RobustCircuit – Background and Concept

Our initiative is motivated by our common realization that imprecision in neural circuit assembly can play important roles for flexible development and robust function.  Yet, studies on neural circuit assembly more often focus on the remarkable precision of connectivity, rather than the importance of its imprecision.  We want to understand how and when developmental imprecision can lead to robustness in the outcome.  Loss of robustness and increased variability play important, yet poorly understood roles in neural circuit wiring and consequently for brain function.  Already in the 1940s, Waddington and colleagues observed that neuro-developmental perturbation typically results in a wider phenotypic range than wild type [4].  We posit that variability in neural circuit assembly can result from imprecise genotype-phenotype mapping, i.e. only a range of the phenotypic manifestation can be predicted for a given genotype [5, 6].  An example of this was recently published by a team of RobustCircuit PIs in flies [7].  

Operational Definitions (based on [1]): We refer to a system’s robustness as its ability to tolerate perturbation.  We operationally define a process as imprecise, when its future states are not predictable.  Hence, our use of the term imprecision includes processes ranging from true randomness (e.g. rolling a dice, equal probabilities for all outcomes) to probabilistic (stochastic) or noisy processes that are biased (e.g. directional filopodial exploration).  We regard only a 100% predictable system as deterministic, and all imprecise processes non-deterministic.

Scientific Concept and Background

Neural circuits must be precise enough to produce reliable physiological and behavioral output.  The ‘wiring diagram’ underlying a neural circuit is defined by the types and specificity of its synaptic connections.  In analogy to wiring diagrams for electrical circuits and modern microprocessors, noise can be regarded as the enemy of precision: more noise in the production process equals less precision.  Biological systems are inherently noisy [1, 11-13].  Hence, noise is often discussed as an unavoidable problem, one that developmental mechanisms must have evolved to ‘deal with’, and minimize in order to achieve sufficiently precise wiring.

This view is incomplete.  Neural circuit assembly is not only precise, but also highly flexible.  Electrical circuits are highly sensitive to the destruction of individual connections, let alone the removal of entire cable tracts or a large number of essential components.  In contrast, examples abound where neural circuit development does not only flexibly deal with ‘destruction’, but in fact actively utilizes it as a developmental principle (e.g. synaptic pruning [14,15]).  Consequently, neural circuits exhibit a type of robustness that is entirely absent from more precise, but less flexibly encoded electrical circuitry.  Electrical circuits are a ‘sticky metaphor’ for neural circuits, because we commonly draw wiring diagrams for both (Fig. 1). However, electrical circuits are an inadequate metaphor for neural circuit development, because there is no endpoint information in the genetic code or environmental input for the final circuit.  Instead, neurons grow, akin to autonomous agents, and make individual choices following a set of rules.  The nature of how molecular and cellular choices are made is not only often imprecise, but utilizes this imprecision to ensure flexibility and robustness (see text box for definitions) (1, 6, 16).

The roles and relevance of imprecision for robustness in neural circuit assembly

Developmental imprecisions may positively or negatively affect robustness in the outcome.  The classic example for the positive utilization of imprecision is the use of noise in development as a ‘symmetry breaker’.  An easy way to ensure a choice between two otherwise equally good options is to make use of variability that originates from an inherently noisy process [1, 17].  Symmetry breaking is e.g. fundamental to cell competition, a common developmental mechanism.  Competition can robustly establish a precise ratio of neuronal cell fates, or single out a specific number of neurons amongst a variable number of cells, or single out a specific number of synapses for a single neuron (1, 16).  The singling out process does not determine which competitor will win, but it can ensure a precise number or pattern of winner neurons, axons or synapses.  For axons and dendrites, probabilistic branch formation often forms the basis for competition and can be required to make the process robust to variable space constraints or variable localization of synaptic partners.  For example, a growing dendritic tree may cover a region of variable/unknown extension based on a combination of spreading through self-avoidance and limits to spreading through tiling or other boundary marks.  In addition to the requirement for probabilistic branching in order to have individual branches to actually avoid each other, self-avoidance in Drosophila is well-understood and molecularly based on a homophilic cell adhesion molecule (Dscam1) that is non-deterministically expressed in large numbers of different isoforms and thereby ensures self-avoidance only amongst branches of an individual neuron, while non-self neighbors are not recognized.  Hence, self-avoidance requires both molecular (probabilistic isoform splicing) and subcellular (branching) imprecisions to ensure robustness of dendritic tree spreading.

Probabilistic branching is similarly required for robust identification of synaptic partners at variable and unknown locations.  The synaptotropic principle (Fig. 2) was first described by Vaughn and subsequently found for both axon and dendrite branching.  Synaptotropic growth is based on two simple rules: first, stabilize branches only when they meet a synaptic partner; second, use this meeting point as a new starting point for further probabilistic branching (Fig. 2).  Hence, based on the necessary imprecision of the branch process, the axonal or dendritic branches effectively grow towards where most synaptic partners are.  Probabilistic exploration also represents an optimization problem: highly targeted exploration in the direction where synaptic partners are most likely avoids wasted energy of searching in low-probability regions, but also reduces robustness of identifying partners in those regions (Fig. 3A).  The opposite strategy of comprehensive exploration of all regions ensures full robustness, but is very costly (Fig. 3C).  Both developmental and functional processes represent evolutionarily selected trade-offs of precision and energy consumption. Probabilistic exploration (Fig. 3B) may therefore represent a cost/benefit optimization.

At the molecular level, the above-mentioned probabilistic splicing of Dscam1 is a prime example for an imprecise process required for robust dendritic patterning during development.  In mature neurons, expression of ion channels can be surprisingly variable, while circuit function is robust, e.g. to variable temperatures. In other examples for neuronal function, different types of noise have been shown to play important roles in neuronal firing patterns [14], to ensure precision of a population code of diversely tuned neurons [15], or to increase a dynamic range [16].

At the population level, imprecise processes can also be essential to preserve variability of the individual developmental outcomes.  The idea that variability of individuals (or individual components) can be required for robustness at the population level has been described as a bet hedging strategy (Fig. 4):  If a specific genotype produces very similar individuals, all individuals can end up ‘on the wrong side of selection’.  If, however, a specific genotype produces individuals with variable phenotypes, then some of those individuals may fit the selection criterion.            

These few selected examples highlight that imprecisions and flexibility can range from being simply tolerated to indirectly and directly beneficial for neural circuit assembly.  The examples also highlight the similarities of the principles that underlie the roles of imprecise processes for robustness at different scales.  In the RobustCircuit team effort we strive to test the generality of these principles by studying these ideas across different cell types and across scales from molecules to behaviors.  To achieve this goal, we focus in all projects on experimentally and quantitatively amenable imprecisions and robust outcomes utilizing fly neural circuit assembly as a model.  In all projects, we therefore strive to quantitatively test whether a given imprecision is tolerated, or indirectly or directly beneficial for a specified robustness of the system.

References

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