Modelling the emergence of whisker barrels

Segregation of Multimodal Inputs Into Discrete Midbrain Compartments During an Early Critical Period

The lateral cortex of the inferior colliculus (LCIC) is a multimodal subdivision of the midbrain inferior colliculus (IC) that plays a key role in sensory integration. The LCIC is compartmentally-organized, exhibiting a series of discontinuous patches or modules surrounded by an extramodular matrix. In adult mice, somatosensory afferents target LCIC modular zones, while auditory afferents terminate throughout the encompassing matrix. Recently, we defined an early LCIC critical period (birth: postnatal day 0 to P12) based upon the concurrent emergence of its neurochemical compartments (modules: glutamic acid decarboxylase, GAD+; matrix: calretinin, CR+), matching Eph-ephrin guidance patterns, and specificity of auditory inputs for its matrix. Currently lacking are analogous experiments that address somatosensory afferent shaping and the construction of discrete LCIC multisensory maps. Combining living slice tract-tracing and immunocytochemical approaches in a developmental series of GAD67-GFP knock-in mice, the present study characterizes: (1) the targeting of somatosensory terminals for emerging LCIC modular fields; and (2) the relative separation of somatosensory and auditory inputs over the course of its established critical period. Results indicate a similar time course and progression of LCIC projection shaping for both somatosensory (corticocollicular) and auditory (intracollicular) inputs. While somewhat sparse and intermingling at birth, modality-specific projection patterns soon emerge (P4–P8), coincident with peak guidance expression and the appearance of LCIC compartments. By P12, an adult-like arrangement is in place, with fully segregated multimodal afferent arrays. Quantitative measures confirm increasingly distinct input maps, exhibiting less projection overlap with age. Potential mechanisms whereby multisensory LCIC afferent systems recognize and interface with its emerging modular-matrix framework are discussed.

Biological action at a distance: Correlated pattern formation in adjacent tessellation domains without communication

Tessellations emerge in many natural systems, and the constituent domains often contain regular patterns, raising the intriguing possibility that pattern formation within adjacent domains might be correlated by the geometry, without the direct exchange of information between parts comprising either domain. We confirm this paradoxical effect, by simulating pattern formation via reaction-diffusion in domains whose boundary shapes tessellate, and showing that correlations between adjacent patterns are strong compared to controls that self-organize in domains with equivalent sizes but unrelated shapes. The effect holds in systems with linear and non-linear diffusive terms, and for boundary shapes derived from regular and irregular tessellations. Based on the prediction that correlations between adjacent patterns should be bimodally distributed, we develop methods for testing whether a given set of domain boundaries constrained pattern formation within those domains. We then confirm such a prediction by analysing the development of ‘subbarrel’ patterns, which are thought to emerge via reaction-diffusion, and whose enclosing borders form a Voronoi tessellation on the surface of the rodent somatosensory cortex. In more general terms, this result demonstrates how causal links can be established between the dynamical processes through which biological patterns emerge and the constraints that shape them.

Patterns can form in biological systems as a net effect of dynamical interactions that are excitatory over short distances and inhibitory over larger distances. Patterns that form in this way are known to reflect the shape of the boundary conditions that contain them. But observing that a particular pattern is contained by a boundary is not enough to determine whether or not that boundary was a constraint on pattern formation. Here we develop a novel test for the influence of boundary shape on pattern formation, based on comparing patterns contained by boundaries whose shapes tessellate and thus are geometrically related. Applying this test to patterns of cell density measured in the developing neocortex confirms that cortical column boundaries constrain pattern formation during the first postnatal weeks. In more general terms, our analysis reveals that strong relationships between patterns that form in adjacent biological domains are to be expected based purely on geometrical effects, even if no information is exchanged between those domains during the process of pattern formation. Our analysis provides a means for testing current theories about the fundamental role that constraints play in organising biological systems.

Computation, wiring, and plasticity in synaptic clusters

Synaptic clusters on dendrites are extraordinarily compact computational building blocks. They contribute to key local computations through biophysical and biochemical signaling that utilizes convergence in space and time as an organizing principle. However, these computations can only arise in very special contexts. Dendritic cluster computations, their highly organized input connectivity, and the mechanisms for their formation are closely linked, yet these have not been analyzed as parts of a single process. Here, we examine these linkages. The sheer density of axonal and dendritic arborizations means that there are far more potential connections (close enough for a spine to reach an axon) than actual ones. We see how dendritic clusters draw upon electrical, chemical, and mechano-chemical signaling to implement the rules for formation of connections and subsequent computations. Crucially, the same mechanisms that underlie their functions also underlie their formation.