Introductory Life Science Mathematics and Quantitative Neuroscience Courses

We describe two sets of courses designed to enhance the mathematical, statistical, and computational training of life science undergraduates at Emory College. The first course is an introductory sequence in differential and integral calculus, modeling with differential equations, probability, and inferential statistics. The second is an upper-division course in computational neuroscience. We provide a description of each course, detailed syllabi, examples of content, and a brief discussion of the main issues encountered in developing and offering the courses

Dynamic Grouping of Hippocampal Neural Activity During Cognitive Control of Two Spatial Frames

Hippocampal neurons represent two concurrent streams of spatial information by transiently organizing into subpopulations of coactive neurons and can reflect the most behaviorally relevant information at any given time

Theta-paced flickering between place-cell maps in the hippocampus

The ability to recall discrete memories is thought to depend on the formation of attractor states in recurrent neural networks. In such networks, representations can be reactivated reliably from subsets of the cues that were present when the memory was encoded, at the same time as interference from competing representations is minimized. Theoretical studies have pointed to the recurrent CA3 system of the hippocampus as a possible attractor network. Consistent with predictions from these studies, experiments have shown that place representations in CA3 and downstream CA1 tolerate small changes in the configuration of the environment but switch to uncorrelated representations when dissimilarities become larger. The kinetics supporting such network transitions, at the subsecond time scale, is poorly understood, however. Here we show that instantaneous transformation of the spatial context (\u2018teleportation\u2019) does not change the hippocampal representation all at once but is followed by temporary bistability in the discharge activity of CA3 ensembles. Rather than sliding through a continuum of intermediate activity states, the CA3 network undergoes a short period of competitive flickering between pre-formed representations for past and present environment, before settling on the latter. Network flickers are extremely fast, often with complete replacement of the active ensemble from one theta cycle to the next. Within individual cycles, segregation is stronger towards the end, when firing starts to decline, pointing to the theta cycle as a temporal unit for expression of attractor states in the hippocampus. Repetition of pattern-completion processes across successive theta cycles may facilitate error correction and enhance discriminative power in the presence of weak and ambiguous input cues

Conductance Ratios and Cellular Identity

Recent experimental evidence suggests that coordinated expression of ion channels plays a role in constraining neuronal electrical activity. In particular, each neuronal cell type of the crustacean stomatogastric ganglion exhibits a unique set of positive linear correlations between ionic membrane conductances. These data suggest a causal relationship between expressed conductance correlations and features of cellular identity, namely electrical activity type. To test this idea, we used an existing database of conductance-based model neurons. We partitioned this database based on various measures of intrinsic activity, to approximate distinctions between biological cell types. We then tested individual conductance pairs for linear dependence to identify correlations. Contrary to experimental evidence, in which all conductance correlations are positive, 32% of correlations seen in this database were negative relationships. In addition, 80% of correlations seen here involved at least one calcium conductance, which have been difficult to measure experimentally. Similar to experimental results, each activity type investigated had a unique combination of correlated conductances. Finally, we found that populations of models that conform to a specific conductance correlation have a higher likelihood of exhibiting a particular feature of electrical activity. We conclude that regulating conductance ratios can support proper electrical activity of a wide range of cell types, particularly when the identity of the cell is well-defined by one or two features of its activity. Furthermore, we predict that previously unseen negative correlations and correlations involving calcium conductances are biologically plausible

Attention Enhances the Retrieval and Stability of Visuospatial and Olfactory Representations in the Dorsal Hippocampus

Attention enhances the encoding and retrieval of olfactory and visuospatial representations by modulating place field stability, firing rate, and neuronal synchronization of pyramidal cells in the hippocampus

Silicon central pattern generators for cardiac diseases

Belgium Herbarium image of Meise Botanic Garden

A Diffusive Homeostatic Signal Maintains Neural Heterogeneity and Responsiveness in Cortical Networks

Gaseous neurotransmitters such as nitric oxide (NO) provide a unique and often overlooked mechanism for neurons to communicate through diffusion within a network, independent of synaptic connectivity. NO provides homeostatic control of intrinsic excitability. Here we conduct a theoretical investigation of the distinguishing roles of NO-mediated diffusive homeostasis in comparison with canonical non-diffusive homeostasis in cortical networks. We find that both forms of homeostasis provide a robust mechanism for maintaining stable activity following perturbations. However, the resulting networks differ, with diffusive homeostasis maintaining substantial heterogeneity in activity levels of individual neurons, a feature disrupted in networks with non-diffusive homeostasis. This results in networks capable of representing input heterogeneity, and linearly responding over a broader range of inputs than those undergoing non-diffusive homeostasis. We further show that these properties are preserved when homeostatic and Hebbian plasticity are combined. These results suggest a mechanism for dynamically maintaining neural heterogeneity, and expose computational advantages of non-local homeostatic processes

Silicon central pattern generators for cardiac diseases

Cardiac rhythm management devices provide therapies for both arrhythmias and resynchronisation but not heart failure, which affects millions of patients worldwide. This paper reviews recent advances in biophysics and mathematical engineering that provide a novel technological platform for addressing heart disease and enabling beat-to-beat adaptation of cardiac pacing in response to physiological feedback. The technology consists of silicon hardware central pattern generators (hCPGs) that may be trained to emulate accurately the dynamical response of biological central pattern generators (bCPGs). We discuss the limitations of present CPGs and appraise the advantages of analog over digital circuits for application in bioelectronic medicine. To test the system, we have focused on the cardio-respiratory oscillators in the medulla oblongata that modulate heart rate in phase with respiration to induce respiratory sinus arrhythmia (RSA). We describe here a novel, scalable hCPG comprising physiologically realistic (Hodgkin–Huxley type) neurones and synapses. Our hCPG comprises two neurones that antagonise each other to provide rhythmic motor drive to the vagus nerve to slow the heart. We show how recent advances in modelling allow the motor output to adapt to physiological feedback such as respiration. In rats, we report on the restoration of RSA using an hCPG that receives diaphragmatic electromyography input and use it to stimulate the vagus nerve at specific time points of the respiratory cycle to slow the heart rate. We have validated the adaptation of stimulation to alterations in respiratory rate. We demonstrate that the hCPG is tuneable in terms of the depth and timing of the RSA relative to respiratory phase. These pioneering studies will now permit an analysis of the physiological role of RSA as well as its any potential therapeutic use in cardiac disease