Christian Tetzlaff

Self-organized criticality in developing neuronal networks.

Recently evidence has accumulated that many neural networks exhibit self-organized criticality. In this state, activity is similar across temporal scales and this is beneficial with respect to information flow. If subcritical, activity can die out, if supercritical epileptiform patterns may occur. Little is known about how developing networks will reach and stabilize criticality. Here we monitor the development between 13 and 95 days in vitro (DIV) of cortical cell cultures (n = 20) and find four different phases, related to their morphological maturation: An initial low-activity state (≈19 DIV) is followed by a supercritical (≈20 DIV) and then a subcritical one (≈36 DIV) until the network finally reaches stable criticality (≈58 DIV). Using network modeling and mathematical analysis we describe the dynamics of the emergent connectivity in such developing systems. Based on physiological observations, the synaptic development in the model is determined by the drive of the neurons to adjust their connectivity for reaching on average firing rate homeostasis. We predict a specific time course for the maturation of inhibition, with strong onset and delayed pruning, and that total synaptic connectivity should be strongly linked to the relative levels of excitation and inhibition. These results demonstrate that the interplay between activity and connectivity guides developing networks into criticality suggesting that this may be a generic and stable state of many networks in vivo and in vitro.

Time scales of memory, learning, and plasticity

After only about 10 days would the storage capacity of our nervous system be reached if we stored every bit of input. The nervous system relies on at least two mechanisms that counteract this capacity limit: compression and forgetting. But the latter mechanism needs to know how long an entity should be stored: some memories are relevant only for the next few minutes, some are important even after the passage of several years. Psychology and physiology have found and described many different memory mechanisms, and these mechanisms indeed use different time scales. In this prospect we review these mechanisms with respect to their time scale and propose relations between mechanisms in learning and memory and their underlying physiological basis.

Synaptic scaling in combination with many generic plasticity mechanisms stabilizes circuit connectivity.

Synaptic scaling is a slow process that modifies synapses, keeping the firing rate of neural circuits in specific regimes. Together with other processes, such as conventional synaptic plasticity in the form of long term depression and potentiation, synaptic scaling changes the synaptic patterns in a network, ensuring diverse, functionally relevant, stable, and input-dependent connectivity. How synaptic patterns are generated and stabilized, however, is largely unknown. Here we formally describe and analyze synaptic scaling based on results from experimental studies and demonstrate that the combination of different conventional plasticity mechanisms and synaptic scaling provides a powerful general framework for regulating network connectivity. In addition, we design several simple models that reproduce experimentally observed synaptic distributions as well as the observed synaptic modifications during sustained activity changes. These models predict that the combination of plasticity with scaling generates globally stable, input-controlled synaptic patterns, also in recurrent networks. Thus, in combination with other forms of plasticity, synaptic scaling can robustly yield neuronal circuits with high synaptic diversity, which potentially enables robust dynamic storage of complex activation patterns. This mechanism is even more pronounced when considering networks with a realistic degree of inhibition. Synaptic scaling combined with plasticity could thus be the basis for learning structured behavior even in initially random networks.

The Formation of Multi-synaptic Connections by the Interaction of Synaptic and Structural Plasticity and Their Functional Consequences

Cortical connectivity emerges from the permanent interaction between neuronal activity and synaptic as well as structural plasticity. An important experimentally observed feature of this connectivity is the distribution of the number of synapses from one neuron to another, which has been measured in several cortical layers. All of these distributions are bimodal with one peak at zero and a second one at a small number (3–8) of synapses. In this study, using a probabilistic model of structural plasticity, which depends on the synaptic weights, we explore how these distributions can emerge and which functional consequences they have. We find that bimodal distributions arise generically from the interaction of structural plasticity with synaptic plasticity rules that fulfill the following biological realistic constraints: First, the synaptic weights have to grow with the postsynaptic activity. Second, this growth curve and/or the input-output relation of the postsynaptic neuron have to change sub-linearly (negative curvature). As most neurons show such input-output-relations, these constraints can be fulfilled by many biological reasonable systems. Given such a system, we show that the different activities, which can explain the layer-specific distributions, correspond to experimentally observed activities. Considering these activities as working point of the system and varying the pre- or postsynaptic stimulation reveals a hysteresis in the number of synapses. As a consequence of this, the connectivity between two neurons can be controlled by activity but is also safeguarded against overly fast changes. These results indicate that the complex dynamics between activity and plasticity will, already between a pair of neurons, induce a variety of possible stable synaptic distributions, which could support memory mechanisms.

Opposing Effects of Neuronal Activity on Structural Plasticity

The connectivity of the brain is continuously adjusted to new environmental influences by several activity-dependent adaptive processes. The most investigated adaptive mechanism is activity-dependent functional or synaptic plasticity regulating the transmission efficacy of existing synapses. Another important but less prominently discussed adaptive process is structural plasticity, which changes the connectivity by the formation and deletion of synapses. In this review, we show, based on experimental evidence, that structural plasticity can be classified similar to synaptic plasticity into two categories: (i) Hebbian structural plasticity, which leads to an increase (decrease) of the number of synapses during phases of high (low) neuronal activity and (ii) homeostatic structural plasticity, which balances these changes by removing and adding synapses. Furthermore, based on experimental and theoretical insights, we argue that each type of structural plasticity fulfills a different function. While Hebbian structural changes enhance memory lifetime, storage capacity, and memory robustness, homeostatic structural plasticity self-organizes the connectivity of the neural network to assure stability. However, the link between functional synaptic and structural plasticity as well as the detailed interactions between Hebbian and homeostatic structural plasticity are more complex. This implies even richer dynamics requiring further experimental and theoretical investigations.

Analysis of synaptic scaling in combination with hebbian plasticity in several simple networks.

Conventional synaptic plasticity in combination with synaptic scaling is a biologically plausible plasticity rule that guides the development of synapses toward stability. Here we analyze the development of synaptic connections and the resulting activity patterns in different feed-forward and recurrent neural networks, with plasticity and scaling. We show under which constraints an external input given to a feed-forward network forms an input trace similar to a cell assembly (Hebb, 1949) by enhancing synaptic weights to larger stable values as compared to the rest of the network. For instance, a weak input creates a less strong representation in the network than a strong input which produces a trace along large parts of the network. These processes are strongly influenced by the underlying connectivity. For example, when embedding recurrent structures (excitatory rings, etc.) into a feed-forward network, the input trace is extended into more distant layers, while inhibition shortens it. These findings provide a better understanding of the dynamics of generic network structures where plasticity is combined with scaling. This makes it also possible to use this rule for constructing an artificial network with certain desired storage properties.

Formation and Maintenance of Robust Long-Term Information Storage in the Presence of Synaptic Turnover

A long-standing problem is how memories can be stored for very long times despite the volatility of the underlying neural substrate, most notably the high turnover of dendritic spines and synapses. To address this problem, here we are using a generic and simple probabilistic model for the creation and removal of synapses. We show that information can be stored for several months when utilizing the intrinsic dynamics of multi-synapse connections. In such systems, single synapses can still show high turnover, which enables fast learning of new information, but this will not perturb prior stored information (slow forgetting), which is represented by the compound state of the connections. The model matches the time course of recent experimental spine data during learning and memory in mice supporting the assumption of multi-synapse connections as the basis for long-term storage.

Synaptic plasticity in a recurrent neural network for versatile and adaptive behaviors of a walking robot

Walking animals, like insects, with little neural computing can effectively perform complex behaviors. For example, they can walk around their environment, escape from corners/deadlocks, and avoid or climb over obstacles. While performing all these behaviors, they can also adapt their movements to deal with an unknown situation. As a consequence, they successfully navigate through their complex environment. The versatile and adaptive abilities are the result of an integration of several ingredients embedded in their sensorimotor loop. Biological studies reveal that the ingredients include neural dynamics, plasticity, sensory feedback, and biomechanics. Generating such versatile and adaptive behaviors for a many degrees-of-freedom (DOFs) walking robot is a challenging task. Thus, in this study, we present a bio-inspired approach to solve this task. Specifically, the approach combines neural mechanisms with plasticity, exteroceptive sensory feedback, and biomechanics. The neural mechanisms consist of adaptive neural sensory processing and modular neural locomotion control. The sensory processing is based on a small recurrent neural network consisting of two fully connected neurons. Online correlation-based learning with synaptic scaling is applied to adequately change the connections of the network. By doing so, we can effectively exploit neural dynamics (i.e., hysteresis effects and single attractors) in the network to generate different turning angles with short-term memory for a walking robot. The turning information is transmitted as descending steering signals to the neural locomotion control which translates the signals into motor actions. As a result, the robot can walk around and adapt its turning angle for avoiding obstacles in different situations. The adaptation also enables the robot to effectively escape from sharp corners or deadlocks. Using backbone joint control embedded in the the locomotion control allows the robot to climb over small obstacles. Consequently, it can successfully explore and navigate in complex environments. We firstly tested our approach on a physical simulation environment and then applied it to our real biomechanical walking robot AMOSII with 19 DOFs to adaptively avoid obstacles and navigate in the real world.

The Use of Hebbian Cell Assemblies for Nonlinear Computation.

When learning a complex task our nervous system self-organizes large groups of neurons into coherent dynamic activity patterns. During this, a network with multiple, simultaneously active, and computationally powerful cell assemblies is created. How such ordered structures are formed while preserving a rich diversity of neural dynamics needed for computation is still unknown. Here we show that the combination of synaptic plasticity with the slower process of synaptic scaling achieves (i) the formation of cell assemblies and (ii) enhances the diversity of neural dynamics facilitating the learning of complex calculations. Due to synaptic scaling the dynamics of different cell assemblies do not interfere with each other. As a consequence, this type of self-organization allows executing a difficult, six degrees of freedom, manipulation task with a robot where assemblies need to learn computing complex non-linear transforms and – for execution – must cooperate with each other without interference. This mechanism, thus, permits the self-organization of computationally powerful sub-structures in dynamic networks for behavior control.

An information theoretic model of information processing in the Drosophila olfactory system: the role of inhibitory neurons for system efficiency

Fruit flies (Drosophila melanogaster) rely on their olfactory system to process environmental information. This information has to be transmitted without system-relevant loss by the olfactory system to deeper brain areas for learning. Here we study the role of several parameters of the flys olfactory system and the environment and how they influence olfactory information transmission. We have designed an abstract model of the antennal lobe, the mushroom body and the inhibitory circuitry. Mutual information between the olfactory environment, simulated in terms of different odor concentrations, and a sub-population of intrinsic mushroom body neurons (Kenyon cells) was calculated to quantify the efficiency of information transmission. With this method we study, on the one hand, the effect of different connectivity rates between olfactory projection neurons and firing thresholds of Kenyon cells. On the other hand, we analyze the influence of inhibition on mutual information between environment and mushroom body. Our simulations show an expected linear relation between the connectivity rate between the antennal lobe and the mushroom body and firing threshold of the Kenyon cells to obtain maximum mutual information for both low and high odor concentrations. However, contradicting all-day experiences, high odor concentrations cause a drastic, and unrealistic, decrease in mutual information for all connectivity rates compared to low concentration. But when inhibition on the mushroom body is included, mutual information remains at high levels independent of other system parameters. This finding points to a pivotal role of inhibition in fly information processing without which the system efficiency will be substantially reduced.