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1. The effect of growth on the electrotonic structure and synaptic integrative properties of the lateral giant (LG) interneuron was assessed from anatomic and electrophysiological measurements of LGs in small (1-2.4 cm) and large (9-11.2 cm) crayfish and from calculated responses of mathematical models of these neurons. Postsynaptic responses of small and large LGs were compared with model responses to determine whether the differences in the neurons' responses result from growth-related changes in their physical characteristics. 2. LG neurons in the terminal abdominal ganglia of small and large crayfish are similar in shape but differ in size according to an approximately isometric pattern of growth. The soma diameter of the large LG is 2.2 times larger than the small LG, the major ipsilateral dendrite is 2.8 times longer and 3.6 times greater in diameter, and the axon is 7.6 times longer and 4.5 times greater in diameter. The projected area of the major ipsilateral dendrite of LG in the horizontal plane of the terminal abdominal ganglion is 27 times larger in the large than in the small crayfish. 3. LG's input resistance was nearly 80% smaller in the large (167 K omega) than in the small (742 K omega) crayfish when measured at or near the initial axon segment. The cell's membrane time constant displayed an opposite relationship, with the value in the large crayfish (20.9 ms) nearly two-and-a-half times larger than the value in the small crayfish (8.6 ms). 4. Simultaneous recordings were made from the distal portion of the ipsilateral dendrite and the initial axon segment of small and large LGs to determine how excitatory postsynaptic potentials (EPSPs) are attenuated or filtered by the electrotonic properties of the different sized cells. In the small LG, the fast alpha and the slower beta components of compound EPSPs evoked by sensory nerve stimulation were similarly attenuated. In the large LG, the alpha component of the compound EPSP was much more attenuated and smoothed than the slower beta component. 5. Multicompartment models of small and large LGs were constructed and used to test whether differences in the two neurons' physical properties could account for the differences in their passive response properties.(ABSTRACT TRUNCATED AT 250 WORDS)
Quantifying the complexity of neural activity has provided fundamental insights into cognition, consciousness, and clinical conditions. However, the most widely used approach to estimate the complexity of neural dynamics, Lempel-Ziv complexity (LZ), has fundamental limitations that substantially restrict its domain of applicability. In this article we leverage the information-theoretic foundations of LZ to overcome these limitations by introducing a complexity estimator based on state-space models -- which we dub Complexity via State-space Entropy Rate (CSER). While having a performance equivalent to LZ in discriminating states of consciousness, CSER boasts two crucial advantages: 1) CSER offers a principled decomposition into spectral components, which allows us to rigorously investigate the relationship between complexity and spectral power; and 2) CSER provides a temporal resolution two orders of magnitude better than LZ, which allows complexity analyses of e.g. event-locked neural signals. As a proof of principle, we use MEG, EEG and ECoG datasets of humans and monkeys to show that CSER identifies the gamma band as the main driver of complexity changes across states of consciousness; and reveals early entropy increases that precede the standard ERP in an auditory mismatch negativity paradigm by approximately 20ms. Overall, by overcoming the main limitations of LZ and substantially extending its range of applicability, CSER opens the door to novel investigations on the fine-grained spectral and temporal structure of the signal complexity associated with cognitive processes and conscious states.
1. The postembryonic development of the crayfish LG tailflip command neuron's response to mechanosensory input was studied with standard electrophysiological techniques in animals between 1 and 12 cm long. 2. LG neurons are present in each abdominal hemisegment where they receive direct and indirect excitatory input from mechanosensory afferents. In both small and large crayfish, electrical stimulation of an abdominal ganglionic nerve containing those afferents evoked a compound excitatory postsynaptic potential (EPSP) with an early, reliable alpha component and a later, depression-prone beta wave. It is known that the alpha and beta components are produced by inputs from primary mechanosensory afferents and interneurons, respectively. 3. In crayfish < 2 cm long, LG was excited by the alpha component. When superthreshold, the alpha component triggered a single spike; additional excitation provided by the later beta wave presumably was preempted by refractoriness following the alpha spike and by recurrent inhibition of LG excited by the spike. LG was excited reliably by the alpha component in response to repeated superthreshold stimulation. 4. In crayfish between 2 and 3 cm, LG was excited more readily by the beta wave than by the alpha component. LG's beta spike response habituated to repeated stimulation at 1 Hz, and the beta EPSP depressed whereas the alpha component was largely unchanged. The appearance of the cellular substrates of habituation correlates with the reported onset of behavioral habituation of the tailflip response. Higher stimulus levels brought the alpha EPSP to threshold. Repetitive stimulation at these levels reliably evoked LG spikes from the alpha EPSP.(ABSTRACT TRUNCATED AT 250 WORDS)
We introduce a notion of emergence for coarse-grained macroscopic variables associated with highlymultivariate microscopic dynamical processes, in the context of a coupled dynamical environment.Dynamical independence instantiates the intuition of an emergent macroscopic process as one possessing the characteristics of a dynamical system "in its own right", with its own dynamical laws distinct from those of the underlying microscopic dynamics. We quantify (departure from) dynamical independence by a transformation-invariant Shannon information-based measure of dynamical dependence. We emphasise the data-driven discovery of dynamically-independent macroscopic variables, and introduce the idea of a multiscale "emergence portrait" for complex systems. We show how dynamical dependence may be computed explicitly for linear systems via state-space modelling, in both time and frequency domains, facilitating discovery of emergent phenomena at all spatiotemporal scales. We discuss application of the state-space operationalisation to inference of the emergence portrait for neural systems from neurophysiological time-series data. We also examine dynamical independence for discrete-and continuous-time deterministic dynamics, with potential application to Hamiltonian mechanics and classical complex systems such as flocking and cellular automata.
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