Sensory Systems/Zebrafish

The Zebrafish Olfactory System
The zebrafish (Danio rerio) is a freshwater teleost native in Southeast Asia [1]. Water flow through the nose is laminar and unidirectional. Even when a zebrafish is not moving, water flow is provided by motile cilia such that a constant odourant supply is provided. Hence, a zebrafish constantly screens the odour space by moving through the environment. The first relay station of odour information is the olfactory bulb. Information passing in the olfactory bulb is an extremely complex process which includes multiple steps of transformation performed by the underlying circuitry. For instance, an odour consisting of different molecules activates a specific set of odourant receptors on olfactory sensory neurons, which terminate in the olfactory bulb in an array of glomeruli. Hence, an odour is encoded in a combinatorial fashion of glomerular activation patterns. An adult zebrafish olfactory bulb contains about 140 stereotyped glomeruli [2]. A glomerulus is a functional unit consisting of synaptic connections within three different cell classes(Figure 1)[3].


 * The incoming olfactory sensory neurons expressing the same odorant receptor. All synaptic connections are excitatory.
 * Inhibitory interneurons responsible for multiple transformations of the odour signal. In Zebrafish, interneurons can be subdivided into periglomerular cells, granule cells and short axon cells, each of which has distinct morphological features.
 * Mitral cells, which relay the signal out of the olfactory bulb to higher brain areas. In adult Zebrafish there are about 1’500 mitral cells. 70% of these mitral cells receive input from one distinct glomerulus [4].



For the olfactory system, the broad concept of receptive fields present in the visual system is only valid in a very general sense. As described above, a glomerulus receives input from olfactory sensory neurons expressing the same odourant receptor. As a result, a rough spatial chemotopic map is spanned across the olfactory bulb. In other words, different classes of natural odours of the Zebrafish (amino acids, bile acids, nucleotides) activate different anatomical domains of the olfactory bulb [1].

Pattern Decorrelation
A computational step ongoing in the glomeruli of the zebrafish is pattern decorrelation, which reduces the overlap between activity patterns representing similar odours. Think of two similar fragrances such as cumin seed essential and fennel seed essential. Due to the similar molecular composition, both fragrances initially evoke a similar glomerular activation pattern. Initially, these activation patterns are therefore highly correlated. In other words, odourants with similar molecular features activate overlapping combinations of glomeruli. Subsequently, most of the correlations decrease and the glomerular activity gets redistributed and settles to a steady state. From a computational point of view pattern decorrelation is an useful early step in many pattern classification procedures. It does not increase the information content of an odour representation and it does not increase the performance of an optimal classifier. Rather, it can improve the performance of suboptimal classifiers by increasing the tolerance region(Figure 2) [5]. In nervous systems this process could be important for learning odours and subsequent identification of these odours [1].









Odour evoked glomerular activity patterns can be measured optically by introducing calcium sensors selectively into the olfactory sensory neurons [6]. This was done in Zebrafishes to analyze the glomerular activity pattern evoked by 16 amino acids, which belong to the natural odour space of zebrafishes. To study pattern decorrelation, responses to highly similar amino acids (Phe, Tyr or Trp) were measured across the mitral cells by multiphoton calcium imaging. Multiphoton calcium imaging revealed that the activity patterns in spatially clustered mitral cells initially overlapped. This overlap subsequently decreased because subsets of these mitral cells became less active or silent, resulting in a local, but not a global, sparsening of MC activity. Concomitantly, the activity of inhibitory interneurons increased and became more dense. Figure 3 shows real data of the activity of Mitral cells before and after a Zebrafish olfactory bulb is exposed to two different odourants.

Other Possible Simulation Approaches of Pattern Decorrelation
Analytical approaches and simulations showed that generic networks of Stochastic networks of rectifying elements (SNOREs) with uniform synaptic weights decorrelate specific input patterns by a mechanism referred to as reTIDe [1]. Thresholding the input pattern is the first step in reTIDe. SNOREs consist of threshold-linear units that are randomly connected by synapses of uniform weight. For any positively correlated and normally distributed input patterns, this nonlinearity always results in decorrelation and that decorrelation monotonically increases with the threshold level [7]. This decorrelation is then amplified by feeding the thresholded output patterns back into the network through recurrent connections until a steady state is reached [6]. For mathematical proof and analysis, refer to ONLINE METHOD of the referenced paper [7].
 * Recurrence-enhanced threshold-induced decorrelation (reTIDe)


 * Optimizing a weight matrix to model activities of interneurons
 * $$ W \cdot X(t) = X(t+1) $$

W is a weight matrix which represents activity of interneurons between Mitral cells. For instance, its element represents connectivity strength from Mitral cell to Mitral cell. X(t) is a matrix representing firing rates to stimulus 1 and 2 of each individual Mitral cell at time t. Given more data set of X in time, it is probable that the weight matrix W can be optimized.

Conclusions
Pattern decorrelation in the olfactory bulb is a computational step which has been observed in the zebrafish. However, there has not been proposed a mathematical model to explain pattern decorrelation on a mechanistic basis. A model of how excitatory and inhibitory neurons interact together in the olfactory bulb will help to understand how pattern decorrelation is performed on a neurons level. But even so, such a model implies a full connectivity map of the olfactory bulb. This goal mainly depends on the achievements of the acquisition of large datasets with scanning electron microscopy techniques and dense EM-based reconstruction of this data in the next years.

Acknowledgement
We express our special gratitude to Prof. Rainer Friedrich for his advice on this work.