A Comparison between Mouse, In Silico, and Robot Odor Plume Navigation Reveals Advantages of Mouse Odor Tracking.

Localization of odors is essential to animal survival, and thus animals are adept at odor navigation. In natural conditions animals encounter odor sources in which odor is carried by air flow varying in complexity. We sought to identify potential minimalist strategies that can effectively be used for odor-based navigation and asses their performance in an increasingly chaotic environment. To do so, we compared mouse, in silico model, and Arduino-based robot odor-localization behavior in a standardized odor landscape. Mouse performance remains robust in the presence of increased complexity, showing a shift in strategy towards faster movement with increased environmental complexity. Implementing simple binaral and temporal models of tropotaxis and klinotaxis, an in silico model and Arduino robot, in the same environment as the mice, are equally successful in locating the odor source within a plume of low complexity. However, performance of these algorithms significantly drops when the chaotic nature of the plume is increased. Additionally, both algorithm-driven systems show more successful performance when using a strictly binaral model at a larger sensor separation distance and more successful performance when using a temporal and binaral model when using a smaller sensor separation distance. This suggests that with an increasingly chaotic odor environment, mice rely on complex strategies that allow for robust odor localization that cannot be resolved by minimal algorithms that display robust performance at low levels of complexity. Thus, highlighting that an animal's ability to modulate behavior with environmental complexity is beneficial for odor localization.

Rotating waves in simple scalar excitable media: approximations and numerical solutions.

Rotating waves, in a two-dimensional annular region, are studied using a number of semi-analytical methods. For our kinetics, we use a simple one-variable phase model that arises as the normal form in the transition between excitability and oscillation at a saddle-node invariant circle (SNIC) bifurcation. After deriving asymptotic expressions for the scalar dispersion relationship, we use this to compare the approximations to a direct numerical simulation of the governing nonlinear partial differential equation. All of the approximation methods are based on writing the full solution [Formula: see text] as [Formula: see text] + "perturbation" terms where V is some function and [Formula: see text] is the radial phase shift. Finding an expression for the radial phase shift is the main aim of this paper. It is found that the total twist of the spiral is not a monotone function of the excitability. The largest twist occurs in the vicinity of the transition from excitable to oscillatory behavior.

On the human sensorimotor-cortex beta rhythm: sources and modeling.

Cortical oscillations in the beta band (13-35 Hz) are known to be modulated by the GABAergic agonist benzodiazepine. To investigate the mechanisms generating the approximately 20-Hz oscillations in the human cortex, we administered benzodiazepines to healthy adults and monitored cortical oscillatory activity by means of magnetoencephalography. Benzodiazepine increased the power and decreased the frequency of beta oscillations over rolandic areas. Minimum current estimates indicated the effect to take place around the hand area of the primary sensorimotor cortex. Given that previous research has identified sources of the beta rhythm in the motor cortex, our results suggest that these same motor-cortex beta sources are modulated by benzodiazepine. To explore the mechanisms underlying the increase in beta power with GABAergic inhibition, we simulated a conductance-based neuronal network comprising excitatory and inhibitory neurons. The model accounts for the increase in the beta power, the widening of the spectral peak, and the slowing down of the rhythms with benzodiazepines, implemented as an increase in GABAergic conductance. We found that an increase in IPSCs onto inhibitory neurons was more important for generating neuronal synchronization in the beta band than an increase in IPSCs onto excitatory pyramidal cells.

The effects of spike frequency adaptation and negative feedback on the synchronization of neural oscillators.

There are several different biophysical mechanisms for spike frequency adaptation observed in recordings from cortical neurons. The two most commonly used in modeling studies are a calcium-dependent potassium current I(ahp) and a slow voltage-dependent potassium current, I(m). We show that both of these have strong effects on the synchronization properties of excitatorily coupled neurons. Furthermore, we show that the reasons for these effects are different. We show through an analysis of some standard models, that the M-current adaptation alters the mechanism for repetitive firing, while the afterhyperpolarization adaptation works via shunting the incoming synapses. This latter mechanism applies with a network that has recurrent inhibition. The shunting behavior is captured in a simple two-variable reduced model that arises near certain types of bifurcations. A one-dimensional map is derived from the simplified model.

Model for olfactory discrimination and learning in Limax procerebrum incorporating oscillatory dynamics and wave propagation.

We extend our model of the procerebral (PC) lobe of Limax, which is comprised of a layer of coupled oscillators and a layer of memory neurons, each layer 4 rows by 20 columns, corresponding to the cell body layer (burster cells) and neuropil layer (nonburster cells) of the PC lobe. A gradient of connections in the layer of model burster cells induces periodic wave propagation, as measured in the PC lobe. We study odor representations in the biological PC lobe using the technique of Kimura and coworkers. Lucifer yellow injection into intact Limax after appetitive or aversive odor learning results in a band or patch of labeled cells in the PC lobe with the band long axis normal to the axis of wave propagation. Learning two odors yields two parallel bands of labeled PC cells. We introduce olfactory input to our model PC lobe such that each odor maximally activates a unique row of four cells which produces a short-term memory trace of odor stimulation. A winner-take-all synaptic competition enabled by collapse of the phase gradient during odor presentation produces a single short-term memory band for each odor. The short-term memory is converted to long-term memory if odor stimulation is followed by activation of an input pathway for the unconditioned stimulus (US) which presumably results in release of one or more neuromodulatory amines or peptides in the PC lobe.

Oscillations in a refractory neural net.

A functional differential equation that arises from the classic theory of neural networks is considered. As the length of the absolute refractory period is varied, there is, as shown here, a super-critical Hopf bifurcation. As the ratio of the refractory period to the time constant of the network increases, a novel relaxation oscillation occurs. Some approximations are made and the period of this oscillation is computed.

Inhibition-based rhythms: experimental and mathematical observations on network dynamics.

An increasingly large body of data exists which demonstrates that oscillations of frequency 12-80 Hz are a consequence of, or are inextricably linked to, the behaviour of inhibitory interneurons in the central nervous system. This frequency range covers the EEG bands beta 1 (12-20 Hz), beta 2 (20-30 Hz) and gamma (30-80 Hz). The pharmacological profile of both spontaneous and sensory-evoked EEG potentials reveals a very strong influence on these rhythms by drugs which have direct effects on GABA(A) receptor-mediated synaptic transmission (general anaesthetics, sedative/hypnotics) or indirect effects on inhibitory neuronal function (opiates, ketamine). In addition, a number of experimental models of, in particular, gamma-frequency oscillations, have revealed both common denominators for oscillation generation and function, and subtle differences in network dynamics between the different frequency ranges. Powerful computer and mathematical modelling techniques based around both clinical and experimental observations have recently provided invaluable insight into the behaviour of large networks of interconnected neurons. In particular, the mechanistic profile of oscillations generated as an emergent property of such networks, and the mathematical derivation of this complex phenomenon have much to contribute to our understanding of how and why neurons oscillate. This review will provide the reader with a brief outline of the basic properties of inhibition-based oscillations in the CNS by combining research from laboratory models, large-scale neuronal network simulations, and mathematical analysis.

Linearization of F-I curves by adaptation.

We show that negative feedback to highly nonlinear frequency-current (F-I) curves results in an effective linearization. (By highly nonlinear we mean that the slope at threshold is infinite or very steep.) We then apply this to a specific model for spiking neurons and show that the details of the adaptation mechanism do not affect the results. The crucial points are that the adaptation is slow compared to other processes and the unadapted F-I curve is highly nonlinear.

The analysis of synaptically generated traveling waves.

Mathematical and computational models for the propagation of activity in excitatorily coupled neurons are simulated and analyzed. The basic measurable quantity--velocity--is found for a wide class of models. Numerical bifurcation techniques, asymptotic analysis, and numerical simulations are used to show that there are distinct scaling laws for the velocity as a function of a variety of parameters. In particular, the obvious linear relationships between speed and spatial spread or synaptic decay rate are shown. More surprisingly, it is shown that the velocity scales as a power law with synaptic coupling strength and that the exponent is dependent only on the rising phase of the synapse.

Minimal model of oscillations and waves in the Limax olfactory lobe with tests of the model's predictive power.

Propagating waves are observed in the olfactory or procerebral (PC) lobe of the terrestrial mollusk, Limax maximus. Wave propagation is altered by cutting through the various layers of the PC lobe both parallel and transverse to the direction of wave propagation. We present a model for the PC lobe based on two layers of coupled cells. The top layer represents the cell layer of the PC lobe, and the bottom layer corresponds to the neuropil of the PC lobe. To get wave propagation, we induce a coupling gradient so that the most apical cells receive a greater input from neighbors than the basal cells. The top layer in the model is composed of oscillators coupled locally, whereas the bottom layer is comprised of oscillators with global coupling. Odor stimulation is represented by an increase in the strength of coupling between the two layers. This model allows us to explain a number of experimental observations: 1) the intact PC lobe exhibits regular propagating waves, which travel from the apical to the basal end; 2) there is a gradient in the local frequency of slices cut transverse to the axis of wave propagation, with apical slices oscillating faster than basal slices; 3) with partial cuts through the cell layer or the neuropil layer, the apical and basal ends remain tightly coupled; 4) removal of the neuropil layer does not prevent wave propagation in the cell layer; 5) odor stimulation causes the waves to collapse and the cells in the PC lobe oscillate synchronously; and 6) by allowing a single parameter to vary in the model, we capture the reversal of waves in low chloride medium.

Wave propagation mediated by GABAB synapse and rebound excitation in an inhibitory network: a reduced model approach.

A reduction method is used to analyze a spatially structured network model of inhibitory neurons. This network model displays wave propagation of postinhibitory rebound activity, which depends on GABAB synaptic interactions among the neurons. The reduced model allows explicit solutions for the wavefronts and their velocity as a function of various parameters, such as the synaptic coupling strength. These predictions are shown to agree well with the numerical simulations of the conductance-based biophysical model.

Propagating activity patterns in large-scale inhibitory neuronal networks.

The propagation of activity is studied in a spatially structured network model of gamma-aminobutyric acid-containing (GABAergic) neurons exhibiting postinhibitory rebound. In contrast to excitatory-coupled networks, recruitment spreads very slowly because cells fire only after the postsynaptic conductance decays, and with two possible propagation modes. If the connection strength decreases monotonically with distance (on-center), then propagation occurs in a discontinuous manner. If the self- and nearby connections are absent (off-center), propagation can proceed smoothly. Modest changes in the synaptic reversal potential can result in depolarization-mediated waves that are 25 times faster. Functional and developmental roles for these behaviors and implications for thalamic circuitry are suggested.

Type I membranes, phase resetting curves, and synchrony.

Type I membrane oscillators such as the Connor model (Connor et al. 1977) and the Morris-Lecar model (Morris and Lecar 1981) admit very low frequency oscillations near the critical applied current. Hansel et al. (1995) have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive. We use singular perturbation methods and averaging to show that this is a general property of Type I membrane models. We show in a limited sense that so called Type II resetting occurs with models that obtain rhythmicity via a Hopf bifurcation. We also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions.

Activation and repolarization patterns are governed by different structural characteristics of ventricular myocardium: experimental study with voltage-sensitive dyes and numerical simulations.

INTRODUCTION: Substantial progress has been made in our understanding of transmural activation across ventricular muscle through studies of excitation patterns and potential distributions. In contrast, repolarization sequences are poorly understood because of experimental difficulties in mapping action potential durations (APDs) using extracellular electrodes. METHODS AND RESULTS: Langendorff-perfused guinea pig hearts and isolated coronary-perfused left ventricular sheet preparations were stained with the voltage-sensitive dye RH-421 and optical APs were recorded with a photodiode array. Epicardial maps were constructed using a triangulation method applied to matrices of activation and repolarization times determined from (dF/dt)max and (d2F/dt2)max' respectively. Numerical simulations were carried out based on: (1) a modified Luo-Rudy model; (2) the three-dimensional architecture of ventricular fibers; and (3) the intrinsic spatial distribution of APDs. In ventricular sheets, epicardial stimulation elicited elliptical activation patterns with the major axis aligned with the longitudinal axis of epicardial fibers. When the pacing electrode was progressively inserted from epicardium to endocardium, the major axes rotated gradually, clockwise by 45 degrees, and the eccentricity decreased from 2 to 1.14. Repolarization showed a relatively uniform pattern, independent of pacing site, beginning at the apex and spreading to the base. CONCLUSION: In experiments and simulations, the helical rotation of epicardial excitation isochrones caused by pacing at increasing depth in the myocardium correlated with the helical three-dimensional architecture of ventricular fibers. In contrast, repolarization was independent of the activation sequence and was mainly guided by spatial differences in APDs between apex and base.

Rotary DNA motors.

Many molecular motors move unidirectionally along a DNA strand powered by nucleotide hydrolysis. These motors are multimeric ATPases with more than one hydrolysis site. We present here a model for how these motors generate the requisite force to process along their DNA track. This novel mechanism for force generation is based on a fluctuating electrostatic field driven by nucleotide hydrolysis. We apply the principle to explain the motion of certain DNA helicases and the portal protein, the motor that bacteriophages use to pump the genome into their capsids. The motor can reverse its direction without reversing the polarity of its electrostatic field, that is, without major structural modifications of the protein. We also show that the motor can be driven by an ion gradient; thus the mechanism may apply as well to the bacterial flagellar motor and to ATP synthase.

On the origin and dynamics of the vasomotion of small arteries.

A system of differential equations describing stationary vasomotion is formulated. It incorporates the ionic transports, cell-membrane potential, muscle contraction of the vessel smooth muscle cells, and the mechanics of a thick-walled cylinder. It is shown that the interaction of Ca2+ and K+ fluxes mediated by voltage-gated and voltage-calcium-gated channels, respectively, brings about periodicity of those transports. This results on a time-periodic cytoplasmic calcium concentration, myosin light chains phosphorylation, and crossbridges formation with the attending muscle stress. The vessel's transmural pressure determines a hoop stress. The resultant hoop, elastic, and muscle stresses determine the rate of change of the vessel's diameter: vasomotion. The model results agree with the experimental observations. The sensitivity of the vasomotion's dependence on parameter values and its significance to experimental protocols are examined. Further, it is hypothesized that the dependence of calcium-channel openings on voltage is shifted by changes on transmural pressure. Thus, Harder's experimental results are reproduced, among them the decreasing of vessel diameter with increasing pressure. Those behaviors are associated with a pattern of change of the singularities of the system of equations describing the model. This suggests a functional relationship on the interactions of Ca2+ and K+ fluxes responsible for the myogenic response; it may not result from a single molecular mechanism. The model is constructed so that additional experimental information can be readily incorporated.

Dynamics of single-motor molecules: the thermal ratchet model.

We present a model for single-motor molecules--myosin, dynein, or kinesin--that is powered either by thermal fluctuations or by conformational change. In the thermally driven model, the cross-bridge fluctuates about its equilibrium position against an elastic restoring force. The attachment and detachment of the cross-bridge are determined by modeling the electrostatic attraction between the cross-bridge and the fiber binding sites, so that binding depends on the strain in the cross-bridge and its velocity with respect to the fiber. The model correctly predicts the empirical force-velocity characteristics for populations of motor molecules. For a single motor, the apparent cross-bridge step size per ATP hydrolysis depends nonlinearly on the load. When the elastic energy driving the cross-bridge is generated by a conformational change, the velocity and duty cycle are much larger than is observed experimentally for myosin.