Connections of the olfactory bulb in the piranha (Serrasalmus nattereri)

Summary The connections of the olfactory bulb were studied in the piranha using the Nauta and horseradish-peroxidase methods. Three olfactory tracts project to seven terminal fields in the telencephalon and one in the diencephalon, all of them bilaterally. The contralateral olfactory bulb also receives a small input. All contralateral projections decussate in the anterior commissure and are relatively weak compared to the ipsilateral projections. HRP-containing cells were found in all of the ipsilateral telencephalic aggregates receiving an olfactory tract projection; the contralateral side was free of labeled cell bodies. Although only about one fourth of the entire telencephalon receives a direct olfactory input, the high degree of differentiation of the olfactory system suggests that the piranha depends substantially on the sense of olfaction and that this species may be a good model for further studies on olfactory mechanisms.     

Divisive Gain Modulation with Dynamic Stimuli in Integrate-and-Fire Neurons

The modulation of the sensitivity, or gain, of neural responses to input is an important component of neural computation. It has been shown that divisive gain modulation of neural responses can result from a stochastic shunting from balanced (mixed excitation and inhibition) background activity. This gain control scheme was developed and explored with static inputs, where the membrane and spike train statistics were stationary in time. However, input statistics, such as the firing rates of pre-synaptic neurons, are often dynamic, varying on timescales comparable to typical membrane time constants. Using a population density approach for integrate-and-fire neurons with dynamic and temporally rich inputs, we find that the same fluctuation-induced divisive gain modulation is operative for dynamic inputs driving nonequilibrium responses. Moreover, the degree of divisive scaling of the dynamic response is quantitatively the same as the steady-state responses—thus, gain modulation via balanced conductance fluctuations generalizes in a straight-forward way to a dynamic setting.     

Effects of Time-Dependent Stimuli in a Competitive Neural Network Model of Perceptual Rivalry

We analyze a competitive neural network model of perceptual rivalry that receives time-varying inputs. Time-dependence of inputs can be discrete or smooth. Spike frequency adaptation provides negative feedback that generates network oscillations when inputs are constant in time. Oscillations that resemble perceptual rivalry involve only one population being “ON” at a time, which represents the dominance of a single percept at a time. As shown in Laing and Chow (J. Comput. Neurosci. 12(1):39–53, 2002), for sufficiently high contrast, one can derive relationships between dominance times and contrast that agree with Levelt’s propositions (Levelt in On binocular rivalry, 1965). Time-dependent stimuli give rise to novel network oscillations where both, one, or neither populations are “ON” at any given time. When a single population receives an interrupted stimulus, the fundamental mode of behavior we find is phase-locking, where the temporally driven population locks its state to the stimulus. Other behaviors are analyzed as bifurcations from this forced oscillation, using fast/slow analysis that exploits the slow timescale of adaptation. When both populations receive time-varying input, we find mixtures of fusion and sole population dominance, and we partition parameter space into particular oscillation types. Finally, when a single population’s input contrast is smoothly varied in time, 1:n mode-locked states arise through period-adding bifurcations beyond phase-locking. Our results provide several testable predictions for future psychophysical experiments on perceptual rivalry.     

Stimulus and network dynamics collide in a ratiometric model of the antennal lobe macroglomerular complex

Time is considered to be an important encoding dimension in olfaction, as neural populations generate odour-specific spatiotemporal responses to constant stimuli. However, during pheromone mediated anemotactic search insects must discriminate specific ratios of blend components from rapidly time varying input. The dynamics intrinsic to olfactory processing and those of naturalistic stimuli can therefore potentially collide, thereby confounding ratiometric information. In this paper we use a computational model of the macroglomerular complex of the insect antennal lobe to study the impact on ratiometric information of this potential collision between network and stimulus dynamics. We show that the model exhibits two different dynamical regimes depending upon the connectivity pattern between inhibitory interneurons (that we refer to as fixed point attractor and limit cycle attractor), which both generate ratio-specific trajectories in the projection neuron output population that are reminiscent of temporal patterning and periodic hyperpolarisation observed in olfactory antennal lobe neurons. We compare the performance of the two corresponding population codes for reporting ratiometric blend information to higher centres of the insect brain. Our key finding is that whilst the dynamically rich limit cycle attractor spatiotemporal code is faster and more efficient in transmitting blend information under certain conditions it is also more prone to interference between network and stimulus dynamics, thus degrading ratiometric information under naturalistic input conditions. Our results suggest that rich intrinsically generated network dynamics can provide a powerful means of encoding multidimensional stimuli with high accuracy and efficiency, but only when isolated from stimulus dynamics. This interference between temporal dynamics of the stimulus and temporal patterns of neural activity constitutes a real challenge that must be successfully solved by the nervous system when faced with naturalistic input.     

DNA Polymorphism in a Subdivided Population: The Expected Number of Segregating Sites in the Two-Subpopulation Model

Using the two subpopulation model, the expected numbers of segregating sites in a number of DNA sequences randomly sampled from a subdivided population were examined for several types of population subdivisions. It is shown that, in the case where the pattern of migration is symmetrical such as the finite island model, the expected number of segregating sites is independent of the migration rate when two or three DNA sequences are randomly sampled from the same subpopulation, but depends on the migration rate when more than three DNA sequences are sampled. It is also shown that the population subdivision can increase the amount of DNA polymorphism even in a subpopulation in some cases.     

Exact analytical results for integrate-and-fire neurons driven by excitatory shot noise

A neuron receives input from other neurons via electrical pulses, so-called spikes. The pulse-like nature of the input is frequently neglected in analytical studies; instead, the input is usually approximated to be Gaussian. Recent experimental studies have shown, however, that an assumption underlying this approximation is often not met: Individual presynaptic spikes can have a significant effect on a neuron’s dynamics. It is thus desirable to explicitly account for the pulse-like nature of neural input, i.e. consider neurons driven by a shot noise – a long-standing problem that is mathematically challenging. In this work, we exploit the fact that excitatory shot noise with exponentially distributed weights can be obtained as a limit case of dichotomous noise, a Markovian two-state process. This allows us to obtain novel exact expressions for the stationary voltage density and the moments of the interspike-interval density of general integrate-and-fire neurons driven by such an input. For the special case of leaky integrate-and-fire neurons, we also give expressions for the power spectrum and the linear response to a signal. We verify and illustrate our expressions by comparison to simulations of leaky-, quadratic- and exponential integrate-and-fire neurons.     

Synaptic depression increases the selectivity of a neuron to its preferred pattern and binarizes the neural code

The preferred pattern of a neuron is defined here by the set of features detected by its excitatory inputs. It is shown that the Leaky integrate-and-fire (LIF) model of a neuron has a poor selectivity to its preferred pattern. Its response is determined by the total current injected by input spike trains. Thus, a few inputs with a high activity (an incomplete pattern) can elicit the same response as many inputs (a complete pattern) with a weak activity. A theoretical model of depressing synapse with linear recovery is proposed which eliminates this problem. Using this model, the time-averaged current injected in the soma by a spike train becomes independent on its frequency. The neural code thus becomes binary, and the response strength of the target neuron depends only on the number of active inputs. Simulations show that a biological model of strong synaptic depression has effects similar to those of the ideal linear model. The best selectivity is obtained with long somatic decay time constants (>50 ms) and with depression recovery time constants larger or equal to the somatic decay time constant. Thus, by eliminating information carried in the input firing rate, a neuron can improve its pattern recognition performance.     

The effects of reversibility and noise on stochastic phosphorylation cycles and cascades

The phosphorylation-dephosphorylation cycle is a common motif in cellular signaling networks. Previous work has revealed that, when driven by a noisy input signal, these cycles may exhibit bistable behavior. Here, a recently introduced theorem on network bistability is applied to prove that the existence of bistability is dependent on the stochastic nature of the system. Furthermore, the thermodynamics of simple cycles and cascades is investigated in the stochastic setting. Because these cycles are driven by the ATP hydrolysis potential, they may operate far from equilibrium. It is shown that sufficient high ATP hydrolysis potential is necessary for the existence of a bistable steady state. For the single-cycle system, the ensemble average behavior follows the ultrasensitive response expected from analysis of the corresponding deterministic system, but with significant fluctuations. For the two-cycle cascade, the average behavior begins to deviate from the expected response of the deterministic system. Examination of a two-cycle cascade reveals that the bistable steady state may be either propagated or abolished along a cascade, depending on the parameters chosen. Likewise, the variance in the response can be maximized or minimized by tuning the number of enzymes in the second cycle.     

Effects of conduction delays on the existence and stability of one to one phase locking between two pulse-coupled oscillators

Gamma oscillations can synchronize with near zero phase lag over multiple cortical regions and between hemispheres, and between two distal sites in hippocampal slices. How synchronization can take place over long distances in a stable manner is considered an open question. The phase resetting curve (PRC) keeps track of how much an input advances or delays the next spike, depending upon where in the cycle it is received. We use PRCs under the assumption of pulsatile coupling to derive existence and stability criteria for 1:1 phase-locking that arises via bidirectional pulse coupling of two limit cycle oscillators with a conduction delay of any duration for any 1:1 firing pattern. The coupling can be strong as long as the effect of one input dissipates before the next input is received. We show the form that the generic synchronous and anti-phase solutions take in a system of two identical, identically pulse-coupled oscillators with identical delays. The stability criterion has a simple form that depends only on the slopes of the PRCs at the phases at which inputs are received and on the number of cycles required to complete the delayed feedback loop. The number of cycles required to complete the delayed feedback loop depends upon both the value of the delay and the firing pattern. We successfully tested the predictions of our methods on networks of model neurons. The criteria can easily be extended to include the effect of an input on the cycle after the one in which it is received.     

The rodent accessory olfactory system

The accessory olfactory system contributes to the perception of chemical stimuli in the environment. This review summarizes the structure of the accessory olfactory system, the stimuli that activate it, and the responses elicited in the receptor cells and in the brain. The accessory olfactory system consists of a sensory organ, the vomeronasal organ, and its central projection areas: the accessory olfactory bulb, which is connected to the amygdala and hypothalamus, and also to the cortex. In the vomeronasal organ, several receptors—in contrast to the main olfactory receptors—are sensitive to volatile or nonvolatile molecules. In a similar manner to the main olfactory epithelium, the vomeronasal organ is sensitive to common odorants and pheromones. Each accessory olfactory bulb receives input from the ipsilateral vomeronasal organ, but its activity is modulated by centrifugal projections arising from other brain areas. The processing of vomeronasal stimuli in the amygdala involves contributions from the main olfactory system, and results in long-lasting responses that may be related to the activation of the hypothalamic–hypophyseal axis over a prolonged timeframe. Different brain areas receive inputs from both the main and the accessory olfactory systems, possibly merging the stimulation of the two sensory organs to originate a more complex and integrated chemosensory perception.     

Gamma neurons mediate dopaminergic input during aversive olfactory memory formation in Drosophila

Mushroom body (MB)-dependent olfactory learning in Drosophila provides a powerful model to investigate memory mechanisms. MBs integrate olfactory conditioned stimulus (CS) inputs with neuromodulatory reinforcement (unconditioned stimuli, US), which for aversive learning is thought to rely on dopaminergic (DA) signaling to DopR, a D1-like dopamine receptor expressed in MBs. A wealth of evidence suggests the conclusion that parallel and independent signaling occurs downstream of DopR within two MB neuron cell types, with each supporting half of memory performance. For instance, expression of the Rutabaga (Rut) adenylyl cyclase in γ neurons is sufficient to restore normal learning to rut mutants, whereas expression of Neurofibromatosis 1 (NF1) in α/β neurons is sufficient to rescue NF1 mutants. DopR mutations are the only case where memory performance is fully eliminated, consistent with the hypothesis that DopR receives the US inputs for both γ and α/β lobe traces. We demonstrate, however, that DopR expression in γ neurons is sufficient to fully support short- and long-term memory. We argue that DA-mediated CS-US association is formed in γ neurons followed by communication between γ and α/β neurons to drive consolidation.     

Infant stepping: a window to the behaviour of the human pattern generator for walking

The aim of this paper is to provide evidence, both published and new, to support the notion that human infants are particularly good subjects for the study of the pattern generator for walking. We and others have shown that stepping can be initiated by sensory input from the legs or by general heightened excitability of the infant. New results are presented here to suggest that weight support through the feet and rapid extension of the legs are important proprioceptive inputs to initiate stepping. Our previous work has shown that infants can step at many different speeds when supported on a treadmill. The step cycle duration shortens as the speed increases, with the changes coming largely from the stance phase, just as in most other terrestrial animals. Moreover, we have shown that infants will step in all directions. Regardless of the direction of stepping, the step cycle changes in the same way with walking speed, suggesting the circuitry that controls different directions of walking share common elements. We have also shown that infant stepping is highly organized. Sensory inputs, whether proprioceptive or touch, are gated in a functional way so that only important sensory inputs generate a response. For example, touch to the lateral surface of the foot elicits a response only in sideways walking, and only in the leading limb. New data is presented here to show that the pattern generators from each limb can operate somewhat independently. On a split-belt treadmill with the 2 belts running at different speeds or in different directions, the legs showed considerable independence in behaviour. Yet, the pattern generators on each side interact to ensure that swing phase does not occur at the same time. These studies have provided insight into the organization of the pattern generator for walking in humans. It will be interesting in the future to study how maturation of the descending tracts changes walking behaviour to allow independent bipedal walking.     

The stabilizing effect of a random environment

It is shown that the lottery competition model permits coexistence in a stochastic environment, but not in a constant environment. Conditions for coexistence and competitive exclusion are determined. Analysis of these conditions shows that the essential requirements for coexistence are overlapping generations and fluctuating birth rates which ensure that each species has periods when it is increasing. It is found that a species may persist provided only that it is favored sufficiently by the environment during favorable periods independently of the extent to which the other species is favored during its favorable periods.Coexistence is defined in terms of the stochastic boundedness criterion for species persistence. Using the lottery model as an example this criterion is justified and compared with other persistence criteria. Properties of the stationary distribution of population density are determined for an interesting limiting case of the lottery model and these are related to stochastic boundedness. An attempt is then made to relate stochastic boundedness for infinite population models to the behavior of finite population models.     

Hysteresis Can Grant Fitness in Stochastically Varying Environment

Although the existence of multiple stable phenotypes of living organisms enables random switching between phenotypes as well as non-random history dependent switching called hysteresis, only random switching has been considered in prior experimental and theoretical models of adaptation to variable environments. This work considers the possibility that hysteresis may also evolve together with random phenotype switching to maximize population growth. In addition to allowing the possibility that switching rates between different phenotypes may depend not only on a continuous environmental input variable, but also on the phenotype itself, the present work considers an opportunity cost of the switching events. This opportunity cost arises as a result of a lag phase experimentally observed after phenotype switching and stochastic behavior of the environmental input. It is shown that stochastic environmental variation results in maximal asymptotic growth rate when organisms display hysteresis for sufficiently slowly varying environmental input. At the same time, sinusoidal input does not cause evolution of memory suggesting that the connection between the lag phase, stochastic environmental variation and evolution of hysteresis is a result of a stochastic resonance type phenomenon.     

Size-Independent Differences between the Mean of Discrete Stochastic Systems and the Corresponding Continuous Deterministic Systems

In this paper, it is shown that for a class of reaction networks, the discrete stochastic nature of the reacting species and reactions results in qualitative and quantitative differences between the mean of exact stochastic simulations and the prediction of the corresponding deterministic system. The differences are independent of the number of molecules of each species in the system under consideration. These reaction networks are open systems of chemical reactions with no zero-order reaction rates. They are characterized by at least two stationary points, one of which is a nonzero stable point, and one unstable trivial solution (stability based on a linear stability analysis of the deterministic system). Starting from a nonzero initial condition, the deterministic system never reaches the zero stationary point due to its unstable nature. In contrast, the result presented here proves that this zero-state is a stable stationary state for the discrete stochastic system, and other finite states have zero probability of existence at large times. This result generalizes previous theoretical studies and simulations of specific systems and provides a theoretical basis for analyzing a class of systems that exhibit such inconsistent behavior. This result has implications in the simulation of infection, apoptosis, and population kinetics, as it can be shown that for certain models the stochastic simulations will always yield different predictions for the mean behavior than the deterministic simulations.     

Gene Genealogy and Variance of Interpopulational Nucleotide Differences

A mathematical theory is developed for computing the probability that m genes sampled from one population (species) and n genes sampled from another are derived from l genes that existed at the time of population splitting. The expected time of divergence between the two most closely related genes sampled from two different populations and the time of divergence (coalescence) of all genes sampled are studied by using this theory. It is shown that the time of divergence between the two most closely related genes can be used as an approximate estimate of the time of population splitting (T) only when T identical to t/(2N) is small, where t and N are the number of generations and the effective population size, respectively. The variance of Nei and Li's estimate (d) of the number of net nucleotide differences between two populations is also studied. It is shown that the standard error (Sd) of d is larger than the mean when T is small (T much less than 1). In this case, Sd is reduced considerably by increasing sample size. When T is large (T greater than 1), however, a large proportion of the variance of d is caused by stochastic factors, and increase in the sample size does not help to reduce Sd. To reduce the stochastic variance of d, one must use data from many independent unlinked gene loci.     

Activity-induced remodeling of olfactory bulb microcircuits revealed by monosynaptic tracing

The continued addition of new neurons to mature olfactory circuits represents a remarkable mode of cellular and structural brain plasticity. However, the anatomical configuration of newly established circuits, the types and numbers of neurons that form new synaptic connections, and the effect of sensory experience on synaptic connectivity in the olfactory bulb remain poorly understood. Using in vivo electroporation and monosynaptic tracing, we show that postnatal-born granule cells form synaptic connections with centrifugal inputs and mitral/tufted cells in the mouse olfactory bulb. In addition, newly born granule cells receive extensive input from local inhibitory short axon cells, a poorly understood cell population. The connectivity of short axon cells shows clustered organization, and their synaptic input onto newborn granule cells dramatically and selectively expands with odor stimulation. Our findings suggest that sensory experience promotes the synaptic integration of new neurons into cell type-specific olfactory circuits.     

The response of cortical neurons to in vivo-like input current: theory and experiment: II. Time-varying and spatially distributed inputs

The response of a population of neurons to time-varying synaptic inputs can show a rich phenomenology, hardly predictable from the dynamical properties of the membrane’s inherent time constants. For example, a network of neurons in a state of spontaneous activity can respond significantly more rapidly than each single neuron taken individually. Under the assumption that the statistics of the synaptic input is the same for a population of similarly behaving neurons (mean field approximation), it is possible to greatly simplify the study of neural circuits, both in the case in which the statistics of the input are stationary (reviewed in La Camera et al. in Biol Cybern, 2008) and in the case in which they are time varying and unevenly distributed over the dendritic tree. Here, we review theoretical and experimental results on the single-neuron properties that are relevant for the dynamical collective behavior of a population of neurons. We focus on the response of integrate-and-fire neurons and real cortical neurons to long-lasting, noisy, in vivo-like stationary inputs and show how the theory can predict the observed rhythmic activity of cultures of neurons. We then show how cortical neurons adapt on multiple time scales in response to input with stationary statistics in vitro. Next, we review how it is possible to study the general response properties of a neural circuit to time-varying inputs by estimating the response of single neurons to noisy sinusoidal currents. Finally, we address the dendrite–soma interactions in cortical neurons leading to gain modulation and spike bursts, and show how these effects can be captured by a two-compartment integrate-and-fire neuron. Most of the experimental results reviewed in this article have been successfully reproduced by simple integrate-and-fire model neurons.