How to fit in: The learning principles of cell differentiation

Abstract

Cell differentiation in multicellular organisms requires cells to respond to complex combinations of extracellular cues, such as morphogen concentrations. Some models of phenotypic plasticity conceptualise the response as a relatively simple function of a single environmental cues (e.g. a linear function of one cue), which facilitates rigorous analysis. Conversely, more mechanistic models such those implementing GRNs allows for a more general class of response functions but makes analysis more difficult. Therefore, a general theory describing how cells integrate multi-dimensional signals is lacking. In this work, we propose a theoretical framework for understanding the relationships between environmental cues (inputs) and phenotypic responses (outputs) underlying cell plasticity. We describe the relationship between environment and cell phenotype using logical functions, making the evolution of cell plasticity equivalent to a simple categorisation learning task. This abstraction allows us to apply principles derived from learning theory to understand the evolution of multi-dimensional plasticity. Our results show that natural selection is capable of discovering adaptive forms of cell plasticity associated with complex logical functions. However, developmental dynamics cause simpler functions to evolve more readily than complex ones. By using conceptual tools derived from learning theory we show that this developmental bias can be interpreted as a learning bias in the acquisition of plasticity functions. Because of that bias, the evolution of plasticity enables cells, under some circumstances, to display appropriate plastic responses to environmental conditions that they have not experienced in their evolutionary past. This is possible when the selective environment mirrors the bias of the developmental dynamics favouring the acquisition of simple plasticity functions-an example of the necessary conditions for generalisation in learning systems. These results illustrate the functional parallelisms between learning in neural networks and the action of natural selection on environmentally sensitive gene regulatory networks. This offers a theoretical framework for the evolution of plastic responses that integrate information from multiple cues, a phenomenon that underpins the evolution of multicellularity and developmental robustness.

Development and Selective Grain Make Plasticity ‘Take the Lead’ in Adaptive Evolution

“…While our results demonstrate that natural selection on phenotypic plasticity would cause the GP map to evolve, they also show that the ability to evolve a certain map is severely limited by the map complexity itself, with complex (e.g., cubic) maps requiring highly fine-grained selection. This would render very complex EP (and GP) maps unreachable by adaptive evolution even in the most fine-grained scenarios [34]. However, complex maps are known to exist, which suggests that other non-selective processes, such as developmental system drift [31,42], may play an important role in developmental evolution [3,38].…”

“…trait correlations) in the maps themselves. This procedure allows us to accelerate the weak selection on variation that is found on natural populations, where it is performed indirectly through individual-level selection of phenotypes [9,10,33,34].…”

“…Thus, each individual in each generation is exposed to 10 different inputs in one of its GRN elements (the element depends on the map being evolved), and its slope S i in a T 1 -T 2 morphospace recorded and compared to the target slope S T . This algorithm is formally equivalent to an inter-generational variation in the inputs [33][34][35]. The similarity with the target slope determines the individual's fitness and, in turn, the probability of each individual to contribute to the next generation:…”

Phenotypes to remember: Evolutionary developmental memory capacity and robustness

“…It requires that the neighborhood (according to a given metric) of the embryonic states must also be in the basin of their PLOS COMPUTATIONAL BIOLOGY corresponding adult states. Therefore, some inputs of variation should produce little or no phenotypic variation at all, a phenomenon that has received a lot of attention under the labels of canalization, robustness or buffering [31,32,[40][41][42]. The recovery performance of the network changes with increasing amount of perturbations (Fig 7).…”

“…In contrast to this, in ontogenetic systems the relevant space is that of nonnegative real numbers, corresponding to concentrations of different molecules, see e.g. [ 32 ]. Due to the nonlinear activation function features of models working with the above mentioned, alternative state representations can markedly differ.…”