Tjeerd Olde Scheper

A Model of Molecular Circadian Clocks: Multiple Mechanisms for Phase Shifting and a Requirement for Strong Nonlinear Interactions:

A fundamental question in the field of circadian rhythms concerns the biochemical and molecular nature of the oscillator. There is strong evidence that circadian oscillators are cell autonomous and rely on periodic gene expression. In Drosophila, Neurospora, Aplysia, and vertebrates, circadian oscillators are thought to be based on molecular autoregulatory loops composed of transcription, translation, and negative feedback by proteins on nuclear transcription. By studying a mathematical model of molecular clocks based on this general concept, the authors sought to determine which features such clocks must have to generate robust and stable oscillations and to allow entrainment by external stimuli such as light. The model produced circadian oscillations as an emergent property even though a time delay in protein synthesis and rate constants of the feedback loop were much shorter than 24 h. Along with the delay in protein production, strong nonlinear interactions in macromolecular synthesis and nuclear feedback appeared to be required for the model to show well-behaved oscillatory behavior. Realistic phase-shifting patterns induced by external stimuli could be achieved by multiple mechanisms—namely, up-and downward perturbations of protein or mRNA synthesis or degradation rates. The model makes testable predictions about interactions between clock elements and mechanisms of entrainment and may help to understand the functions of the intricate molecular interactions governing circadian rhythmogenesis.

Self-organised dynamic recognition states for chaotic neural networks

Chaos offers several advantages to the Engineer over other non-chaotic dynamics. One is that chaotic systems are often significantly easier to control than other linear or non-linear systems, requiring only small, appropriately timed perturbations to constrain them within specific unstable periodic orbits (UPOs). Another is that chaotic attractors contain an infinite number of these UPOs. If individual UPOs can be made to represent specific internal states of a system, then a chaotic attractor can be turned into an infinite state machine. In this paper we investigate this possibility with respect to chaotic neural networks. We present a method by which a network can self-select UPOs in response to specific input values. These UPOs correspond to network recognition states for these input values.

Why metabolic systems are rarely chaotic

One of the mysteries surrounding the phenomenon of chaos is that it can rarely be found in biological systems. This has led to many discussions of the possible presence and interpretation of chaos in biological signals. It has caused empirical biologists to be very sceptical of models that have chaotic properties or even employ chaos for problem solving tasks. In this paper, it is demonstrated that there exists a possible mechanism that is part of the catalytical reaction mechanisms which may be responsible for controlling enzymatic reactions such that they do not become chaotic. It is proposed that where these mechanisms are not present or not effective, chaos may still occur in biological systems.One of the mysteries surrounding the phenomenon of chaos is that it can rarely be found in biological systems. This has led to many discussions of the possible presence and interpretation of chaos in biological signals. It has caused empirical biologists to be very sceptical of models that have chaotic properties or even employ chaos for problem solving tasks. In this paper, it is demonstrated that there exists a possible mechanism that is part of the catalytical reaction mechanisms which may be responsible for controlling enzymatic reactions such that they do not become chaotic. It is proposed that where these mechanisms are not present or not effective, chaos may still occur in biological systems.

Adaptation based on memory dynamics in a chaotic neural network

The complex dynamics that emerge from systems governed by deterministic chaos offer significant advantages to the neuromorphic engineer. Included in these is the potential for a very large memory store and the ease with which chaotic systems can be controlled. By definition, a chaotic system is a periodic. However, during the course of its trajectory through state space, the chaotic system will come infinitely close to points that it has previously visited. These almost repeating trajectories are referred to as Unstable Periodic Orbits (UPOs). Normally, under the influence of chaos, the trajectory would move away exponentially fast from its previous path, thereby describing a new path on the surface of the attractor. It is possible to apply a simple delayed feedback control mechanism to a chaotic system that will constrain it within one of its UPOs. This article presents a neural implementation of this delayed feedback mechanism. The network presented here is able to stabilize different UPOs in response to different input signals, with each UPO corresponding to a dynamic recognition state for that input. We also present two learning rules for this network, which enables it to adapt to novel inputs in a self-organized manner.

Dynamic hebbian cross-correlation learning resolves the spike timing dependent plasticity conundrum

Spike Timing-Dependent Plasticity has been found to assume many different forms. The classic STDP curve, with one potentiating and one depressing window, is only one of many possible curves that describe synaptic learning using the STDP mechanism. It has been shown experimentally that STDP curves may contain multiple LTP and LTD windows of variable width, and even inverted windows. The underlying STDP mechanism that is capable of producing such an extensive, and apparently incompatible, range of learning curves is still under investigation. In this paper, it is shown that STDP originates from a combination of two dynamic Hebbian cross-correlations of local activity at the synapse. The correlation of the presynaptic activity with the local postsynaptic activity is a robust and reliable indicator of the discrepancy between the presynaptic neuron and the postsynaptic neurons activity. The second correlation is between the local postsynaptic activity with dendritic activity which is a good indicator of matching local synaptic and dendritic activity. We show that this simple time-independent learning rule can give rise to many forms of the STDP learning curve. The rule regulates synaptic strength without the need for spike matching or other supervisory learning mechanisms. Local differences in dendritic activity at the synapse greatly affect the cross-correlation difference which determines the relative contributions of different neural activity sources. Dendritic activity due to nearby synapses, action potentials, both forward and back-propagating, as well as inhibitory synapses will dynamically modify the local activity at the synapse, and the resulting STDP learning rule. The dynamic Hebbian learning rule ensures furthermore, that the resulting synaptic strength is dynamically stable, and that interactions between synapses do not result in local instabilities. The rule clearly demonstrates that synapses function as independent localized computational entities, each contributing to the global activity, not in a simply linear fashion, but in a manner that is appropriate to achieve local and global stability of the neuron and the entire dendritic structure.

Short Term Depression Unmasks the Ghost Frequency

Short Term Plasticity (STP) has been shown to exist extensively in synapses throughout the brain. Its function is more or less clear in the sense that it alters the probability of synaptic transmission at short time scales. However, it is still unclear what effect STP has on the dynamics of neural networks. We show, using a novel dynamic STP model, that Short Term Depression (STD) can affect the phase of frequency coded input such that small networks can perform temporal signal summation and determination with high accuracy. We show that this property of STD can readily solve the problem of the ghost frequency, the perceived pitch of a harmonic complex in absence of the base frequency. Additionally, we demonstrate that this property can explain dynamics in larger networks. By means of two models, one of chopper neurons in the Ventral Cochlear Nucleus and one of a cortical microcircuit with inhibitory Martinotti neurons, it is shown that the dynamics in these microcircuits can reliably be reproduced using STP. Our model of STP gives important insights into the potential roles of STP in self-regulation of cortical activity and long-range afferent input in neuronal microcircuits.

Harmonic Versus Chaos Controlled Oscillators in Hexapedal Locomotion

The behavioural diversity of chaotic oscillator can be controlled into periodic dynamics and used to model locomotion using central pattern generators. This paper shows how controlled chaotic oscillators may improve the adaptation of the robot locomotion behaviour to terrain uncertainties when compared to nonlinear harmonic oscillators. This is quantitatively assesses by the stability, changes of direction and steadiness of the robotic movements. Our results show that the controlled Wu oscillator promotes the emergence of adaptive locomotion when deterministic sensory feedback is used. They also suggest that the chaotic nature of chaos controlled oscillators increases the expressiveness of pattern generators to explore new locomotion gaits.

Hebbian cross-correlation learning emerges as spike timing dependent plasticity

In Donald O. Hebbs oft quoted thesis on synaptic plasticity, the change in efficacy in proportion to the degree of correlation between pre- and post-synaptic activity is expressed explicitly. The Hebbian learning rule has been demonstrated in simulations to be reliable and effective and appears to have a solid foundation in biology on the basis of experimental results. However, beyond binary simulation models of the Spike Timing Dependent Plasticity (STDP) rule, it has not been demonstrated that the causal correlation property of synaptic plasticity is as valid and as effective as always has been assumed. To clarify the exact nature of learning by means of spike timing dependent plasticity, a dynamic model has been developed based on the cross-correlation between pre- and post-synaptic activity as expressed by a dynamic activity measure. The components that form the model are centered around the following guiding principles. Firstly, the cross-correlation between local synaptic pre- and post-synaptic activity, as induced by the synapse itself in the post-synaptic cell, determines the strength of the potential for synaptic depression. Even though this may appear to be counter-intuitive, it reflects the depression due to pre-synaptic activity if little or no subsequent post-synaptic activity is present. The second component is the post-synaptic activity induced by the synapse locally. This represents the local response to synaptic input. The third component is the cross-correlation of the post-synaptic activity induced by the synapse with other post-synaptic activity contributing factors such as an action potential and other synapses. These three components form the autonomous learning rule from which Spike Timing Dependent Plasticity learning emerges. Due to the dynamic nature of the autonomous learning rule, it responds in a simple feed-forward manner to the synaptic input in combination to the localised post-synaptic activity. This precludes the need to perform spike matching and post-processing of the simulation and is more biologically relevant. The relation between the local dynamics of a single synapse and the localised dynamics due to post-synaptic activity becomes apparent by different emerging learning rules. The presence of action potentials and synaptic inhibition can change the shape of the STDP learning rule even to the extent that a Hebbian learning rule may become anti-Hebbian and vice versa. The synapse can respond to external input as well as compete with other synapses and tune itself to the local dendritic activity and the global neuronal activity. Synaptic adaptation due to the presence of nearby synapses and global activity has previously not been extensively studied. This work shows that synapses are not mere slaves to the input but perform more complex computations by combining the input with the local post-synaptic activity as well as the global dynamics due to other synapses and action potentials.

Emergent pitch perception using short term plasticity

In pitch perception, the perceived frequency is the sum-mation of the simple and complex sounds that form thecomplex harmonics. The phenomenon of the perceivedmissing fundamental frequency can be described as thefrequency that is then perceived but is not actually presentin the sound [1]. The mechanism in the cochlear nucleusthat seems to be responsible is still unclear, however usingsimple phenomenologcial models we show that short-term plasticity is capable of solving this problem.

The Spike Generation Processes: A Case for Low Level Computation

Over the last couple of years, it can be said that the focus of the computational aspects of neurons has moved from synaptic weight and firing rate encoding to temporal firing encoding. On the other hand, several elements of these models have been based on some conceptual assumptions that imply relative simple dynamic behaviour of neuronal membrane activity in an active-passive process. In line with recent advances that have produced a better understanding of the biochemical processes that occur within cells, it is proposed that the processes that are involved in a membrane depolarisation cascade are less static than have been assumed so far. In particular, the possibilities of low level computation at the membrane level need to be explored more extensively. In this chapter some computational properties of the spike generation processes are explored using phenomenological models.