Marco Arieli Herrera-Valdez

Ensemble Response in Mushroom Body Output Neurons of the Honey Bee Outpaces Spatiotemporal Odor Processing Two Synapses Earlier in the Antennal Lobe

Neural representations of odors are subject to computations that involve sequentially convergent and divergent anatomical connections across different areas of the brains in both mammals and insects. Furthermore, in both mammals and insects higher order brain areas are connected via feedback connections. In order to understand the transformations and interactions that this connectivity make possible, an ideal experiment would compare neural responses across different, sequential processing levels. Here we present results of recordings from a first order olfactory neuropile – the antennal lobe (AL) – and a higher order multimodal integration and learning center – the mushroom body (MB) – in the honey bee brain. We recorded projection neurons (PN) of the AL and extrinsic neurons (EN) of the MB, which provide the outputs from the two neuropils. Recordings at each level were made in different animals in some experiments and simultaneously in the same animal in others. We presented two odors and their mixture to compare odor response dynamics as well as classification speed and accuracy at each neural processing level. Surprisingly, the EN ensemble significantly starts separating odor stimuli rapidly and before the PN ensemble has reached significant separation. Furthermore the EN ensemble at the MB output reaches a maximum separation of odors between 84–120 ms after odor onset, which is 26 to 133 ms faster than the maximum separation at the AL output ensemble two synapses earlier in processing. It is likely that a subset of very fast PNs, which respond before the ENs, may initiate the rapid EN ensemble response. We suggest therefore that the timing of the EN ensemble activity would allow retroactive integration of its signal into the ongoing computation of the AL via centrifugal feedback.

Relating ion channel expression, bifurcation structure, and diverse firing patterns in a model of an identified motor neuron

Neurons show diverse firing patterns. Even neurons belonging to a single chemical or morphological class, or the same identified neuron, can display different types of electrical activity. For example, motor neuron MN5, which innervates a flight muscle of adult Drosophila, can show distinct firing patterns under the same recording conditions. We developed a two-dimensional biophysical model and show that a core complement of just two voltage-gated channels is sufficient to generate firing pattern diversity. We propose Shab and DmNav to be two candidate genes that could encode these core currents, and find that changes in Shab channel expression in the model can reproduce activity resembling the main firing patterns observed in MN5 recordings. We use bifurcation analysis to describe the different transitions between rest and spiking states that result from variations in Shab channel expression, exposing a connection between ion channel expression, bifurcation structure, and firing patterns in models of membrane potential dynamics.

Membranes with the same ion channel populations but different excitabilities.

Electrical signaling allows communication within and between different tissues and is necessary for the survival of multicellular organisms. The ionic transport that underlies transmembrane currents in cells is mediated by transporters and channels. Fast ionic transport through channels is typically modeled with a conductance-based formulation that describes current in terms of electrical drift without diffusion. In contrast, currents written in terms of drift and diffusion are not as widely used in the literature in spite of being more realistic and capable of displaying experimentally observable phenomena that conductance-based models cannot reproduce (e.g. rectification). The two formulations are mathematically related: conductance-based currents are linear approximations of drift-diffusion currents. However, conductance-based models of membrane potential are not first-order approximations of drift-diffusion models. Bifurcation analysis and numerical simulations show that the two approaches predict qualitatively and quantitatively different behaviors in the dynamics of membrane potential. For instance, two neuronal membrane models with identical populations of ion channels, one written with conductance-based currents, the other with drift-diffusion currents, undergo transitions into and out of repetitive oscillations through different mechanisms and for different levels of stimulation. These differences in excitability are observed in response to excitatory synaptic input, and across different levels of ion channel expression. In general, the electrophysiological profiles of membranes modeled with drift-diffusion and conductance-based models having identical ion channel populations are different, potentially causing the input-output and computational properties of networks constructed with these models to be different as well. The drift-diffusion formulation is thus proposed as a theoretical improvement over conductance-based models that may lead to more accurate predictions and interpretations of experimental data at the single cell and network levels.

Reduced models for the pacemaker dynamics of cardiac cells

We introduce three- and two-dimensional biophysical models of cardiac excitability derived from a 14-dimensional model of the sinus venosus [Rasmusson, R., et al., 1990. Am. J. Physiol. 259, H352-369]. The reduced models capture normal pacemaking dynamics with a small complement of ionic currents. The two-dimensional model bears some similarities with the Morris-Lecar model [Morris, C., Lecar, H., 1981. Biophysical Journal, 35, 193-213]. Because they were reduced from a biophysical model, both models depend on parameters that were obtained from experimental data. Even though the correspondence with the original model is not exact, parameters may be adjusted to tune the reductions to fit experimental traces. As a consequence, unlike other generic low-dimensional models, the models introduced here provide a means to relate physiologically relevant characteristics of pacemaker potentials such as diastolic depolarization, plateau, and action potential frequency, to biophysical variables such as the relative abundance of membrane channels and channel kinetic rates. In particular, these models can lead to an explicit description of how the shape of cardiac action potentials depends on the relative contributions and states of inward and outward currents. By being physiologically derived and computationally efficient, the models presented in this article are useful tools for theoretical studies of excitability at the cellular and network levels.

Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administration capacity

BackgroundInfluenza viruses are a major cause of morbidity and mortality worldwide. Vaccination remains a powerful tool for preventing or mitigating influenza outbreaks. Yet, vaccine supplies and daily administration capacities are limited, even in developed countries. Understanding how such constraints can alter the mitigating effects of vaccination is a crucial part of influenza preparedness plans. Mathematical models provide tools for government and medical officials to assess the impact of different vaccination strategies and plan accordingly. However, many existing models of vaccination employ several questionable assumptions, including a rate of vaccination proportional to the population at each point in time.MethodsWe present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters. We refer to this as the non-proportional model of vaccination and compare it to the proportional scheme typically found in the literature.ResultsThe proportional and non-proportional models behave similarly for a few different vaccination scenarios. However, there are parameter regimes involving the vaccination campaign duration and daily supply limit for which the non-proportional model predicts smaller epidemics that peak later, but may last longer, than those of the proportional model. We also use the non-proportional model to predict the mitigating effects of variably timed vaccination campaigns for different levels of vaccination coverage, using specific constraints on daily administration capacity.ConclusionsThe non-proportional model of vaccination is a theoretical improvement that provides more accurate predictions of the mitigating effects of vaccination on influenza outbreaks than the proportional model. In addition, parameters such as vaccine supply and daily administration limit can be easily adjusted to simulate conditions in developed and developing nations with a wide variety of financial and medical resources. Finally, the model can be used by government and medical officials to create customized pandemic preparedness plans based on the supply and administration constraints of specific communities.

Differential contribution of voltage-dependent potassium currents to neuronal excitability.

The excitability of a neuron depends on the different inward and outward currents that flow across its membrane. The specific role of A-type and persistent K-currents in shaping neuronal excitability remains partially unexplained by electrophysiological data. Drosophila motor neurons provide a model system to study the differential contributions of voltage-dependent K-currents to the dynamics of the membrane potential. In this work, the theoretical plausibility of existing hypotheses about the differential involvement of A-type currents in delaying spiking activity is examined through a mathematical model constructed using known macroscopic biophysical properties of voltage-dependent, slowly inactivating and fast inactivating A-type Drosophila channels. The model is constrained first by electrophysiological data, and an analysis of the membrane dynamics is performed through systematic variation of the ratios of the maximal whole-membrane currents. Different ratios among the numbers of the different channels in the model capture the basic features of responses to square pulse stimulation previously observed in Drosophila motor neurons for embryo, larvae and adult motor neurons, Kenyon cells, and giant cultured cells. The model supports the notion that slowly inactivating potassium currents are necessary for sustained spiking activity. The model also supports the hypothesis that early inactivating A-type K+ (Shal) channels are responsible for experimentally observed delays in the onset of spiking. In contrast, Shaker A-type channels with more depolarized steady state inactivation also contribute to the delay to first spike, but less than Shal. Instead, Shaker channels gate single and repetitive spiking. Furthermore, the model elucidates a biophysical mechanism that allows neurons to diversify their function, in this case by combining additive and resonant properties. Our modeling results are consistent with experimental results from different preparations including Drosophilaand lobster.

Biophysical modeling of excitability and membrane integration at the single cell and network levels

Ion channels facilitate the diffusion of specific ions across neuronal membranes. If large enough, this movement of charge creates currents that may change the membrane potential. Biophysical models of membrane potential assume the trans-membrane currents flow within an “equivalent electrical circuit” in which ion channels are represented by resistors arranged in parallel. The functions representing the trans-membrane currents mediated by channels are typically written using Ohm’s law. It is possible to describe channel-mediated currents by taking diffusion into consideration [1], but such formulations are not widely used in the literature. Here we present a model of membrane potential in which channel gating and current density are derived from first principles of thermodynamics, assuming that currents are produced by electrodiffusion. These models display properties that cannot be observed in conductance-based models, such as rectification of membrane currents. Guidelines for parameter estimation, and specific rules to adjust the model against experimental data, are presented along with examples of parameter regimes that yield representations of specific electrophysiological signatures with a biophysically sound baseline. Bifurcation analysis is used to describe transitions between qualitatively different behaviors of the model and link them to functionally relevant properties observable in neurons of different types. Network extensions are constructed using realistic synaptic input and local field potential oscillations to illustrate how networks may display potentially different responses to afferent input depending on the intrinsic properties of the participating neurons. The electrodiffusion formulation presented here constitutes a theoretical improvement over conductance-based models that may advance our current understanding of dynamical behavior in single cells and networks.

Predicting changes in neuronal excitability type in response to genetic manipulations of K+-channels

The way a neuron undergoes rest-spiking transitionsdetermines the type of excitability and the computationalproperties of a neuron. Such transitions are particularlyimportant in the motor system, specifically with respect tomotor-unit recruitment and gradation of force. If weregard the electrophysiological activity of a neuron as adynamical system, the rest-spiking transition can bethought of as a bifurcation. That is, a qualitative change inthe trajectories followed by the variables in the system.Recordings from Drosophila neurons show that the spik-ing activity of a neuron undergoes qualitative changes asoccurs after genetic manipulations that affect the popula-tion of potassium channels [1]. We developed a singlecompartment model of the dynamics of the identifiedmotor neuron MN5 from Drosophila based on publishedexperimental results [2]. In vivo, MN5 controls the dorsal-longitudinal fiight muscle, firing trains of action poten-tials with a frequency between 6 and 25 Hz depending onthe excitatory drive it receives. Bifurcation studies wereperformed to elucidate the changes in phase space as afunction of different biophysical parameters includinghalf activation potentials, gating charge, close-open ratesand number of membrane channels. Bifurcation analysisand simulations predict that the number of channels andthe half-activation potential for the delayed rectifiers andA-type potassium channels can explain changes in spikingbehavior resulting from genetic manipulations asreported in [1,2]. For instance, decreasing the half activa-tion potential for the delayed rectifier channel induces achange in bifurcation from saddle-node (no subthresholdoscillations before spiking) to Hopf (subthreshold oscilla-tions before sustained spikes). Biophysical parametersobtained from MN5 patch clamp recordings will be usedin the future to restrict the parameter space specifically forMN5. The theoretical results from this study can be testedusing targeted genetic manipulations of potassium chan-nels.

Passive current transfer in wildtype and genetically modified Drosophila motoneuron dendrites

As dendritic branching order increases, integration of elec-trical signals is increasingly influenced by dendritic geom-etry regardless of active membrane properties [1]. Studiesbased on current-transfer measures suggest that changesin input resistance can contribute to optimize transfer ofpostsynaptic currents [2]. Optimization occurs when thevoltage attenuation factor and input conductance are lin-early related independently of input location. Multi-com-partment passive models from detailed dendriticbranching structures of the Drosophila motoneuron,MN5, were constructed to start characterizing the relation-ship between dendritic geometry, signal propagation andspiking output in neurons. MN5 has a monopolar struc-ture, with a main neurite giving rise to the axon and dif-ferent highly branched dendritic subtrees. Current transferwas characterized as a function of axial resistance for dif-ferent morphological phenotypes as induced by differentgenetic manipulations. Experimental estimations of axialresistance in MN5 and in other neurons [3] cover a widerange of values (ca. 45–400 Ohms/cm). Our results fromwild type dendritic trees show a linear relationshipbetween input conductance and attenuation factor foraxial resistances in the lower range. However, optimiza-tion is lost when axial resistance is large (see Figure 1), butstill within physiological ranges. Nevertheless, when eachsubtree is considered in isolation, the optimization prin-ciple holds for a wide range of axial resistances, suggestingthat the dendritic structure in MN5 supports independentcomputation in separate subtrees. Furthermore, differentdendritic geometries can be induced by genetic manipula-tions of K

The role of the large-conductance calcium-dependent potassium channel, BK/Slowpoke, in shaping motor neuron firing during rhythmic activity

Rhythmic muscle contractions underlie a number of crucial motor behaviors, such as respiration and locomotion. The timing of contractions is determined by the intrinsic activity and synaptic interactions of neurons within what are called central pattern generating (CPG) networks [1,2]. In many systems, motor neurons (MNs) are not part of the classically-defined CPG. However, research suggests that ionic currents in MNs may shape the timing of the final motor output [3,4]. A lot of work has focused particularly on the role of potassium currents in shaping responsiveness and firing of MNs [3,5]. Large-conductance calcium-dependent potassium (BK) currents, encoded by members of the Slowpoke (Slo) gene family, can contribute to action potential repolarization, regulation of firing frequency and interspike interval, repetitive firing, and burst termination [6]. Mutations of Slo genes also lead to a variety of motor disturbances [6]. We developed a biophysical model of bursting activity in MNs to explore the circumstances under which a BK/Slo current expressed in MNs can shape the timing of motor output underlying locomotion. We identify mechanisms by which the BK/Slo current changes the bursting output of MNs, and describe the different behaviors that are observed for varying membrane densities of the underlying channel. We also present preliminary data consisting of electrophysiological recordings from larval Drosophila showing that the changes in motor output predicted by the model are indeed observed when genetic manipulations of Slo channel density (RNA interference constructs) are targeted to MNs [7]. Our results not only further understanding of the specific role of BK/Slo channels in MNs, but contribute more generally to the growing knowledge on the role intrinsic MN properties play in shaping rhythmic motor output.