell clusters can be explained with a model that uses a passive ER that takes up Ca2+ when the cell is depolarized and the cytosolic Ca2+ concentration is elevated, and releases Ca2+ when the cell is repolarized and the cytosolic Ca2+ is at a lower concentration. We find that Ca2+-induced Ca2+ release is not necessary to explain the data, and indeed the model is inconsistent with the data if Ca2+-induced Ca2+ release is a dominating factor. Finally, we show that a three-compartment model that includes a subspace compartment between the ER and the plasma membrane provides the best agreement with the experimental Ca2+ data.

Animals↗
PubMed2004

Calcium and glycolysis mediate multiple bursting modes in pancreatic islets.

Pancreatic islets of Langerhans produce bursts of electrical activity when exposed to stimulatory glucose levels. These bursts often have a regular repeating pattern, with a period of 10-60 s. In some cases, however, the bursts are episodic, clustered into bursts of bursts, which we call compound bursting. Consistent with this are recordings of free Ca2+ concentration, oxygen consumption, mitochondrial membrane potential, and intraislet glucose levels that exhibit very slow oscillations, with faster oscillations superimposed. We describe a new mathematical model of the pancreatic beta-cell that can account for these multimodal patterns. The model includes the feedback of cytosolic Ca2+ onto ion channels that can account for bursting, and a metabolic subsystem that is capable of producing slow oscillations driven by oscillations in glycolysis. This slow rhythm is responsible for the slow mode of compound bursting in the model. We also show that it is possible for glycolytic oscillations alone to drive a very slow form of bursting, which we call "glycolytic bursting." Finally, the model predicts that there is bistability between stationary and oscillatory glycolysis for a range of parameter values. We provide experimental support for this model prediction. Overall, the model can account for a diversity of islet behaviors described in the literature over the past 20 years.

Animals↗
PubMed2004

Complex bursting in pancreatic islets: a potential glycolytic mechanism.

The electrical activity of insulin-secreting pancreatic islets of Langerhans is characterized by bursts of action potentials. Most often this bursting is periodic, but in some cases it is modulated by an underlying slower rhythm. We suggest that the modulatory rhythm for this complex bursting pattern is due to oscillations in glycolysis, while the bursting itself is generated by some other slow process. To demonstrate this hypothesis, we couple a minimal model of glycolytic oscillations to a minimal model for activity-dependent bursting in islets. We show that the combined model can reproduce several complex bursting patterns from mouse islets published in the literature, and we illustrate how these complex oscillations are produced through the use of a fast/slow analysis.

Action Potentials↗
PubMed2004

Rhythmic secretion of prolactin in rats: action of oxytocin coordinated by vasoactive intestinal polypeptide of suprachiasmatic nucleus origin.

Prolactin (PRL) is secreted from lactotrophs of the anterior pituitary gland of rats in a unique pattern in response to uterine cervical stimulation (CS) during mating. Surges of PRL secretion occur in response to relief from hypothalamic dopaminergic inhibition and stimulation by hypothalamic releasing neurohormones. In this study, we characterized the role of oxytocin (OT) in this system and the involvement of vasoactive intestinal polypeptide (VIP) from the suprachiasmatic nucleus (SCN) in controlling OT and PRL secretion of CS rats. The effect of OT on PRL secretion was demonstrated in cultured lactotrophs showing simultaneous enhanced secretion rate and increased intracellular Ca(2+). Neurosecretory OT cells of the hypothalamic paraventricular nucleus that express VIP receptors were identified by using immunocytochemical techniques in combination with the retrogradely transported neuronal tracer Fluoro-Gold (iv injected). OT measurements of serial blood samples obtained from ovariectomized (OVX) CS rats displayed a prominent increase at the time of the afternoon PRL peak. The injection of VIP antisense oligonucleotides into the SCN abolished the afternoon increase of OT and PRL in CS-OVX animals. These findings suggest that VIP from the SCN contributes to the regulation of OT and PRL secretion in CS rats. We propose that in CS rats the regulatory mechanism(s) for PRL secretion comprise coordinated action of neuroendocrine dopaminergic and OT cells, both governed by the daily rhythm of VIP-ergic output from the SCN. This hypothesis is illustrated with a mathematical model.

Animals↗
PubMed2004

A calcium-based phantom bursting model for pancreatic islets.

Insulin-secreting beta-cells, located within the pancreatic islets of Langerhans, are excitable cells that produce regular bursts of action potentials when stimulated by glucose. This system has been the focus of mathematical investigation for two decades, spawning an array of mathematical models. Recently, a new class of models has been introduced called 'phantom bursters' [Bertram et al. (2000) Biophys. J. 79, 2880-2892], which accounts for the wide range of burst frequencies exhibited by islets via the interaction of more than one slow process. Here, we describe one implementation of the phantom bursting mechanism in which intracellular Ca2+ controls the oscillations through both direct and indirect negative feedback pathways. We show how the model dynamics can be understood through an extension of the fast/slow analysis that is typically employed for bursting oscillations. From this perspective, the model makes use of multiple degrees of freedom to generate the full range of bursting oscillations exhibited by beta-cells. The model also accounts for a wide range of experimental phenomena, including the ubiquitous triphasic response to the step elevation of glucose and responses to perturbations of internal Ca2+ stores. Although it is not presently a complete model of all beta-cell properties, it demonstrates the design principles that we anticipate will underlie future progress in beta-cell modeling.

Action Potentials↗
PubMed2004

Mathematical aspects of protein structure determination with NMR orientational restraints.

The field of structural biology is becoming increasingly important as new technological developments facilitate the collection of data on the atomic structures of proteins and nucleic acids. The solid-state NMR method is a relatively new biophysical technique that holds particular promise for determining the structures of peptides and proteins that are located within the cell membrane. This method provides information on the orientation of the peptide planes relative to an external magnetic field. In this article, we discuss some of the mathematical methods and tools that are useful in deriving the atomic structure from these orientational data. We first discuss how the data are viewed as tensors, and how these tensors can be used to construct an initial atomic model, assuming ideal stereochemistry. We then discuss methods for refining the models using global optimization, with stereochemistry constraints treated as penalty functions. These two processes, initial model building followed by refinement, are the two crucial steps between data collection and the final atomic model.

Magnetic Resonance Spectroscopy↗