Richard Bertram

Topological and phenomenological classification of bursting oscillations.

We describe a classification scheme for bursting oscillations which encompasses many of those found in the literature on bursting in excitable media. This is an extension of the scheme of Rinzel (in Mathematical Topics in Population Biology, Springer, Berlin, 1987), put in the context of a sequence of horizontal cuts through a two-parameter bifurcation diagram. We use this to describe the phenomenological character of different types of bursting, addressing the issue of how well the bursting can be characterized given the limited amount of information often available in experimental settings.

Ion Channels and Signaling in the Pituitary Gland

Endocrine pituitary cells are neuronlike; they express numerous voltage-gated sodium, calcium, potassium, and chloride channels and fire action potentials spontaneously, accompanied by a rise in intracellular calcium. In some cells, spontaneous electrical activity is sufficient to drive the intracellular calcium concentration above the threshold for stimulus-secretion and stimulus-transcription coupling. In others, the function of these action potentials is to maintain the cells in a responsive state with cytosolic calcium near, but below, the threshold level. Some pituitary cells also express gap junction channels, which could be used for intercellular Ca(2+) signaling in these cells. Endocrine cells also express extracellular ligand-gated ion channels, and their activation by hypothalamic and intrapituitary hormones leads to amplification of the pacemaking activity and facilitation of calcium influx and hormone release. These cells also express numerous G protein-coupled receptors, which can stimulate or silence electrical activity and action potential-dependent calcium influx and hormone release. Other members of this receptor family can activate calcium channels in the endoplasmic reticulum, leading to a cell type-specific modulation of electrical activity. This review summarizes recent findings in this field and our current understanding of the complex relationship between voltage-gated ion channels, ligand-gated ion channels, gap junction channels, and G protein-coupled receptors in pituitary cells.

The Ca2+ Dynamics of Isolated Mouse β-Cells and Islets: Implications for Mathematical Models

[Ca(2+)](i) and electrical activity were compared in isolated beta-cells and islets using standard techniques. In islets, raising glucose caused a decrease in [Ca(2+)](i) followed by a plateau and then fast (2-3 min(-1)), slow (0.2-0.8 min(-1)), or a mixture of fast and slow [Ca(2+)](i) oscillations. In beta-cells, glucose transiently decreased and then increased [Ca(2+)](i), but no islet-like oscillations occurred. Simultaneous recordings of [Ca(2+)](i) and electrical activity suggested that differences in [Ca(2+)](i) signaling are due to differences in islet versus beta-cell electrical activity. Whereas islets exhibited bursts of spikes on medium/slow plateaus, isolated beta-cells were depolarized and exhibited spiking, fast-bursting, or spikeless plateaus. These electrical patterns in turn produced distinct [Ca(2+)](i) patterns. Thus, although isolated beta-cells display several key features of islets, their oscillations were faster and more irregular. beta-cells could display islet-like [Ca(2+)](i) oscillations if their electrical activity was converted to a slower islet-like pattern using dynamic clamp. Islet and beta-cell [Ca(2+)](i) changes followed membrane potential, suggesting that electrical activity is mainly responsible for the [Ca(2+)] dynamics of beta-cells and islets. A recent model consisting of two slow feedback processes and passive endoplasmic reticulum Ca(2+) release was able to account for islet [Ca(2+)](i) responses to glucose, islet oscillations, and conversion of single cell to islet-like [Ca(2+)](i) oscillations. With minimal parameter variation, the model could also account for the diverse behaviors of isolated beta-cells, suggesting that these behaviors reflect natural cell heterogeneity. These results support our recent model and point to the important role of beta-cell electrical events in controlling [Ca(2+)](i) over diverse time scales in islets.

Modeling N-methyl-D-aspartate-induced bursting in dopamine neurons

Burst firing of dopaminergic neurons of the substantia nigra pars compacta can be induced in vitro by the glutamate agonist N-methyl-D-aspartate. It has been suggested that the interburst hyperpolarization is due to Na+ extrusion by a ouabain-sensitive pump [Johnson et al. (1992) Science 258, 665-667]. We formulate and explore a theoretical model, with a minimal number of currents, for this novel mechanism of burst generation. This minimal model is further developed into a more elaborate model based on observations of additional currents and hypotheses about their spatial distribution in dopaminergic neurons [Hounsgaard (1992) Neuroscience 50, 513-518; Llinás et al. (1984) Brain Res. 294, 127-132]. Using the minimal model, we confirm that interaction between the regenerative, inward N-methyl-D-aspartate-mediated current and the outward Na(+)-pump current is sufficient to generate the slow oscillation (approximately 0.5 Hz) underlying the burst. The negative-slope region of the N-methyl-D-aspartate channels current-voltage relation is indispensable for this slow rhythm generation. The time-scale of Na(+)-handling determines the bursts slow frequency. Moreover, we show that, given the constraints of sodium handling, such bursting is best explained mechanistically by using at least two spatial, cable-like compartments: a soma where action potentials are produced and a dendritic compartment where the slow rhythm is generated. Our result is consistent with recent experimental evidence that burst generation originates in distal dendrites [Seutin et al. (1994) Neuroscience 58, 201-206]. Responses of the model to a number of electrophysiological and pharmacological stimuli are consistent with known responses observed under similar conditions. These include the persistence of the slow rhythm when the tetrodotoxin-sensitive Na+ channel is blocked and when the soma is voltage-clamped at -60 mV. Using our more elaborate model, we account for details of the observed frequency adaptation in N-methyl-D-aspartate-induced bursting, the origin of multiple spiking and bursting mechanisms, and the interaction between two different bursting mechanisms. Besides reproducing several well established firing patterns, this model also suggests that new firing modes, not yet recorded, might also occur in dopaminergic neurons. This model provides mechanistic insights and explanations into the origin of a variety of experimentally observed membrane potential firing patterns in dopaminergic neurons, including N-methyl-D-aspartate-induced bursting and its dendritic origin. Such a model, capable of reproducing a number of realistic behaviors of dopaminergic neurons, could be useful in further studies of the basal ganglia-thalamocortical motor circuit. It may also shed light on bursting that involves N-methyl-D-aspartate channel activity in other neuron types.

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

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

An improved hydrogen bond potential: impact on medium resolution protein structures.

A new semi‐empirical force field has been developed to describe hydrogen‐bonding interactions with a directional component. The hydrogen bond potential supports two alternative target angles, motivated by the observation that carbonyl hydrogen bond acceptor angles have a bimodal distribution. It has been implemented as a module for a macromolecular refinement package to be combined with other force field terms in the stereochemically restrained refinement of macromolecules. The parameters for the hydrogen bond potential were optimized to best fit crystallographic data from a number of protein structures. Refinement of medium‐resolution structures with this additional restraint leads to improved structure, reducing both the free R‐factor and over‐fitting. However, the improvement is seen only when stringent hydrogen bond selection criteria are used. These findings highlight common misconceptions about hydrogen bonding in proteins, and provide explanations for why the explicit hydrogen bonding terms of some popular force field sets are often best switched off.

Modeling Study of the Effects of Overlapping Ca2+ Microdomains on Neurotransmitter Release

Although single-channel Ca2+ microdomains are capable of gating neurotransmitter release in some instances, it is likely that in many cases the microdomains from several open channels overlap to activate vesicle fusion. We describe a mathematical model in which transmitter release is gated by single or overlapping Ca2+ microdomains produced by the opening of nearby Ca2+ channels. This model accounts for the presence of a mobile Ca2+ buffer, provided either that the buffer is unsaturable or that it is saturated near an open channel with Ca2+ binding kinetics that are rapid relative to Ca2+ diffusion. We show that the release time course is unaffected by the location of the channels (at least for distances up to 50 nm), but paired-pulse facilitation is greater when the channels are farther from the release sites. We then develop formulas relating the fractional release following selective or random channel blockage to the cooperative relationship between release and the presynaptic Ca2+ current. These formulas are used with the transmitter release model to study the dependence of this form of cooperativity, which we call Ca2+ current cooperativity, on mobile buffers and on the local geometry of Ca2+ channels. We find that Ca2+ current cooperativity increases with the number of channels per release site, but is considerably less than the number of channels, the theoretical upper bound. In the presence of a saturating mobile buffer the Ca2+ current cooperativity is greater, and it increases more rapidly with the number of channels. Finally, Ca2+ current cooperativity is an increasing function of channel distance, particularly in the presence of saturating mobile buffer.

The Phantom Burster Model for Pancreatic β-Cells

Pancreatic beta-cells exhibit bursting oscillations with a wide range of periods. Whereas periods in isolated cells are generally either a few seconds or a few minutes, in intact islets of Langerhans they are intermediate (10-60 s). We develop a mathematical model for beta-cell electrical activity capable of generating this wide range of bursting oscillations. Unlike previous models, bursting is driven by the interaction of two slow processes, one with a relatively small time constant (1-5 s) and the other with a much larger time constant (1-2 min). Bursting on the intermediate time scale is generated without need for a slow process having an intermediate time constant, hence phantom bursting. The model suggests that isolated cells exhibiting a fast pattern may nonetheless possess slower processes that can be brought out by injecting suitable exogenous currents. Guided by this, we devise an experimental protocol using the dynamic clamp technique that reliably elicits islet-like, medium period oscillations from isolated cells. Finally, we show that strong electrical coupling between a fast burster and a slow burster can produce synchronized medium bursting, suggesting that islets may be composed of cells that are intrinsically either fast or slow, with few or none that are intrinsically medium.

Auditory-Dependent Vocal Recovery in Adult Male Zebra Finches Is Facilitated by Lesion of a Forebrain Pathway That Includes the Basal Ganglia

The integration of two neural pathways generates learned song in zebra finches. The vocal motor pathway (VMP) is a direct connection between HVC (proper name) and the robust nucleus of the arcopallium (RA), whereas the anterior forebrain pathway (AFP) comprises an indirect circuit from HVC to RA that traverses the basal ganglia. Partial ablation (microlesion) of HVC in adult birds alters the integration of VMP and AFP synaptic input within RA and destabilizes singing. However, the vocal pattern shows surprising resilience because birds subsequently recover their song in ∼1 week. Here, we show that deafening prevents vocal recovery after HVC microlesions, indicating that birds require auditory feedback to restore/relearn their vocal patterns. We then tested the role of the AFP (basal ganglia circuit) in this feedback-based recovery by ablating the output nucleus of the AFP [lateral magnocellular nucleus of the anterior nidopallium (LMAN)]. We found that LMAN ablation after HVC microlesions induced a sudden recovery of the vocal pattern. Thus, the AFP cannot be the neural locus of an instructive/learning mechanism that uses auditory feedback to guide vocal recovery, at least in this form of adult vocal plasticity. Instead, the AFP appears to be the source of the variable motor patterns responsible for vocal destabilization. In part, auditory feedback may restore song by strengthening the VMP component of synaptic input to RA relative to the AFP component.

Simulated-annealing real-space refinement as a tool in model building

Methods have been developed that further automate the building of macromolecular structures into electron-density maps. The software supports molecular-dynamics real-space refinement of an atomic model to local regions of a map within the context of a popular molecular-modeling program, O [Jones et al. (1991), Acta Cryst. A47, 110-119]. It is implemented as a module to the CNS refinement package [Brünger et al. (1998), Acta Cryst. D54, 905-921], controlled by a graphical user interface and commands executed directly through the molecular-graphics package. The method is illustrated with examples of the building and rebuilding of protein and nucleic acid models in which laborious manual adjustments are avoided. The resulting models show improved convergence during subsequent reciprocal-space refinement. The novel feature of the RSRef2000 software is the combination of simulated-annealing optimization with local real-space refinement, allowing several local minima to be explored quickly and automatically within the context of interactive model building.