Kingsley J. A. Cox

Monitoring activity in neuronal populations with single-cell resolution in a behaving vertebrate.

Vertebrate behaviours are produced by activity in populations of neurons, but the techniques typically used to study activity allow only one or very few nerve cells to be monitored at a time. This limitation has prompted the development of methods of imaging activity in the nervous system. The overall goal of these methods is to image neural activity non-invasively in populations of neurons, ideally with high spatial and temporal resolution. We have moved closer to this goal by using confocal calcium imaging to monitor neural activity in the transparent larvae of zebrafish. Neurons were labelled either by backfilling from injections of the calcium indicator (Calcium Green dextran) into muscle or spinal cord of larvae or by injections into blastomeres early in development. The labelled neurons were bright enough at resting calcium levels to allow the identification of individual neurons in the live, intact fish, based upon their dendritic and axonal morphology. The neurons from the live animal could also be reconstructed in three dimensions for morphometric study. Neurons increased their fluorescence during activity produced by direct electrical stimulation and during escape behaviours elicited by an abrupt touch to the head or tail of the fish. The rise in calcium associated with a single action potential could be detected as an increase in fluorescence of at least 7--10%, but neurons typically showed much larger increases during behaviour. Calcium signals in the dendrites, soma and nucleus could be resolved, especially when using the line-scanning mode, which provides 2-ms temporal resolution. The imaging was used to study activity in populations of motoneurons and hindbrain neurons during the escape behaviour fish use to avoid predators. We found a massive activation of the motoneuron pool and a differential activation of populations of hindbrain neurons during escapes. The latter finding confirms predictions that the activity pattern of hindbrain neurons may help to determine the directionality of the escape. This approach should prove useful for studying the activity of populations of neurons throughout the nervous system in both normal and mutant lines of fish. 1998

Labeling blastomeres with a calcium indicator: a non-invasive method of visualizing neuronal activity in zebrafish.

Injections of the calcium indicator calcium green dextran (CGD) into zebrafish embryos at the 1-4 cell stages were used to monitor the activity of neurons in larval fish. Dye was pressure injected into a single cell and the fish allowed to develop until post-hatching, when they were embedded in agar and viewed under a confocal microscope. Labeled larval cells, including identifiable neuronal classes such as Rohon-Beard cells and olfactory neurons, were clearly visible with extensive labeling of the whole fish following injections at the one cell embryonic stage, and a mosaic labeling pattern following injections at the 2 or 4 cell stages. Activity of neurons in the spinal cord, as indicated by intracellular calcium concentration changes, was observed directly by monitoring fluorescence changes of individual spinal neurons and groups of spinal neurons on a confocal microscope. Fluorescence increases of between 9 and 55% in spinal neurons were seen during escape responses produced when the fish was tapped on the tail. This technique can potentially be used to monitor the activity of any neuron or group of neurons with respect to behavior non-invasively in intact living zebrafish.

Hebbian errors in learning: An analysis using the Oja model

BACKGROUND Recent work on long term potentiation in brain slices shows that Hebbs rule is not completely synapse-specific, probably due to intersynapse diffusion of calcium or other factors. We previously suggested that such errors in Hebbian learning might be analogous to mutations in evolution. METHODS AND FINDINGS We examine this proposal quantitatively, extending the classical Oja unsupervised model of learning by a single linear neuron to include Hebbian inspecificity. We introduce an error matrix E, which expresses possible crosstalk between updating at different connections. When there is no inspecificity, this gives the classical result of convergence to the first principal component of the input distribution (PC1). We show the modified algorithm converges to the leading eigenvector of the matrix EC, where C is the input covariance matrix. In the most biologically plausible case when there are no intrinsically privileged connections, E has diagonal elements Q and off-diagonal elements (1-Q)/(n-1), where Q, the quality, is expected to decrease with the number of inputs n and with a synaptic parameter b that reflects synapse density, calcium diffusion, etc. We study the dependence of the learning accuracy on b, n and the amount of input activity or correlation (analytically and computationally). We find that accuracy increases (learning becomes gradually less useful) with increases in b, particularly for intermediate (i.e., biologically realistic) correlation strength, although some useful learning always occurs up to the trivial limit Q=1/n. CONCLUSIONS AND SIGNIFICANCE We discuss the relation of our results to Hebbian unsupervised learning in the brain. When the mechanism lacks specificity, the network fails to learn the expected, and typically most useful, result, especially when the input correlation is weak. Hebbian crosstalk would reflect the very high density of synapses along dendrites, and inevitably degrades learning.

Synaptic Darwinism and neocortical function

Abstract We propose that certain brain systems, such as those of neocortex, exploit a fusion of ideas from neural networks and evolutionary computation, and that several previously puzzling features of thalamocortical circuitry and physiology can be understood as consequences of this fusion. The starting point is a consideration of anatomical errors in the recently described digital strengthening of synaptic connections, which are analogous to mutations. A mathematical model of this process shows the equivalence of the intrinsic error rate and a “correlation ratio” which reflects the spatial variation in the degree of synchrony of neural firing. The correlation ratio plays a similar role to fitness ratios in genetic algorithms. It is argued that a major trend in brain evolution has been decreases in the intrinsic error rate, allowing increases in circuit complexity, but that biophysical limits to this trend have forced the neocortex to adopt a virtual error-reduction strategy. This requires online measurement of correlation ratios and control of the plasticity of the connections formed by individual neurons.

Implications of synaptic digitisation and error for neocortical function

Abstract Recent work in hippocampus suggests that correlation-based synaptic strengthening occurs both imprecisely and digitally. We explore this in a model in which synapses are created according to a fitness function and are occasionally incorrectly placed. Synapses spread beyond the high fitness (wm) area to lower fitness (wp) areas to an extent that depends on the error rate and the fitness ratio wm/wp. This limits the accuracy of connections and thus the size of neural networks. We suggest that in neocortex layer 6 cells measure wm/wp and control the plasticity of thalamic relay cells via their burst/tonic transition. If errors do occur despite this mechanism, they can act as seeds for new learning. This in turn requires offline rewiring of layer 6 connections by processes that resemble REM and slow-wave sleep.

Imaging Neural Activity With Single Cell Resolution in an Intact, Behaving Vertebrate

JOSEPH R. FETCHO, KINGSLEY J. A. COX, AND DONALD M. O’MALLEY Depurtment ofNeurobiology and Behavior, State University ofNew York at Stony Brook, Stony Brook, New York I1 794-5230 Introduction Most behaviors are produced by activity in popula- tions of neurons, but the physiological approaches com- monly used to study neural circuits allow the activity of only one or very few neurons to be monitored at a time. What is needed are approaches that allow the monitoring of activity in a group of cells-preferably a large group- while simultaneously permitting the identification and the recording of activity from each cell. Progress along these lines has been made with the use of electrode arrays (Wilson and McNaughton, 1994). An alternative, very promising approach-i.e., imaging-offers an easy de- termination of both the activity and the identity of cells (Wu et ul., 1994; O’Donovan et al., 1993). In this method, the neurons are labeled with an indicator dye that signals their activity, and the dye is then used to monitor the cells that are active during a particular be- havior. The ideal situation would be one in which a pop- ulation of neurons could be labeled and their activities observed with single-cell resolution in an intact, behav- ing animal. This ideal is difficult to achieve with verte- brates because most of them are opaque, so the neurons cannot be seen in the intact animal. Notable exceptions are the larvae of many fishes, which are transparent and thus especially suitable for imaging neurons. We have developed approaches in which a fluorescent calcium in- dicator is used to monitor neural activity in intact fish. Neurons that are labeled with the indicator increase in

Hebbian learning from higher-order correlations requires crosstalk minimization

Activity-dependent synaptic plasticity should be extremely connection specific, though experiments have shown it is not, and biophysics suggests it cannot be. Extreme specificity (near-zero “crosstalk”) might be essential for unsupervised learning from higher-order correlations, especially when a neuron has many inputs. It is well known that a normalized nonlinear Hebbian rule can learn “unmixing” weights from inputs generated by linearly combining independently fluctuating nonGaussian sources using an orthogonal mixing matrix. We previously reported that even if the matrix is only approximately orthogonal, a nonlinear-specific Hebbian rule can usually learn almost correct unmixing weights (Cox and Adams in Front Comput Neurosci 3: doi:10.3389/neuro.10.011.20092009). We also reported simulations that showed that as crosstalk increases from zero, the learned weight vector first moves slightly away from the crosstalk-free direction and then, at a sharp threshold level of inspecificity, jumps to a completely incorrect direction. Here, we report further numerical experiments that show that above this threshold, residual learning is driven instead almost entirely by second-order input correlations, as occurs using purely Gaussian sources or a linear rule, and any amount of crosstalk. Thus, in this “ICA” model learning from higher-order correlations, required for unmixing, requires high specificity. We compare our results with a recent mathematical analysis of the effect of crosstalk for exactly orthogonal mixing, which revealed that a second, even lower, threshold, exists below which successful learning is impossible unless weights happen to start close to the correct direction. Our simulations show that this also holds when the mixing is not exactly orthogonal. These results suggest that if the brain uses simple Hebbian learning, it must operate with extraordinarily accurate synaptic plasticity to ensure powerful high-dimensional learning. Synaptic crowding would preclude this when inputs are numerous, and we propose that the neocortex might be distinguished by special circuitry that promotes extreme specificity for high-dimensional nonlinear learning.

From Life to Mind: 2 Prosaic Miracles?

The origin of life from matter and the subsequent emergence of mind were fundamental events. Our work is based on the idea that the chemical/genetic/mathematical framework developed over the last 150 years to explain the first is conceptually similar to the neural/psychological/mathematical framework needed to understand the second. First we outline the first, seemingly adequate, framework and then we explain some related, unusual and controversial, ideas that offer a “translation” into neural terms. The core idea is that the extraordinary, mysterious and qualitatively unique features of “life” and “mind” arise because of extraordinary (though completely explicable) levels of accuracy of the relevant elementary processes (base-copying and synaptic strengthening). The living and the mental might hinge on prosaic, though accurate, lower-level machinery.