Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures

Dynamic and thermodynamic models of adaptation

The concept of biological adaptation was closely connected to some mathematical, engineering and physical ideas from the very beginning. Cannon in his "The wisdom of the body" (1932) systematically used the engineering vision of regulation. In 1938, Selye enriched this approach by the notion of adaptation energy. This term causes much debate when one takes it literally, as a physical quantity, i.e. a sort of energy. Selye did not use the language of mathematics systematically, but the formalization of his phenomenological theory in the spirit of thermodynamics was simple and led to verifiable predictions. In 1980s, the dynamics of correlation and variance in systems under adaptation to a load of environmental factors were studied and the universal effect in ensembles of systems under a load of similar factors was discovered: in a crisis, as a rule, even before the onset of obvious symptoms of stress, the correlation increases together with variance (and volatility). During 30 years, this effect has been supported by many observations of groups of humans, mice, trees, grassy plants, and on financial time series. In the last ten years, these results were supplemented by many new experiments, from gene networks in cardiology and oncology to dynamics of depression and clinical psychotherapy. Several systems of models were developed: the thermodynamic-like theory of adaptation of ensembles and several families of models of individual adaptation. Historically, the first group of models was based on Selye's concept of adaptation energy and used fitness estimates. Two other groups of models are based on the idea of hidden attractor bifurcation and on the advection-diffusion model for distribution of population in the space of physiological attributes. We explore this world of models and experiments, starting with classic works, with particular attention to the results of the last ten years and open questions.

Cytosolic PSD-95 interactor alters functional organization of neural circuits and AMPA receptor signaling independent of PSD-95 binding

Cytosolic PSD-95 interactor (cypin) regulates many aspects of neuronal development and function, ranging from dendritogenesis to synaptic protein localization. While it is known that removal of postsynaptic density protein-95 (PSD-95) from the postsynaptic density decreases synaptic N-methyl-D-aspartate (NMDA) receptors and that cypin overexpression protects neurons from NMDA-induced toxicity, little is known about cypin's role in AMPA receptor clustering and function. Experimental work shows that cypin overexpression decreases PSD-95 levels in synaptosomes and the PSD, decreases PSD-95 clusters/μm², and increases mEPSC frequency. Analysis of microelectrode array (MEA) data demonstrates that cypin or cypinΔPDZ overexpression increases sensitivity to CNQX (cyanquixaline) and AMPA receptor-mediated decreases in spike waveform properties. Network-level analysis of MEA data reveals that cypinΔPDZ overexpression causes networks to be resilient to CNQX-induced changes in local efficiency. Incorporating these findings into a computational model of a neural circuit demonstrates a role for AMPA receptors in cypin-promoted changes to networks and shows that cypin increases firing rate while changing network functional organization, suggesting cypin overexpression facilitates information relay but modifies how information is encoded among brain regions. Our data show that cypin promotes changes to AMPA receptor signaling independent of PSD-95 binding, shaping neural circuits and output to regions beyond the hippocampus.

Simple model of complex dynamics of activity patterns in developing networks of neuronal cultures

Living neuronal networks in dissociated neuronal cultures are widely known for their ability to generate highly robust spatiotemporal activity patterns in various experimental conditions. Such patterns are often treated as neuronal avalanches that satisfy the power scaling law and thereby exemplify self-organized criticality in living systems. A crucial question is how these patterns can be explained and modeled in a way that is biologically meaningful, mathematically tractable and yet broad enough to account for neuronal heterogeneity and complexity. Here we derive and analyse a simple network model that may constitute a response to this question. Our derivations are based on few basic phenomenological observations concerning the input-output behavior of an isolated neuron. A distinctive feature of the model is that at the simplest level of description it comprises of only two variables, the network activity variable and an exogenous variable corresponding to energy needed to sustain the activity, and few parameters such as network connectivity and efficacy of signal transmission. The efficacy of signal transmission is modulated by the phenomenological energy variable. Strikingly, this simple model is already capable of explaining emergence of network spikes and bursts in developing neuronal cultures. The model behavior and predictions are consistent with published experimental evidence on cultured neurons. At the larger, cellular automata scale, introduction of the energy-dependent regulatory mechanism results in the overall model behavior that can be characterized as balancing on the edge of the network percolation transition. Network activity in this state shows population bursts satisfying the scaling avalanche conditions. This network state is self-sustainable and represents energetic balance between global network-wide processes and spontaneous activity of individual elements.