Degeneracy rules

Abstract

Biological systems, including the nervous system, can show enormous variability in their cellular and system-wide properties. In particular, in the nervous system, nerve cell properties such as ion channel densities can vary widely even between neurons of the same type, both between animals of the same species, and even between cells of the same type within a given animal. Beyond cellular variability, nervous systems also exhibit variability of synaptic properties, again even between synapses of the same type. In the case of synapses, especially those whose plasticity is thought to underlie learning and the formation, retention, and recall of memories, variability is generally accepted to go hand in hand with plasticity, and to be a 'feature' rather than a 'bug' of nervous system operation. In an article in this issue of The Journal of Physiology, Mukunda & Narayanan (2017) present a physiologically detailed computational modelling study that examines the variability of presynaptic terminal properties such as the presence and density of voltage-gated ion channels and calcium regulation mechanisms. Among other approaches, the study relies on global sensitivity analysis, in which thousands of synapse model versions are randomly generated and automatically tested for their ability to reproduce behaviour observed at living synapses, in this case at hippocampal Schaffer collateral synapses. Specifically, suitable synapse model versions are identified by their filtering properties (low-pass, band-pass, or high-pass with respect to presynaptic spike frequency) and by their plasticity profiles (i.e. short-term facilitation or depression). This general approach of analysing neuronal or network function by producing and studying multiple functional model versions rather than focusing on a single, possibly idiosyncratic, model version is termed 'ensemble modelling' (Prinz, 2010). Ensemble modelling is becoming an increasingly popular tool for embracing biological variability by generating similarly variable model ensembles, rather than dismissing variability as an unwanted side effect of biological 'sloppiness' or 'noisiness'. As was previously shown for cell-intrinsic parameters and postsynaptic properties, this study (Mukunda & Narayanan, 2017) finds that presynaptic terminal properties of models that produce biologically realistic and almost identical filtering properties and plasticity profiles can also vary over wide, several-fold ranges from synapse to synapse. The study thereby contributes to a rapidly growing list of biological systems in which experimentation and computational modelling have demonstrated parameter variability despite similar system output. Like others before them, the authors call this phenomenon 'parameter degeneracy' (although this commentator prefers the term 'non-uniqueness'; Prinz et al. 2004). While individual parameters in this and other systems can vary widely, they do not necessarily vary independently. Previous studies have shown that variable parameters often exhibit pair-wise or even higher order correlations (Schulz et al. 2007), albeit these correlations can be fairly weak (Taylor et al. 2009). Through parameter correlations, dynamical systems such as the brain may gain the ability to adjust to perturbations or to changes in one parameter by compensating with changes in one or several other parameters, thereby maintain functional system behaviour. Another approach in Mukunda & Narayanan (2017) uses virtual knock-out simulations (i.e. the complete removal of a given type of presynaptic voltage-gated ion channel from all functional models) to examine how individual ion channel types underlie and shape individual synaptic filtering and plasticity outcomes. Because, as stated above, presynaptic parameters do not always vary independently, it is perhaps not surprising to find that there is no simple one-to-one mapping between presynaptic parameters and particular features of synaptic filtering and plasticity. Rather, it appears that the emergence of particular synaptic characteristics (such as whether the synapse exhibits facilitation or depression, and what presynaptic spike frequencies it transmits most efficiently) should be thought of – as the authors phrase it – in a holistic, interactive way. This may appear like a daunting message, because it emphasizes that the dynamics of non-linear systems are often difficult to understand or counter-intuitive. However, at the same time the emergence of functional synaptic properties from the interaction of multiple presynaptic and postsynaptic mechanisms also endows the nervous system with robustness and the ability to perform the same function in multiple different ways. Thus, in neuronal systems, in biological systems in general, and in nonlinear dynamical systems outside biology, parameter non-uniqueness may be a fundamental mechanism of system robustness and versatility – degeneracy rules! None declared.