Adam L. Taylor

Invertebrate Central Pattern Generation Moves along

Central pattern generators (CPGs) are circuits that generate organized and repetitive motor patterns, such as those underlying feeding, locomotion and respiration. We summarize recent work on invertebrate CPGs which has provided new insights into how rhythmic motor patterns are produced and how they are controlled by higher-order command and modulatory interneurons.

Multiple models to capture the variability in biological neurons and networks.

How tightly tuned are the synaptic and intrinsic properties that give rise to neuron and circuit function? Experimental work shows that these properties vary considerably across identified neurons in different animals. Given this variability in experimental data, this review describes some of the complications of building computational models to aid in understanding how system dynamics arise from the interaction of system components. We argue that instead of trying to build a single model that captures the generic behavior of a neuron or circuit, it is beneficial to construct a population of models that captures the behavior of the population that provided the experimental data. Studying a population of models with different underlying structure and similar behaviors provides opportunities to discover unsuspected compensatory mechanisms that contribute to neuron and network function.

Functional consequences of animal-to-animal variation in circuit parameters

How different are the neuronal circuits for a given behavior across individual animals? To address this question, we measured multiple cellular and synaptic parameters in individual preparations to see how they correlated with circuit function, using neurons and synapses in the pyloric circuit of the stomatogastric ganglion of the crab Cancer borealis. There was considerable preparation-to-preparation variability in the strength of two identified synapses, in the amplitude of a modulator-evoked current and in the expression of six ion channel genes. Nonetheless, we found strong correlations across preparations among these parameters and attributes of circuit performance. These data illustrate the importance of making multidimensional measurements from single preparations for understanding how variability in circuit output is related to the variability of multiple circuit parameters.

How multiple conductances determine electrophysiological properties in a multicompartment model

Most neurons have large numbers of voltage- and time-dependent currents that contribute to their electrical firing patterns. Because these currents are nonlinear, it can be difficult to determine the role each current plays in determining how a neuron fires. The lateral pyloric (LP) neuron of the stomatogastric ganglion of decapod crustaceans has been studied extensively biophysically. We constructed ∼600,000 versions of a four-compartment model of the LP neuron and distributed 11 different currents into the compartments. From these, we selected ∼1300 models that match well the electrophysiological properties of the biological neuron. Interestingly, correlations that were seen in the expression of channel mRNA in biological studies were not found across the ∼1300 admissible LP neuron models, suggesting that the electrical phenotype does not require these correlations. We used cubic fits of the function from maximal conductances to a series of electrophysiological properties to ask which conductances predominantly influence input conductance, resting membrane potential, resting spike rate, phasing of activity in response to rhythmic inhibition, and several other properties. In all cases, multiple conductances contribute to the measured property, and the combinations of currents that strongly influence each property differ. These methods can be used to understand how multiple currents in any candidate neuron interact to determine the cells electrophysiological behavior.

Automated diagnosis and image understanding with object extraction, object classification, and inferencing in retinal images

Medical imaging is shifting from film to electronic images. The STARE (structured analysis of the retina) system is a sophisticated image management system that will automatically diagnose images, compare images, measure key features in images, annotate image contents, and search for images similar in content. The authors concentrate on automated diagnosis. The images are annotated by segmentation of objects of interest, classification of the extracted objects, and reasoning about the image contents. The inferencing is accomplished with Bayesian networks that learn from image examples of each disease. This effort at image understanding in fundus images anticipates the future use of medical images. As these capabilities mature, the authors expect that ophthalmologists and physicians in other fields that rely in images will use a system like STARE to reduce repetitive work, to provide assistance to physicians in difficult diagnoses or with unfamiliar diseases, and to manage images in large image databases.

Precise Temperature Compensation of Phase in a Rhythmic Motor Pattern

Computational modeling and experimentation in a model system for network dynamics reveal how network phase relationships are temperature-compensated in terms of their underlying synaptic and intrinsic membrane currents.

Membrane Capacitance Measurements Revisited: Dependence of Capacitance Value on Measurement Method in Nonisopotential Neurons

During growth or degeneration neuronal surface area can change dramatically. Measurements of membrane protein concentration, as in ion channel or ionic conductance density, are often normalized by membrane capacitance, which is proportional to the surface area, to express changes independently from cell surface variations. Several electrophysiological protocols are used to measure cell capacitance, all based on the assumption of membrane isopotentiality. Yet, most neurons violate this assumption because of their complex anatomical structure, raising the question of which protocol yields measurements that are closest to the actual total membrane capacitance. We measured the capacitance of identified neurons from crab stomatogastric ganglia using three different protocols: the current-clamp step, the voltage-clamp step, and the voltage-clamp ramp protocols. We observed that the current-clamp protocol produced significantly higher capacitance values than those of either voltage-clamp protocol. Computational models of various anatomical complexities suggest that the current-clamp protocol can yield accurate capacitance estimates. In contrast, the voltage-clamp protocol estimates rapidly deteriorate as isopotentiality is reduced. We provide a mathematical description of these results by analyzing a simple two-compartment model neuron to facilitate an intuitive understanding of these methods. Together, the experiments, modeling, and mathematical analysis indicate that accurate total membrane capacitance measurements cannot be obtained with voltage-clamp protocols in nonisopotential neurons. Furthermore, although current-clamp steps can theoretically yield accurate measurements, experimentalists should be aware of limitations imposed by step duration and numerical errors during fitting procedures to obtain the membrane time constant.

Robustness of a Rhythmic Circuit to Short- and Long-Term Temperature Changes

Recent computational and experimental work has shown that similar network performance can result from variable sets of synaptic and intrinsic properties. Because temperature is a global perturbation that differentially influences every biological process within the nervous system, one might therefore expect that individual animals would respond differently to temperature. Nonetheless, the phase relationships of the pyloric rhythm of the stomatogastric ganglion (STG) of the crab, Cancer borealis, are remarkably invariant between 7 and 23°C (Tang et al., 2010). Here, we report that, when isolated STG preparations were exposed to more extreme temperature ranges, their networks became nonrhythmic, or “crashed”, in a reversible fashion. Animals were acclimated for at least 3 weeks at 7, 11, or 19°C. When networks from the acclimated animals were perturbed by acute physiologically relevant temperature ramps (11–23°C), the network frequency and phase relationships were independent of the acclimation group. At high acute temperatures (>23°C), circuits from the cold-acclimated animals produced less-regular pyloric rhythms than those from warm-acclimated animals. At high acute temperatures, phase relationships between pyloric neurons were more variable from animal to animal than at moderate acute temperatures, suggesting that individual differences across animals in intrinsic circuit parameters are revealed at high temperatures. This shows that individual and variable neuronal circuits can behave similarly in normal conditions, but their behavior may diverge when confronted with extreme external perturbations.

Analysis of oscillations in a reciprocally inhibitory network with synaptic depression

We present and analyze a model of a two-cell reciprocally inhibitory network that oscillates. The principal mechanism of oscillation is short-term synaptic depression. Using a simple model of depression and analyzing the system in certain limits, we can derive analytical expressions for various features of the oscillation, including the parameter regime in which stable oscillations occur, as well as the period and amplitude of these oscillations. These expressions are functions of three parameters: the time constant of depression, the synaptic strengths, and the amount of tonic excitation the cells receive. We compare our analytical results with the output of numerical simulations and obtain good agreement between the two. Based on our analysis, we conclude that the oscillations in our network are qualitatively different from those in networks that oscillate due to postinhibitory rebound, spike-frequency adaptation, or other intrinsic (rather than synaptic) adaptational mechanisms. In particular, our network can oscillate only via the synaptic escape mode of Skinner, Kopell, and Marder (1994).

The effects of temperature on the stability of a neuronal oscillator.

The crab Cancer borealis undergoes large daily fluctuations in environmental temperature (8–24°C) and must maintain appropriate neural function in the face of this perturbation. In the pyloric circuit of the crab stomatogastric ganglion, we pharmacologically isolated the pacemaker kernel (the AB and PD neurons) and characterized its behavior in response to temperature ramps from 7°C to 31°C. For moderate temperatures, the pacemaker displayed a frequency-temperature curve statistically indistinguishable from that of the intact circuit, and like the intact circuit maintained a constant duty cycle. At high temperatures (above 23°C), a variety of different behaviors were seen: in some preparations the pacemaker increased in frequency, in some it slowed, and in many preparations the pacemaker stopped oscillating (“crashed”). Furthermore, these crashes seemed to fall into two qualitatively different classes. Additionally, the animal-to-animal variability in frequency increased at high temperatures. We used a series of Morris-Lecar mathematical models to gain insight into these phenomena. The biophysical components of the final model have temperature sensitivities similar to those found in nature, and can crash via two qualitatively different mechanisms that resemble those observed experimentally. The crash type is determined by the precise parameters of the model at the reference temperature, 11°C, which could explain why some preparations seem to crash in one way and some in another. Furthermore, even models with very similar behavior at the reference temperature diverge greatly at high temperatures, resembling the experimental observations.