Importance of mitochondrial P(O2) in maximal O2 transport and utilization: a theoretical analysis.

In previous calculations of how the O2 transport system limits .VO2(max), it was reasonably assumed that mitochondrial P(O2) (Pm(O2)) could be neglected (set to zero). However, in reality, Pm(O2) must exceed zero and the red cell to mitochondrion diffusion gradient may therefore be reduced, impairing diffusive transport of O2 and .VO2(max). Accordingly, we investigated the influence of Pm(O2) on these calculations by coupling previously used equations for O2 transport to one for mitochondrial respiration relating mitochondrial .VO2 to P(O2). This hyperbolic function, characterized by its P50 and V˙MAX, allowed Pm(O2) to become a model output (rather than set to zero as previously). Simulations using data from exercising normal subjects showed that at .VO2(max), Pm(O2) was usually <1mmHg, and that the effects on .VO2(max) were minimal. However, when O2 transport capacity exceeded mitochondrial V˙MAX, or if P50 were elevated,Pm(O2) often reached double digit values, thereby reducing the diffusion gradient and significantly decreasing .VO2(max).

Genome-wide system analysis reveals stable yet flexible network dynamics in yeast.

Recently, important insights into static network topology for biological systems have been obtained, but still global dynamical network properties determining stability and system responsiveness have not been accessible for analysis. Herein, we explore a genome-wide gene-to-gene regulatory network based on expression data from the cell cycle in Saccharomyces cerevisae (budding yeast). We recover static properties like hubs (genes having several out-going connections), network motifs and modules, which have previously been derived from multiple data sources such as whole-genome expression measurements, literature mining, protein-protein and transcription factor binding data. Further, our analysis uncovers some novel dynamical design principles; hubs are both repressed and repressors, and the intra-modular dynamics are either strongly activating or repressing whereas inter-modular couplings are weak. Finally, taking advantage of the inferred strength and direction of all interactions, we perform a global dynamical systems analysis of the network. Our inferred dynamics of hubs, motifs and modules produce a more stable network than what is expected given randomised versions. The main contribution of the repressed hubs is to increase system stability, while higher order dynamic effects (e.g. module dynamics) mainly increase system flexibility. Altogether, the presence of hubs, motifs and modules induce few flexible modes, to which the network is extra sensitive to an external signal. We believe that our approach, and the inferred biological mode of strong flexibility and stability, will also apply to other cellular networks and adaptive systems.

Deconstructing the core dynamics from a complex time-lagged regulatory biological circuit.

Complex regulatory dynamics is ubiquitous in molecular networks composed of genes and proteins. Recent progress in computational biology and its application to molecular data generate a growing number of complex networks. Yet, it has been difficult to understand the governing principles of these networks beyond graphical analysis or extensive numerical simulations. Here the authors exploit several simplifying biological circumstances which thereby enable to directly detect the underlying dynamical regularities driving periodic oscillations in a dynamical nonlinear computational model of a protein-protein network. System analysis is performed using the cell cycle, a mathematically well-described complex regulatory circuit driven by external signals. By introducing an explicit time delay and using a 'tearing-and-zooming' approach the authors reduce the system to a piecewise linear system with two variables that capture the dynamics of this complex network. A key step in the analysis is the identification of functional subsystems by identifying the relations between state-variables within the model. These functional subsystems are referred to as dynamical modules operating as sensitive switches in the original complex model. By using reduced mathematical representations of the subsystems the authors derive explicit conditions on how the cell cycle dynamics depends on system parameters, and can, for the first time, analyse and prove global conditions for system stability. The approach which includes utilising biological simplifying conditions, identification of dynamical modules and mathematical reduction of the model complexity may be applicable to other well-characterised biological regulatory circuits. [Includes supplementary material].

A biophysical model of multiple-item working memory: a computational and neuroimaging study.

Biophysically based computational models have successfully accounted for the persistent neural activity underlying the maintenance of single items of information in working memory. The aim of the present study was to extend previous models in order to retain multiple items, in agreement with the observed human storage capacity. This was done by implementing cellular mechanisms known to occur during the childhood development of working memory, such as an increased synaptic strength and improved contrast and specificity of the neural response. Our computational study shows that these mechanisms are sufficient to create a neural network which can store information about multiple items through sustained neural activity. Furthermore, by using functional magnetic resonance imaging, we found that the information-activity curve predicted by the model corresponds to that in the human posterior parietal cortex during performance of working memory tasks, which is consistent with previous studies of brain activity related to working memory capacity in humans.

Growing Bayesian network models of gene networks from seed genes.

MOTIVATION: For the last few years, Bayesian networks (BNs) have received increasing attention from the computational biology community as models of gene networks, though learning them from gene-expression data is problematic. Most gene-expression databases contain measurements for thousands of genes, but the existing algorithms for learning BNs from data do not scale to such high-dimensional databases. This means that the user has to decide in advance which genes are included in the learning process, typically no more than a few hundreds, and which genes are excluded from it. This is not a trivial decision. We propose an alternative approach to overcome this problem. RESULTS: We propose a new algorithm for learning BN models of gene networks from gene-expression data. Our algorithm receives a seed gene S and a positive integer R from the user, and returns a BN for the genes that depend on S such that less than R other genes mediate the dependency. Our algorithm grows the BN, which initially only contains S, by repeating the following step R + 1 times and, then, pruning some genes; find the parents and children of all the genes in the BN and add them to it. Intuitively, our algorithm provides the user with a window of radius R around S to look at the BN model of a gene network without having to exclude any gene in advance. We prove that our algorithm is correct under the faithfulness assumption. We evaluate our algorithm on simulated and biological data (Rosetta compendium) with satisfactory results.

Division of labor among distinct subtypes of inhibitory neurons in a cortical microcircuit of working memory.

A conspicuous feature of cortical organization is the wide diversity of inhibitory interneurons; their differential computational functions remain unclear. Here we propose a local cortical circuit in which three major subtypes of interneurons play distinct roles. In a model designed for spatial working memory, stimulus tuning of persistent activity arises from the concerted action of widespread inhibition mediated by perisoma-targeting (parvalbumin-containing) interneurons and localized disinhibition of pyramidal cells via interneuron-targeting (calretinin-containing) interneurons. Moreover, resistance against distracting stimuli (a fundamental property of working memory) is dynamically controlled by dendrite-targeting (calbindin-containing) interneurons. The experimental observation of inverted tuning curves of monkey prefrontal neurons recorded during working memory supports a key model prediction. This work suggests a framework for understanding the division of labor and cooperation among different inhibitory cell types in a recurrent cortical circuit.

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.

GABA(B)-ergic modulation of burst rate and intersegmental coordination in lamprey: experiments and simulations.

Neuromodulators which influence the operation of neural networks act as a rule via several cellular and synaptic mechanisms. Activation of GABA(B)-receptors in the lamprey spinal cord reduce both calcium currents and the peak amplitude of the post-spike afterhyperpolarization (AHP). Activation of GABA(B)-receptors reduce the segmental alternation rate and modifies the intersegmental coordination when the spinal locomotor circuits are activated by NMDA. Using physiological experiments we find that a reduced AHP is not sufficient to account for the observed reduction of the burst rate. Computer simulations revealed that either a reduced AHP or calcium current could alter the phase coordination between the segments similar to earlier experiments.

Interactive effects of the GABABergic modulation of calcium channels and calcium-dependent potassium channels in lamprey.

The GABAB-mediated modulation of spinal neurons in the lamprey is investigated in this study. Activation of GABAB receptors reduces calcium currents through both low- (LVA) and high-voltage activated (HVA) calcium channels, which subsequently results in the reduction of the calcium-dependent potassium (KCa) current. This in turn will reduce the peak amplitude of the afterhyperpolarization (AHP). We used the modulatory effects of GABAB receptor activation on N-methyl-D-aspartate (NMDA)-induced, TTX-resistant membrane potential oscillations as an experimental model in which to separate the effects of GABAB receptor activation on LVA calcium channels from that on KCa channels. We show experimentally and by using simulations that a direct effect on LVA calcium channels can account for the effects of GABAB receptor activation on intrinsic membrane potential oscillations to a larger extent than indirect effects mediated via KCa channels. Furthermore, by conducting experiments and simulations on intrinsic membrane potential oscillations, we find that KCa channels may be activated by calcium entering through LVA calcium channels, providing that the decay kinetics of the calcium that enters through LVA calcium channels is not as slow as the calcium entering via NMDA receptors. A combined experimental and computational analysis revealed that the LVA calcium current also contributes to neuronal firing properties.

Activity-dependent modulation of adaptation produces a constant burst proportion in a model of the lamprey spinal locomotor generator.

The neuronal network underlying lamprey swimming has stimulated extensive modelling on different levels of abstraction. The lamprey swims with a burst frequency ranging from 0.3 to 8-10 Hz with a rostrocaudal lag between bursts in each segment along the spinal cord. The swimming motor pattern is characterized by a burst proportion that is independent of burst frequency and lasts around 30%-40% of the cycle duration. This also applies in preparations in which the reciprocal inhibition in the spinal cord between the left and right side is blocked. A network of coupled excitatory neurons producing hemisegmental oscillations may form the basis of the lamprey central pattern generator (CPG). Here we explored how such networks, in principle, could produce a large frequency range with a constant burst proportion. The computer simulations of the lamprey CPG use simplified, graded output units that could represent populations of neurons and that exhibit adaptation. We investigated the effect of an active modulation of the degree of adaptation of the CPG units to accomplish a constant burst proportion over the whole frequency range when, in addition, each hemisegment is assumed to be self-oscillatory. The degree of adaptation is increased with the degree of stimulation of the network. This will make the bursts terminate earlier at higher burst rates, allowing for a constant burst proportion. Without modulated adaptation the network operates in a limited range of swimming frequencies due to a progressive increase of burst duration with increasing background stimulation. By introducing a modulation of the adaptation, a broad burst frequency range can be produced. The reciprocal inhibition is thus not the primary burst terminating factor, as in many CPG models, and it is mainly responsible for producing alternation between the left and right sides. The results are compared with the Morris-Lecar oscillator model with parameters set to produce a type A and type B oscillator, in which the burst durations stay constant or increase, respectively, when the background stimulation is increased. Here as well, burst duration can be controlled by modulation of the slow variable in a similar way as above. When oscillatory hemisegmental networks are coupled together in a chain a phase lag is produced. The production of a phase lag in chains of such oscillators is compared with chains of Morris-Lecar relaxation oscillators. Models relating to the intact versus isolated spinal cord preparation are discussed, as well as the role of descending inhibition.

Intrinsic function of a neuronal network - a vertebrate central pattern generator.

The cellular bases of vertebrate locomotor behaviour is reviewed using the lamprey as a model system. Forebrain and brainstem cell populations initiate locomotor activity via reticulospinal fibers activating a spinal network comprised of glutamatergic and glycinergic interneurons. The role of different subtypes of Ca2+ channels, Ca2+ dependent K+ channels and voltage dependent NMDA channels at the neuronal and network level is in focus as well as the effects of different metabotropic, aminergic and peptidergic modulators that target these ion channels. This is one of the few vertebrate networks that is understood at a cellular level.

Modulation of burst frequency by calcium-dependent potassium channels in the lamprey locomotor system: dependence of the activity level.

It is crucial to determine the effects on the network level of a modulation of intrinsic membrane properties. The role calcium-dependent potassium channels, KCa, in the lamprey locomotor system has been investigated extensively. Earlier experimental studies have shown that apamin, which affects one type of KCa, increases the cycle duration of the locomotor network, due to effects on the burst termination. The effects of apamin were here larger when the network had a low level of activity (burst frequency 0.5 to 1 Hz) as compared to a higher rate (> 2 Hz). By using a previously developed simulation model based on the lamprey locomotor network, we show that the model could account for the frequency dependence of the apamin modulation, if only the KCa conductance activated by Ca2+ entering during the action potential was altered and not the KCa conductance activated by Ca2+ entering through NMDA channels. The present simulation model of the spinal network in the lamprey can thus account for earlier experimental results with apamin on the network and cellular level that previously appeared enigmatic.

Locomotor-related presynaptic modulation of primary afferents in the lamprey.

Presynaptic modulation of sensory afferent transmission during rhythmic motor activity was investigated in the lamprey spinal cord in vitro. Intracellular recordings were performed from the somata and axons of the glutamatergic sensory neurons from the skin (dorsal cells) during locomotor activity induced by N-methyl-D-aspartate (NMDA). Dorsal cells were phasically depolarized during each ipsilateral ventral root burst. In some soma recordings no or only small amplitude depolarizations were seen, although intracellular recording of their axons revealed the existence of large depolarizations, suggesting that the input synapses are located on the axons. The amplitude of the depolarizations increased during intracellular injection of hyperpolarizing current. The amplitude of the depolarizations increased when the frequency of the locomotor rhythm was increased by elevating the NMDA concentration. The depolarizations were not blocked by specific GABA(A) (bicuculline) or GABA(B) (phaclofen and saclofen) antagonists. To investigate whether the phasic depolarization may influence the monosynaptic excitatory transmission to giant interneurons, the amplitude of the monosynaptic excitatory postsynaptic potential (EPSP) was compared between the onset of the ipsilateral locomotor burst and the burst mid-point. The compound monosynaptic EPSP evoked from dorsal column was significantly smaller during the peak depolarization than at burst onset. The reduction of the amplitude of the EPSPs was not associated with any change of the membrane potential or input resistance of the giant interneurons, suggesting that this effect is mediated by a presynaptic mechanism. Phase-dependent effects were also seen on burst and cycle duration following dorsal column stimulation. Thus, the locomotor-related depolarizations in dorsal cell axons may represent a mechanism for a phasic gain control of sensory transmission during fictive locomotion.

Low-voltage-activated calcium channels in the lamprey locomotor network: simulation and experiment.

To evaluate the role of low-voltage-activated (LVA) calcium channels in the lamprey spinal locomotor network, a previous computer simulation model has been extended to include LVA calcium channels. It is also of interest to explore the consequences of a LVA conductance for the electrical behavior of the single neuron. The LVA calcium channel was modeled with voltage-dependent activation and inactivation using the m3h form, following a Hodgkin-Huxley paradigm. Experimental data from lamprey neurons was used to provide parameter values of the single cell model. The presence of a LVA calcium conductance in the model could account for the occurrence of a rebound depolarization in the simulation model. The influence of holding potential on the occurrence of a rebound as well the latency at which it is elicited was investigated and compared with previous experiments. The probability of a rebound increased at a more depolarized holding potential and the latency was also reduced under these conditions. Furthermore, the effect of changing the holding potential and the reversal potential of the calcium dependent potassium conductance were tested to determine under which conditions several rebound spikes could be elicited after a single inhibitory pulse in the simulation model. A reduction of the slow afterhyperpolarization (sAHP) after the action potential reduced the tendency for a train of rebound spikes. The experimental effects of gamma-aminobutyric acid-B (GABA(B)) receptor activation were simulated by reducing the maximal LVA calcium conductance. A reduced tendency for rebound firing and a slower rising phase with sinusoidal current stimulation was observed, in accordance with earlier experiments. The effect of reducing the slow afterhyperpolarization and reducing the LVA calcium current was tested experimentally in the lamprey spinal cord, during N-methyl-D-aspartate (NMDA)-induced fictive locomotion. The reduction of burst frequency was more pronounced with GABA(B) agonists than with apamin (inhibitor of K(Ca) current) when using high NMDA concentration (high burst frequency). The burst frequency increased after the addition of a LVA calcium current to the simulated segmental network, due to a faster recovery during the inhibitory phase as the activity switches between the sides. This result is consistent with earlier experimental findings because GABA(B) receptor agonists reduce the locomotor frequency. These results taken together suggest that the LVA calcium channels contribute to a larger degree with respect to the burst frequency regulation than the sAHP mechanism at higher burst frequencies. The range in which a regular burst pattern can be simulated is extended in the lower range by the addition of LVA calcium channels, which leads to more stable activity at low locomotor frequencies. We conclude that the present model can account for rebound firing and trains of rebound spikes in lamprey neurons. The effects of GABA(B) receptor activation on the network level is consistent with a reduction of the calcium current through LVA calcium channels even though GABA(B) receptor activation will affect the sAHP indirectly and also presynaptic inhibition.

Calcium-dependent potassium channels play a critical role for burst termination in the locomotor network in lamprey.

1. The possible involvement of calcium-dependent potassium channels (KCa) in the termination of locomotor bursts was investigated by administration of a specific blocker, apamin, in the lamprey spinal cord in vitro. The effects were examined by recording the efferent activity in ventral roots and by intracellular recording from interneurons and motoneurons. During fictive locomotion induced by N-methyl-D-aspartate (NMDA), apamin was found to affect both the frequency of bursting and the regularity of the locomotor pattern. 2. At the single cell level, NMDA can induce pacemaker-like membrane potential oscillations in individual neurons after administration of tetrodotoxin. Apamin (2.5 microM) produced a marked increase of the duration of the depolarizing plateau phase occurring during these NMDA-induced oscillations; this shows that the repolarization of the plateau is initiated by a progressive activation of apamin-sensitive KCa-channels. 3. The action potential is followed by an afterhyperpolarization (AHP) with a fast and a slow phase (sAHP). The latter is known to be caused by apamin-sensitive KCa-channels. During repetitive firing, the interspike interval is dependent on the amplitude and the duration of the sAHP. Apamin caused a reduction of the spike frequency adaptation with a concomitant increase in the firing frequency. In some cells, apamin in addition reduced the threshold for the action potential. Apamin-sensitive KCa-channels thus will be involved in controlling both the onset and the duration of neuronal firing in the lamprey spinal cord. 4. During fictive locomotion induced by NMDA (40-200 microM), a blockade of KCa-channels by apamin produced an increase of the coefficient of variation (mean = 167%, n = 26), which was statistically significant in 21 out of 26 experiments. At 40-150 microM NMDA, an average increase in cycle duration was 77% and statistically significant in 15 out of 20 preparations. At 200 microM NMDA (corresponding to higher burst rate), on the other hand, the average increase was only 6% and the increase was statistically significant in only 1 out 6 cases. For a given experiment, the strength of the apamin effect depended on the level of NMDA drive used, being more pronounced at slow rhythms, when it often caused a complete disruption of the locomotor pattern. At high burst rates, however, the cycle duration was less affected and a disruption of the regular burst pattern did not occur.(ABSTRACT TRUNCATED AT 400 WORDS)

Effects of metabotropic glutamate receptor activation on the cellular and network level in the lamprey spinal cord.

The effects of the metabotropic glutamate receptor (mGluR) agonist ACPD ((1S,3R)-1-aminocyclopentane-1,3-dicarboxylic acid) on single neurones and on the network underlying locomotion in the lamprey have been analysed. ACPD induces a depolarization in lamprey spinal cord neurones, which is insensitive to tetrodotoxin (TTX) and ionotropic glutamate receptor antagonists, but is reversibly blocked by the mGluR antagonist MCPG ((+)-alpha-methyl-4-carboxyphenylglycine). The ACPD-induced depolarization persists in a calcium-free solution or when the calcium channel blocker cadmium is added to the solution. At the network level ACPD causes an increased burst frequency during fictive locomotion by increasing the excitability level of network neurones.

GABAB receptor activation causes a depression of low- and high-voltage-activated Ca2+ currents, postinhibitory rebound, and postspike afterhyperpolarization in lamprey neurons.

1. Activation of gamma-aminobutyric acid-B (GABAB) receptors during N-methyl-D-aspartate (NMDA)-induced fictive locomotor activity in the lamprey spinal cord reduces the burst frequency and changes the intersegmental coordination. Presynaptic inhibition of both the excitatory and inhibitory synaptic transmission from spinal premotor interneurons occurs through GABAB receptor activation. To further analyze the cellular mechanisms underlying the GABABergic modulation of the locomotor network, the present study investigates somatodendritic effects of GABAB receptor activation on interneurons and motoneurons in the lamprey spinal cord in vitro using single-electrode current- and voltage-clamp techniques. 2. High- (HVA) and low- (LVA) voltage-activated calcium currents were studied with single-electrode voltage clamp when Na+ and K+ currents were blocked--using tetrodotoxin, tetraethylammonium (TEA), and CsCl electrodes--after substituting Ca2+ with Ba2+. Cobalt-sensitive inward barium currents, activated at -50 mV, became larger when the holding potential was set to a more hyperpolarized level, thus suggesting the existence of an LVA calcium current. The presence of cobalt-sensitive inward barium currents activated at -30 and -10 mV suggests the existence of an HVA calcium current. GABAB receptor activation (baclofen) reduced the peak amplitude of both the LVA and HVA Ca2+ component. 3. The late phase of the afterhyperpolarization (AHP), which follows the action potential, was reduced in amplitude by cobalt, thus lending further support to the notion that the Ca2+ influx, and the subsequent activation of Ca(2+)-dependent K+ channels (KCa2+), constitutes the major part of the AHP generation. Application of the GABAB agonist baclofen also reduced the peak amplitude of the AHP in interneurons and motoneurons, and this reduction was counteracted by the GABAB antagonist 2(OH)saclofen. Baclofen reduced the duration of action potentials broadened by TEA, thus suggesting that the Ca2+ inflow was reduced. Intracellular injection of the GTP analogue GTP gamma S also reduced the duration of the action potential and the peak amplitude of the AHP in TEA, thus supporting the notion that a GTP-binding protein (G-protein)-mediated GABAB receptor activation reduced the calcium inflow, leading to less activation of KCa channels and, consequently, to a smaller peak amplitude of the AHP. 4. Baclofen suppressed the subthreshold depolarization induced by a depolarizing current pulse injection without affecting either the spike threshold or the resting membrane conductance.(ABSTRACT TRUNCATED AT 400 WORDS)

The spinal GABA system modulates burst frequency and intersegmental coordination in the lamprey: differential effects of GABAA and GABAB receptors.

1. The effect of spinal GABAergic neurons on the segmental neuronal network generating locomotion has been analyzed in the lamprey spinal cord in vitro. It is shown that gamma-aminobutyric acid (GABA)A- and GABAB-mediated effects influence the burst frequency and the intersegmental coordination and that the GABA system is active during normal locomotor activity. 2. Fictive locomotor activity was induced by superfusing the spinal cord with a Ringer solution containing N-methyl-D-aspartate (NMDA, 150 microM). The efferent locomotor activity was recorded by suction electrodes from the ventral roots or intracellularly from interneurons or motoneurons. If a GABA uptake blocker was added to the perfusate, the burst rate decreased. This effect was counteracted by GABAB receptor blockade by phaclofen or 2-(OH)-saclofen. If instead a GABAB receptor agonist (baclofen) was added during fictive locomotion, a depression of the burst rate occurred. It was concluded that a GABAB receptor activation due to an endogenous release of GABA caused a depression of the burst activity with a maintained well-coordinated locomotor activity. 3. If a GABAA receptor antagonist (bicuculline) is applied during fictive locomotion elicited by NMDA, a certain increase of the burst rate occurred. Conversely, if a selective GABAA agonist (muscimol) was administered, the burst rate decreased. Similarly, if the GABAA receptor activity was potentiated by activation of a benzodiazepine site by diazepam, the burst rate was reduced. If, however the GABAergic effect was first enhanced by an uptake blocker (nipecotic acid), an administration of a GABAA antagonist (bicuculline) increased the burst rate, but in addition, the burst pattern became less regular with recurrent shorter periods without clear reciprocal burst activity. The GABAA receptor activity appears important for the rate control and for permitting a regular burst pattern. 4. The intersegmental coordination in the lamprey is characterized by a rostrocaudal constant phase lag of approximately 1% of the cycle duration between the activation of consecutive segments during forward swimming. This rostrocaudal phase lag can be reversed during backward swimming, which can be induced also experimentally in the isolated spinal cord by providing a higher excitability to the caudal segments. In a split-bath configuration, a GABA uptake blocker or a GABAB agonist was administered to the rostral part of the spinal cord, which caused a reversal of the phase lag as during backward swimming. If GABAA receptors were blocked under similar conditions, the intersegmental coordination became irregular. It is concluded that an increased GABA activity in a spinal cord region can modify the intersegmental coordination.(ABSTRACT TRUNCATED AT 400 WORDS)