Isaac Salazar-Ciudad

A fundamental question of developmental biology is pattern formation, or how cells with specific gene expression end up in specific locations in the body to form tissues, organs and, overall, functional anatomy. Pattern formation involves communication through extracellular signals and complex intracellular gene networks integrating these signals to determine cell responses (e.g., further signaling, cell division, cell differentiation, etc.). In this article we address two question: 1) Are there any logical or mathematical principles determining which gene network topologies can lead to pattern formation by cell signaling over space in multicellular systems? 2) Can gene network topologies be classified into a small number of classes that entail similar dynamics and pattern transformation capacities? We combine logical arguments and mathematical proofs to show that, despite the large amount of formally possible gene network topologies, all gene network topologies capable of pattern formation fall into only three fundamental classes and their combinations. Additionally, we show that gene networks within each class share the same logic on how they lead to pattern formation and hence, lead to similar patterns. We characterize the main features of each class. This zoo includes the complete gene networks that, to the best of our knowledge, have been experimentally reported to lead to pattern formation as well as other gene networks that have not yet been found experimentally.

A fundamental question of developmental biology is pattern formation, or how cells with specific gene expression end up in specific locations in the body to form tissues, organs and, overall, functional anatomy. Pattern formation involves communication through extracellular signals and complex intracellular gene networks integrating these signals to determine cell responses (e.g., further signaling, cell division, cell differentiation, etc.). In this article we address two question: 1) Are there any logical or mathematical principles determining which gene network topologies can lead to pattern formation by cell signaling over space in multicellular systems? 2) Can gene network topologies be classified into a small number of classes that entail similar dynamics and pattern transformation capacities? We combine logical arguments and mathematical proofs to show that, despite the large amount of formally possible gene network topologies, all gene network topologies capable of pattern formation fall into only three fundamental classes and their combinations. Additionally, we show that gene networks within each class share the same logic on how they lead to pattern formation and hence, lead to similar patterns. We characterize the main features of each class. This zoo includes the complete gene networks that, to the best of our knowledge, have been experimentally reported to lead to pattern formation as well as other gene networks that have not yet been found experimentally. Significance Statement: Pattern formation is a central problem in developmental biology, yet the principles linking gene regulatory network topology to spatial patterning in multicellular systems are not fully understood. In this work, we identify logical and mathematical principles that determine which gene regulatory network topologies can give rise to spatial pattern formation through extracellular signaling. We further show that these topologies can be systematically classified into a small number of fundamental classes associated with distinct dynamical behaviors. Despite the vast number of a priori possible gene network configurations, the gene networks capable of stationary pattern formation fall into just three fundamental topological classes and their combinations. Gene networks within each class implement a common patterning logic and consequently generate analogous pattern transformations, revealing a unifying organizational framework underlying biological pattern formation.

What morphologies are more likely to appear during evolution is a central question in zoology. Here we offer a novel approach to this question based on first developmental principles. We assumed that morphogenesis results from the genetic regulation of cell properties and behaviors (adhesion, contraction, etc.). We used EmbryoMaker, a general model of development that can simulate any gene network regulating cell properties and behaviors, the mechanical interactions and signaling between cells and the morphologies arising from those. We created spherical initial conditions with anterior and dorsal territories. We performed simulations changing the cell properties and behaviors regulated in these territories to explore which morphologies may have been possible. Thus, we obtained a set of the most basic animal morphologies that can be developmentally possible assuming very simple induction and morphogenesis. Our simulations suggest that elongation, invagination, evagination, condensation and anisotropic growth are the morphogenetic transformations more likely to appear from changes in cell properties and behaviors. We also found some parallels between our simulations and the morphologies of simple animals, some early stages of animal development and fossils attributed to early animals.

During development, cells are subject to stochastic fluctuations in their positions (i.e. cell-level noise) that can potentially lead to morphological noise (i.e. stochastic differences between morphologies that are expected to be equal, e.g. the right and left sides of bilateral organisms). In this study, we explore new and existing hypotheses on buffering mechanisms against cell-level noise. Many of these hypotheses focus on how the boundaries between territories of gene expression remain regular and well defined, despite cell-level noise and division. We study these hypotheses and how irregular territory boundaries lead to morphological noise. To determine the consistency of the different hypotheses, we use a general computational model of development: EmbryoMaker. EmbryoMaker can implement arbitrary gene networks regulating basic cell behaviors (contraction, adhesion, etc.), signaling and tissue biomechanics. We found that buffering mechanisms based on the orientation of cell divisions cannot lead to regular boundaries but that other buffering mechanisms can (homotypic adhesion, planar contraction, non-dividing boundaries, constant signaling and majority rule hypotheses). We also explore the effects of the shape and size of the territories on morphological noise.

A foundational idea of evo‐devo is that morphological variation is not isotropic, that is, it does not occur in all directions. Instead, some directions of morphological variation are more likely than others from DNA‐level variation and these largely depend on development. We argue that this evo‐devo perspective should apply not only to morphology but to evolution at all phenotypic levels. At other phenotypic levels there is no development, but there are processes that can be seen, in analogy to development, as constructing the phenotype (e.g., protein folding, learning for behavior, etc.). We argue that to explain the direction of evolution two types of arguments need to be combined: generative arguments about which phenotypic variation arises in each generation and selective arguments about which of it passes to the next generation. We explain how a full consideration of the two types of arguments improves the explanatory power of evolutionary theory. Also see the video abstract here: https://youtu.be/Egbvma_uaKc

Predicting evolution remains challenging. The field of quantitative genetics provides predictions for the response to directional selection through the breeder’s equation, but these predictions can have errors. The sources of these errors include omission of traits under selection, inaccurate estimates of genetic variance, and nonlinearities in the relationship between genetic and phenotypic variation. Previous research showed that the expected value of these prediction errors is often not zero, so predictions are systematically biased. Here, we propose that this bias, rather than being a nuisance, can be used to improve the predictions. We use this to develop a method to predict evolution, which is built on three key innovations. First, the method predicts change as the breeder’s equation plus a bias term. Second, the method combines information from the breeder’s equation and from the record of past changes in the mean to predict change using a Kalman filter. Third, the parameters of the filter are fitted in each generation using a learning algorithm on the record of past changes. We compare the method to the breeder’s equation in two artificial selection experiments, one using the wing of the fruit fly and another using simulations that include a complex mapping of genotypes to phenotypes. The proposed method outperforms the breeder’s equation, particularly when traits under selection are omitted from the analysis, when data are noisy, and when additive genetic variance is estimated inaccurately or not estimated at all. The proposed method is easy to apply, requiring only the trait means over past generations.