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Challenges in Modeling Neural Development

Posted by Gary_JP_Group on 28 Feb 2007 at 13:53 GMT

In a recent paper (Ringach, 2007), Dario Ringach presents a novel account of cortical development, addressing a broad range of data on the formation of orientation selectivity and ocular dominance columns in the visual system. The model proposed is based on an abstract (rather than mechanistic) statistical approach to connectivity between retina, LGN, and visual cortex. In Ringach’s model, the probability of establishing connections between regions is primarily dependent on a Gaussian function, where the highest probability occurs if the spatial location of receptive fields overlaps completely (given cells of the same signature – ON or OFF). (A similar probability is also computed to determine synaptic efficacy). The resulting statistical characterizing can concisely account for an impressive amount of developmental data, and is part of a broader trend towards statistical approaches to neural development. For instance, a probabilistic Markov model was recently developed to account for the interplay of genes and activity-based mechanisms in normal and genetically-altered stages of early retinocollicular development (Koulakov & Tsigankov, 2004).

Ultimately, however, while a statistical account can help shed new light on some of the fundamental properties of experimental data, it cannot supersede more mechanistic accounts of these phenomena (Koulakov & Chklovskii, 2001), such as those that incorporate precise biophysical mechanisms, including Hebbian learning (Hebb, 1949) and physical constraints (e.g., minimization of wiring length; Koulakov & Chklovskii, 2001). An examination of some of the limits of Ringach’s statistical account helps to explain why. For example, Ringach’s account leaves open questions such as why initial conditions seeding the maps cannot be fully reversed or disrupted by later activity-dependent influences. Likewise important findings in both retinocollicular and retinogeniculate development such as developmental deficiencies associated with genetic (i.e., knockout and transgenic) manipulations (for a review, see McLaughlin & O'Leary, 2005), as well as manipulations that disrupt spontaneous retinal activity during a brief critical period of development (e.g., McLaughlin et al., 2003; Chandrasekaran et al., 2005; Mrsic-Flogel et al., 2005). Map disruptions caused by knockout manipulations or removal of spontaneous retinal activity (for a review, see McLaughlin & O'Leary, 2005) are not directly addressed by the work of Ringach and likely reside outside the scope of a purely statistical approach.

The lack of an integrated theoretical framework for understanding these findings is a tell-tale sign that many fundamental aspects of both molecular and activity-based influences are still poorly understood. Investigating the mechanisms behind neural development will require a re-examination of several factors that are too often overlooked in the bird’s eye view provided by statistical modeling. For instance, repulsive cell-cell signalling cues responsible for intrinsic axonal competition is a mechanism that is still not clearly understood (Honda, 2003), and many accounts, including that of Ringach, simply assume that axons “swap” position when required to fit a particular statistical goal. By doing so, most extant models have made little attempts to capture a wealth of evidence on the role of neural activity in controlling and shaping the axonal branches responsible for establishing contact points between regions (Uesaka et al., 2005).

Going further, detailed models are also required to address the particular interplay of activity-based and activity-independent mechanisms; while most current models assume that activity-based development is initiated during a phase of development where activity-independent mechanisms no longer play a role, recent evidence suggests just the opposite: the genetically-expressed factors continue to exert an influence well beyond the initial stages of activity-independent development (Cline, 2003). Advances in our understanding of cortical map formation may therefore depend on models that account for the continued influence of molecular guidance cues even after the introduction of neural activity. Overall, mechanistic models may be better suited at explaining how certain basic principles such as Hebbian learning lead to dynamic changes over time, i.e., changes in connectivity and synaptic efficacy, as well as the time-course of influence of molecular versus activity-based processes.

More broadly, although it may appear at first sight that a purely statistical view of visual development is in competition with other alternatives such as Hebbian-based correlation approaches, it is perhaps more likely that they represent two sides of the same coin; while one offers a detailed description of what visual development looks like, the other promises an explanation of how fundamental mechanisms involved in development can account for the final layout of orientation, retinotopic, and ocular dominance maps.

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McLaughlin T, Torborg C, Feller M, O'Leary DDM (2003) Retinotopic map refinement requires spontaneous retinal waves during a brief critical period of development. Neuron 40:1147-1160.

Mrsic-Flogel T, Hofer S, Creutzfeldt C, Cloez-Tayarani I, Changeux J, Bonhoeffer T, Hubener M (2005) Altered map of visual space in the superior colliculus of mice lacking early retinal waves. Journal of Neuroscience 25:6921-6928. []

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RE: Challenges in Modeling Neural Development

dario replied to Gary_JP_Group on 02 Mar 2007 at 06:00 GMT

I believe the proposal is fairly specific about the mechanisms involved. Namely, the study shows that a simple thalamo-cortical connectivity rule where the strength and probability of connections fall off with the distance between the location of a cortical cell and the incoming afferents is sufficient to explain a myriad of experimental results. Modeling the details of axon guidance and synaptogenesis was not an integral part of this study for a simple reason: any biophysical mechanism generating the assumed Gaussian connectivity profile would predict the same receptive fields and maps.

As discussed briefly in the manuscript, wiring minimization and statistical connectivity are not necessarily in conflict with each other. One possible scenario is that the two-dimensional structure of the maps (such as the orientation map) is determined by mechanisms that are not explicitly concerned with wiring minimization (such as statistical connectivity). Yet, if intra-cortical connectivity is heavily dominated by local connections within the resulting maps, one is likely to find that subsequent perturbations to the map structure will lead to an increase in wiring length. Thus, we have a chicken-and-egg question: is wiring minimization driving map development? Or does a given map structure plus dominance of local connectivity automatically imply the maps are at a minimum for wiring length? This is a question that needs to be investigated further.

In the introduction, I emphasize that the present study focuses exclusively on the question of how receptive fields and maps emerge in the early stages of development, before the onset of the critical period. I agree this is only one piece of the puzzle (albeit an important one). There is no denying that there are activity dependent processes that shape and maintain these initial structures. However, as discussed by Miller et al (1999), these are separate questions.

I agree with the comment that, in the end, detail models of the entire developmental process will need to address the interplay of activity-based and activity-independent mechanisms, and this is indeed one of the directions that must be explored in future work of the statistical connectivity framework.

As discussed previously (Ringach, J. Neurophysiol., 92:468-76, 2004), the model suggests that the resilience of the maps to manipulations during the critical period is due to the fact that such interventions have no effect on the structure of the RGC mosaic. The structure of local receptive fields is going to be constrained by the available distribution of ON/OFF center cells in the RGC mosaic. There is not much that plasticity can do to overcome this restriction. Instead, statistical connectivity predicts that any manipulations that substantially alter the spatial statistics of the RGC mosaic will have a direct result on the structure of receptive fields and maps in V1.