Gating of homeostatic regulation of intrinsic excitability produces cryptic long-term storage of prior perturbations

Neurons and neuronal circuits must maintain their function throughout the life of the organism despite changing environments. Previous theoretical and experimental work suggests that neurons monitor their activity using intracellular calcium concentrations to regulate their intrinsic excitability. Models with multiple sensors can distinguish among different patterns of activity, but previous work using models with multiple sensors produced instabilities that lead the models' conductances to oscillate and then to grow without bound and diverge. We now introduce a nonlinear degradation term that explicitly prevents the maximal conductances to grow beyond a bound. We combine the sensors' signals into a master feedback signal that can be used to modulate the timescale of conductance evolution. Effectively, this means that the negative feedback can be gated on and off according to how far the neuron is from its target. The modified model recovers from multiple perturbations. Interestingly, depolarizing the models to the same membrane potential with current injection or with simulated high extracellular K+ produces different changes in conductances, arguing that caution must be used in interpreting manipulations that serve as a proxy for increased neuronal activity. Finally, these models accrue traces of prior perturbations that are not visible in their control activity after perturbation but that shape their responses to subsequent perturbations. These cryptic or hidden changes may provide insight into disorders such as posttraumatic stress disorder that only become visible in response to specific perturbations.

Temperature compensation in a small rhythmic circuit

Temperature affects the conductances and kinetics of the ionic channels that underlie neuronal activity. Each membrane conductance has a different characteristic temperature sensitivity, which raises the question of how neurons and neuronal circuits can operate robustly over wide temperature ranges. To address this, we employed computational models of the pyloric network of crabs and lobsters. We produced multiple different models that exhibit a triphasic pyloric rhythm over a range of temperatures and explored the dynamics of their currents and how they change with temperature. Temperature can produce smooth changes in the relative contributions of the currents to neural activity so that neurons and networks undergo graceful transitions in the mechanisms that give rise to their activity patterns. Moreover, responses of the models to deletions of a current can be different at high and low temperatures, indicating that even a well-defined genetic or pharmacological manipulation may produce qualitatively distinct effects depending on the temperature.

Visualization of currents in neural models with similar behavior and different conductance densities

Conductance-based models of neural activity produce large amounts of data that can be hard to visualize and interpret. We introduce visualization methods to display the dynamics of the ionic currents and to display the models’ response to perturbations. To visualize the currents’ dynamics, we compute the percent contribution of each current and display them over time using stacked-area plots. The waveform of the membrane potential and the contribution of each current change as the models are perturbed. To represent these changes over a range of the perturbation control parameter, we compute and display the distributions of these waveforms. We illustrate these procedures in six examples of bursting model neurons with similar activity but that differ as much as threefold in their conductance densities. These visualization methods provide heuristic insight into why individual neurons or networks with similar behavior can respond widely differently to perturbations.

The nervous system contains networks of neurons that generate electrical signals to communicate with each other and the rest of the body. Such electrical signals are due to the flow of ions into or out of the neurons via proteins known as ion channels. Neurons have many different kinds of ion channels that only allow specific ions to pass. Therefore, for a neuron to produce an electrical signal, the activities of several different ion channels need to be coordinated so that they all open and close at certain times.

Researchers have previously used data collected from various experiments to develop detailed models of electrical signals in neurons. These models incorporate information about how and when the ion channels may open and close, and can produce numerical simulations of the different ionic currents. However, it can be difficult to display the currents and observe how they change when several different ion channels are involved.

Alonso and Marder used simple mathematical concepts to develop new methods to display ionic currents in computational models of neurons. These tools use color to capture changes in ionic currents and provide insights into how the opening and closing of ion channels shape electrical signals.

The methods developed by Alonso and Marder could be adapted to display the behavior of biochemical reactions or other topics in biology and may, therefore, be useful to analyze data generated by computational models of many different types of cells. Additionally, these methods may potentially be used as educational tools to illustrate the coordinated opening and closing of ion channels in neurons and other fundamental principles of neuroscience that are otherwise hard to demonstrate.

Circuit Robustness to Temperature Perturbation Is Altered by Neuromodulators

In the ocean, the crab Cancer borealis is subject to daily and seasonal temperature changes. Previous work, done in the presence of descending modulatory inputs, had shown that the pyloric rhythm of the crab increases in frequency as temperature increases but maintains its characteristic phase relationships until it "crashes" at extremely high temperatures. To study the interaction between neuromodulators and temperature perturbations, we studied the effects of temperature on preparations from which the descending modulatory inputs were removed. Under these conditions, the pyloric rhythm was destabilized. We then studied the effects of temperature on preparations in the presence of oxotremorine, proctolin, and serotonin. Oxotremorine and proctolin enhanced the robustness of the pyloric rhythm, whereas serotonin made the rhythm less robust. These experiments reveal considerable animal-to-animal diversity in their crash stability, consistent with the interpretation that cryptic differences in many cell and network parameters are revealed by extreme perturbations.

Animal-to-animal variability in the phasing of the crustacean cardiac motor pattern: an experimental and computational analysis

The cardiac ganglion (CG) of Homarus americanus is a central pattern generator that consists of two oscillatory groups of neurons: "small cells" (SCs) and "large cells" (LCs). We have shown that SCs and LCs begin their bursts nearly simultaneously but end their bursts at variable phases. This variability contrasts with many other central pattern generator systems in which phase is well maintained. To determine both the consequences of this variability and how CG phasing is controlled, we modeled the CG as a pair of Morris-Lecar oscillators coupled by electrical and excitatory synapses and constructed a database of 15,000 simulated networks using random parameter sets. These simulations, like our experimental results, displayed variable phase relationships, with the bursts beginning together but ending at variable phases. The model suggests that the variable phasing of the pattern has important implications for the functional role of the excitatory synapses. In networks in which the two oscillators had similar duty cycles, the excitatory coupling functioned to increase cycle frequency. In networks with disparate duty cycles, it functioned to decrease network frequency. Overall, we suggest that the phasing of the CG may vary without compromising appropriate motor output and that this variability may critically determine how the network behaves in response to manipulations.

A role for compromise: synaptic inhibition and electrical coupling interact to control phasing in the leech heartbeat CpG

How can flexible phasing be generated by a central pattern generator (CPG)? To address this question, we have extended an existing model of the leech heartbeat CPG's timing network to construct a model of the CPG core and explore how appropriate phasing is set up by parameter variation. Within the CPG, the phasing among premotor interneurons switches regularly between two well defined states – synchronous and peristaltic. To reproduce experimentally observed phasing, we varied the strength of inhibitory synaptic and excitatory electrical input from the timing network to follower premotor interneurons. Neither inhibitory nor electrical input alone was sufficient to produce proper phasing on both sides, but instead a balance was required. Our model suggests that the different phasing of the two sides arises because the inhibitory synapses and electrical coupling oppose one another on one side (peristaltic) and reinforce one another on the other (synchronous). Our search of parameter space defined by the strength of inhibitory synaptic and excitatory electrical input strength led to a CPG model that well approximates the experimentally observed phase relations. The strength values derived from this analysis constitute model predictions that we tested by measurements made in the living system. Further, variation of the intrinsic properties of follower interneurons showed that they too systematically influence phasing. We conclude that a combination of inhibitory synaptic and excitatory electrical input interacting with neuronal intrinsic properties can flexibly generate a variety of phase relations so that almost any phasing is possible.

Interdependence of multiple theta generators in the hippocampus: a partial coherence analysis

The extracellularly recorded theta oscillation reflects a dynamic interaction of various synaptic and cellular mechanisms. Because the spatially overlapping dipoles responsible for the generation of theta field oscillation may represent different mechanisms, their separation might provide clues with regard to their origin and significance. We used a novel approach, partial coherence analysis, to reveal the various components of the theta rhythm and the relationship among its generators. Hippocampal field activity was recorded by a 16-site silicon probe in the CA1-dentate gyrus axis of the awake rat. Field patterns, recorded from various intrahippocampal or entorhinal cortex sites, were used to remove activity caused by a common source by the partialization procedure. The findings revealed highly coherent coupling between theta signals recorded (1) from the hippocampal fissure and stratum (str.) oriens of the CA1 region and (2) between CA1 stratum radiatum and the dentate molecular layer. The results of partial coherence analysis indicated that rhythmic input from the entorhinal cortex explained theta coherence between signals recorded from the hippocampal fissure and str. oriens but not the coherence between signals derived from str. radiatum and the dentate molecular layer. After bilateral lesions of the entorhinal cortex, all signals recorded from both below and above the CA1 hippocampal pyramidal cell layer became highly coherent. These observations indicate the presence of two, relatively independent, theta generators in the hippocampus, which are mediated by the entorhinal cortex and the CA3-mossy cell recurrent circuitry, respectively. The CA3-mossy cell theta generator is partially suppressed by the dentate gyrus interneuronal output in the intact brain. We suggest that timing of the action potentials of pyramidal cells during the theta cycle is determined by the cooperation between the active CA3 neurons and the entorhinal input.

Memory from the dynamics of intrinsic membrane currents

Almost all theoretical and experimental studies of the mechanisms underlying learning and memory focus on synaptic efficacy and make the implicit assumption that changes in synaptic efficacy are both necessary and sufficient to account for learning and memory. However, network dynamics depends on the complex interaction between intrinsic membrane properties and synaptic strengths and time courses. Furthermore, neuronal activity itself modifies not only synaptic efficacy but also the intrinsic membrane properties of neurons. This paper presents examples demonstrating that neurons with complex temporal dynamics can provide short-term "memory" mechanisms that rely solely on intrinsic neuronal properties. Additionally, we discuss the potential role that activity may play in long-term modification of intrinsic neuronal properties. While not replacing synaptic plasticity as a powerful learning mechanism, these examples suggest that memory in networks results from an ongoing interplay between changes in synaptic efficacy and intrinsic membrane properties.