Roles of ionic currents in lamprey CpG neurons: a modeling study

The spinal network underlying locomotion in the lamprey consists of a core network of glutamatergic and glycinergic interneurons, previously studied experimentally and through mathematical modeling. We present a new and more detailed computational model of lamprey locomotor network neurons, based primarily on detailed electrophysiological measurements and incorporating new experimental findings. The model uses a Hodgkin-Huxley-like formalism and consists of 86 membrane compartments containing 12 types of ion currents. One of the goals was to introduce a fast, transient potassium current (K(t)) and two sodium-dependent potassium currents, one faster (K(NaF)) and one slower (K(NaS)), in the model. Not only has the model lent support to the interpretation of experimental results but it has also provided predictions for further experimental analysis of single-network neurons. For example, K(t) was shown to be one critical factor for controlling action potential duration. In addition, the model has proved helpful in investigating the possible influence of the slow afterhyperpolarization on repetitive firing during ongoing activation. In particular, the balance between the simulated slow sodium-dependent and calcium-dependent potassium currents has been explored, as well as the possible involvement of dendritic conductances.

Clustering of stored memories in an attractor network with local competition

In this paper we study an attractor network with units that compete locally for activation and we prove that a reduced version of it has fixpoint dynamics. An analysis, complemented by simulation experiments, of the local characteristics of the network's attractors with respect to a parameter controlling the intensity of the local competition is performed. We find that the attractors are hierarchically clustered when the parameter of the local competition is changed.

A hemicord locomotor network of excitatory interneurons: a simulation study

Locomotor burst generation is simulated using a full-scale network model of the unilateral excitatory interneuronal population. Earlier small-scale models predicted that a population of excitatory neurons would be sufficient to produce burst activity, and this has recently been experimentally confirmed. Here we simulate the hemicord activity induced under various experimental conditions, including pharmacological activation by NMDA and AMPA as well as electrical stimulation. The model network comprises a realistic number of cells and synaptic connectivity patterns. Using similar distributions of cellular and synaptic parameters, as have been estimated experimentally, a large variation in dynamic characteristics like firing rates, burst, and cycle durations were seen in single cells. On the network level an overall rhythm was generated because the synaptic interactions cause partial synchronization within the population. This network rhythm not only emerged despite the distributed cellular parameters but relied on this variability, in particular, in reproducing variations of the activity during the cycle and showing recruitment in interneuronal populations. A slow rhythm (0.4-2 Hz) can be induced by tonic activation of NMDA-sensitive channels, which are voltage dependent and generate depolarizing plateaus. The rhythm emerges through a synchronization of bursts of the individual neurons. A fast rhythm (4-12 Hz), induced by AMPA, relies on spike synchronization within the population, and each burst is composed of single spikes produced by different neurons. The dynamic range of the fast rhythm is limited by the ability of the network to synchronize oscillations and depends on the strength of synaptic connections and the duration of the slow after hyperpolarization. The model network also produces prolonged bouts of rhythmic activity in response to brief electrical activations, as seen experimentally. The mutual excitation can sustain long-lasting activity for a realistic set of synaptic parameters. The bout duration depends on the strength of excitatory synaptic connections, the level of persistent depolarization, and the influx of Ca(2+) ions and activation of Ca(2+)-dependent K(+) current.

A mathematical model of the mitochondrial NADH shuttles and anaplerosis in the pancreatic beta-cell

The pancreatic beta-cells respond to an increased glycolytic flux by secreting insulin. The signal propagation goes via mitochondrial metabolism, which relays the signal to different routes. One route is an increased ATP production that, via ATP-sensitive K(+) (K(ATP)) channels, modulates the cell membrane potential to allow calcium influx, which triggers insulin secretion. There is also at least one other "amplifying" route whose nature is debated; possible candidates are cytosolic NADPH production or malonyl-CoA production. We have used mathematical modeling to analyze this relay system. The model comprises the mitochondrial NADH shuttles and the mitochondrial metabolism. We found robust signaling toward ATP, malonyl-CoA, and NADPH production. The signal toward NADPH production was particularly strong. Furthermore, the model reproduced the experimental findings that blocking the NADH shuttles attenuates the signaling to ATP production while retaining the rate of glucose oxidation (Eto K, Tsubamoto Y, Terauchi Y, Sugiyama T, Kishimoto T, Takahashi N, Yamauchi N, Kubota N, Murayama S, Aizawa T, Akanuma Y, Aizawa S, Kasai H, Yazaki Y, Kadowaki T. Science 283: 981-985, 1999) and provides an explanation for this apparent paradox. The model also predicts that the mitochondrial malate dehydrogenase reaction may proceed backward, toward malate production, if the activity of malic enzyme is sufficiently high. An increased fatty acid oxidation rate was found to attenuate the signaling strengths. This theoretical study has implications for our understanding of both the healthy and the diabetic beta-cell.

Modeling a vertebrate motor system: pattern generation, steering and control of body orientation

The lamprey is one of the few vertebrates in which the neural control system for goal-directed locomotion including steering and control of body orientation is well described at a cellular level. In this report we review the modeling of the central pattern-generating network, which has been carried out based on detailed experimentation. In the same way the modeling of the control system for steering and control of body orientation is reviewed, including neuromechanical simulations and robotic devices.

Attractor dynamics in a modular network model of neocortex

Starting from the hypothesis that the mammalian neocortex to a first approximation functions as an associative memory of the attractor network type, we formulate a quantitative computational model of neocortical layers 2/3. The model employs biophysically detailed multi-compartmental model neurons with conductance based synapses and includes pyramidal cells and two types of inhibitory interneurons, i.e., regular spiking non-pyramidal cells and basket cells. The simulated network has a minicolumnar as well as a hypercolumnar modular structure and we propose that minicolumns rather than single cells are the basic computational units in neocortex. The minicolumns are represented in full scale and synaptic input to the different types of model neurons is carefully matched to reproduce experimentally measured values and to allow a quantitative reproduction of single cell recordings. Several key phenomena seen experimentally in vitro and in vivo appear as emergent features of this model. It exhibits a robust and fast attractor dynamics with pattern completion and pattern rivalry and it suggests an explanation for the so-called attentional blink phenomenon. During assembly dynamics, the model faithfully reproduces several features of local UP states, as they have been experimentally observed in vitro, as well as oscillatory behavior similar to that observed in the neocortex.

Towards cortex sized artificial neural systems

We propose, implement, and discuss an abstract model of the mammalian neocortex. This model is instantiated with a sparse recurrently connected neural network that has spiking leaky integrator units and continuous Hebbian learning. First we study the structure, modularization, and size of neocortex, and then we describe a generic computational model of the cortical circuitry. A characterizing feature of the model is that it is based on the modularization of neocortex into hypercolumns and minicolumns. Both a floating- and fixed-point arithmetic implementation of the model are presented along with simulation results. We conclude that an implementation on a cluster computer is not communication but computation bounded. A mouse and rat cortex sized version of our model executes in 44% and 23% of real-time respectively. Further, an instance of the model with 1.6 x 10(6) units and 2 x 10(11) connections performed noise reduction and pattern completion. These implementations represent the current frontier of large-scale abstract neural network simulations in terms of network size and running speed.

Biophysically detailed modelling of microcircuits and beyond

Realistic bottom-up modelling has been seminal to understanding which properties of microcircuits control their dynamic behaviour, such as the locomotor rhythms generated by central pattern generators. In this article of the TINS Microcircuits Special Feature, we review recent modelling work on the leech-heartbeat and lamprey-swimming pattern generators as examples. Top-down mathematical modelling also has an important role in analyzing microcircuit properties but it has not always been easy to reconcile results from the two modelling approaches. Most realistic microcircuit models are relatively simple and need to be made more detailed to represent complex processes more accurately. We review methods to add neuromechanical feedback, biochemical pathways or full dendritic morphologies to microcircuit models. Finally, we consider the advantages and challenges of full-scale simulation of networks of microcircuits.

A mathematical model of the Pyrosequencing reaction system

The Pyrosequencing technology is a newly developed DNA sequencing method that monitors DNA nucleotide incorporation in real-time. A set of coupled enzymatic reactions, together with bioluminescence, detects incorporated nucleotides in the form of light pulses, yielding a characteristic light profile. In this study, a biochemical model of the Pyrosequencing reaction system is suggested and implemented. The model is constructed utilizing an assumption of irreversible Michaelis-Menten rate equations and a constant incorporation efficiency. The kinetic parameters are studied and values are chosen to obtain as reliable simulation results as possible. The results presented here show strong resemblance with real experiments. The model is able to capture the dynamics of a single light pulse with great accuracy, as well as the overall characteristics of a whole pyrogram trade mark. The plus- and minus-shift effects observed in experiments are successfully reconstructed by two constant efficiency factors. Furthermore, pulse broadening can partly be explained by apyrase inhibition and successive dilution.

The cortex as a central pattern generator

Vertebrate spinal cord and brainstem central pattern generator (CPG) circuits share profound similarities with neocortical circuits. CPGs can produce meaningful functional output in the absence of sensory inputs. Neocortical circuits could be considered analogous to CPGs as they have rich spontaneous dynamics that, similar to CPGs, are powerfully modulated or engaged by sensory inputs, but can also generate output in their absence. We find compelling evidence for this argument at the anatomical, biophysical, developmental, dynamic and pathological levels of analysis. Although it is possible that cortical circuits are particularly plastic types of CPG ('learning CPGs'), we argue that present knowledge about CPGs is likely to foretell the basic principles of the organization and dynamic function of cortical circuits.

A working memory model based on fast Hebbian learning

Recent models of the oculomotor delayed response task have been based on the assumption that working memory is stored as a persistent activity state (a 'bump' state). The delay activity is maintained by a finely tuned synaptic weight matrix producing a line attractor. Here we present an alternative hypothesis, that fast Hebbian synaptic plasticity is the mechanism underlying working memory. A computational model demonstrates a working memory function that is more resistant to distractors and network inhomogeneity compared to previous models, and that is also capable of storing multiple memories.

A model of phosphofructokinase and glycolytic oscillations in the pancreatic beta-cell

We have constructed a model of the upper part of the glycolysis in the pancreatic beta-cell. The model comprises the enzymatic reactions from glucokinase to glyceraldehyde-3-phosphate dehydrogenase (GAPD). Our results show, for a substantial part of the parameter space, an oscillatory behavior of the glycolysis for a large range of glucose concentrations. We show how the occurrence of oscillations depends on glucokinase, aldolase and/or GAPD activities, and how the oscillation period depends on the phosphofructokinase activity. We propose that the ratio of glucokinase and aldolase and/or GAPD activities are adequate as characteristics of the glucose responsiveness, rather than only the glucokinase activity. We also propose that the rapid equilibrium between different oligomeric forms of phosphofructokinase may reduce the oscillation period sensitivity to phosphofructokinase activity. Methodologically, we show that a satisfying description of phosphofructokinase kinetics can be achieved using the irreversible Hill equation with allosteric modifiers. We emphasize the use of parameter ranges rather than fixed values, and the use of operationally well-defined parameters in order for this methodology to be feasible. The theoretical results presented in this study apply to the study of insulin secretion mechanisms, since glycolytic oscillations have been proposed as a cause of oscillations in the ATP/ADP ratio which is linked to insulin secretion.

A Bayesian attractor network with incremental learning

A realtime online learning system with capacity limits needs to gradually forget old information in order to avoid catastrophic forgetting. This can be achieved by allowing new information to overwrite old, as in a so-called palimpsest memory. This paper describes an incremental learning rule based on the Bayesian confidence propagation neural network that has palimpsest properties when employed in an attractor neural network. The network does not suffer from catastrophic forgetting, has a capacity dependent on the learning time constant and exhibits faster convergence for newer patterns.

Mechanisms for lateral turns in lamprey in response to descending unilateral commands: a modeling study

Straight locomotion in the lamprey is, at the segmental level, characterized by alternating bursts of motor activity with equal duration and spike frequency on the left and the right sides of the body. Lateral turns are characterized by three main changes in this pattern: (1) in the turn cycle, the spike frequency, burst duration, and burst proportion (burst duration/cycle duration) increase on the turning side; (2) the cycle duration increases in both the turn cycle and the succeeding cycle; and (3) in the cycle succeeding the turn cycle, the burst duration increases on the non-turning side (rebound). We investigated mechanisms for the generation of turns in single-segment models of the lamprey locomotor spinal network. Activation of crossing inhibitory neurons proved a sufficient mechanism to explain all three changes in the locomotor rhythm during a fictive turn. Increased activation of these cells inhibits the activity of the opposite side during the prolonged burst of the turn cycle, and slows down the locomotor rhythm. Secondly, this activation of the crossing inhibitory neurons is accompanied by an increased calcium influx into the cells. This gives a suppressed activity on the turning side and a contralateral rebound after the turn, through activation of calcium-dependent potassium channels.

Modeling of substance P and 5-HT induced synaptic plasticity in the lamprey spinal CPG: consequences for network pattern generation

Consequences of synaptic plasticity in the lamprey spinal CPG are analyzed by means of simulations. This is motivated by the effects substance P (a tachykinin) and serotonin (5-hydroxytryptamin; 5-HT) have on synaptic transmission in the locomotor network. Activity-dependent synaptic depression and potentiation have recently been shown experimentally using paired intracellular recordings. Although normally activity-dependent plasticity presumably does not contribute to the patterning of network activity, this changes in the presence of the neuromodulators substance P and 5-HT, which evoke significant plasticity. Substance P can induce a faster and larger depression of inhibitory connections but potentiation of excitatory inputs, whereas 5-HT induces facilitation of both inhibitory and excitatory inputs. Changes in the amplitude of the first postsynaptic potential are also seen. These changes could thus be a potential mechanism underlying the modulatory role these substances have on the rhythmic network activity. The aim of the present study has been to implement the activity dependent synaptic depression and facilitation induced by substance P and 5-HT into two alternative models of the lamprey spinal locomotor network, one relying on reciprocal inhibition for bursting and one in which each hemicord is capable of oscillations. The consequences of the plasticity of inhibitory and excitatory connections are then explored on the network level. In the intact spinal cord, tachykinins and 5-HT, which can be endogenously released, increase and decrease the frequency of the alternating left-right burst pattern, respectively. The frequency decreasing effect of 5-HT has previously been explained based on its conductance decreasing effect on K(Ca) underlying the postspike afterhyperpolarization (AHP). The present simulations show that short-term synaptic plasticity may have strong effects on frequency regulation in the lamprey spinal CPG. In the network model relying on reciprocal inhibition, the observed effects substance P and 5-HT have on network behavior (i.e., a frequency increase and decrease respectively) can to a substantial part be explained by their effects on the total extent and time dynamics of synaptic depression and facilitation. The cellular effects of these substances will in the 5-HT case further contribute to its network effect.