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.

Author summary

In organisms composed of many cell types, the differentiation of cells relies on their ability to respond to complex extracellular cues, such as morphogen concentrations, a phenomenon known as cell plasticity. Although cell plasticity plays a crucial role in development and evolution, it is not clear how, and if, cell plasticity can enhance adaptation to a novel environment and/or facilitate robust developmental processes. In some models, the relationships between the environmental cues (inputs) and the phenotypic responses (outputs) are conceptualised as one-to-one (i.e. simple ‘reaction norms’); whereas the phenotype of plastic cells commonly depends on several simultaneous inputs (i.e. many-to-one, multi-dimensional reaction norms). One alternative is the use of a gene-regulatory network (GRN) models that allow for much more general responses; but this can make analysis difficult. In this work we use a theoretical framework based on logical functions and learning theory to characterize such multi-dimensional reaction norms produced by GRNs. This allows us to reveal a strong and previously unnoticed bias towards the acquisition of simple forms of cell plasticity, which increases their ability to adapt to novel environments. Recognising this bias helps us to understand when the evolution of cell plasticity will increase the ability of plastic cells to adapt to novel environments, to respond appropriately to complex extracellular cues and to enhance developmental robustness. Since this set of properties are required for the evolution of multicellularity, our approach can also contribute to our understanding of this evolutionary transition.