How Criticality of Gene Regulatory Networks Affects the Resulting Morphogenesis under Genetic Perturbations

Whereas the relationship between criticality of gene regulatory networks (GRNs) and dynamics of GRNs at a single cell level has been vigorously studied, the relationship between the criticality of GRNs and system properties at a higher level has remained unexplored. Here we aim at revealing a potential role of criticality of GRNs at a multicellular level which are hard to uncover through the single-cell-level studies, especially from an evolutionary viewpoint. Our model simulated the growth of a cell population from a single seed cell. All the cells were assumed to have identical GRNs. We induced genetic perturbations to the GRN of the seed cell by adding, deleting, or switching a regulatory link between a pair of genes. From numerical simulations, we found that the criticality of GRNs facilitated the formation of nontrivial morphologies when the GRNs were critical in the presence of the evolutionary perturbations. Moreover, the criticality of GRNs produced topologically homogenous cell clusters by adjusting the spatial arrangements of cells, which led to the formation of nontrivial morphogenetic patterns. Our findings corresponded to an epigenetic viewpoint that heterogeneous and complex features emerge from homogeneous and less complex components through the interactions among them. Thus, our results imply that highly structured tissues or organs in morphogenesis of multicellular organisms might stem from the criticality of GRNs.Comment: 34 pages, 17 figures, 1 tabl

Self-organizing particle systems

This is a pre-copyedited, author-produced PDF of an article accepted for publication in Advances in Complex Systems following peer review. The version of record, Malte Harder and Daniel Polani, ‘Self-organizing particle systems’, Advs. Complex Syst. 16, 1250089, published October 22, 2012, is available online via doi: https://doi.org/10.1142/S0219525912500890 Published by World Scientific Publishing.The self-organization of cells into a living organism is a very intricate process. Under the surface of orchestrating regulatory networks there are physical processes which make the information processing possible, that is required to organize such a multitude of individual entities. We use a quantitative information theoretic approach to assess self-organization of a collective system. In particular, we consider an interacting particle system, that roughly mimics biological cells by exhibiting differential adhesion behavior. Employing techniques related to shape analysis, we show that these systems in most cases exhibit self-organization. Moreover, we consider spatial constraints of interactions, and additionaly show that particle systems can self-organize without the emergence of pattern-like structures. However, we will see that regular pattern-like structures help to overcome limitations of self-organization that are imposed by the spatial structure of interactions.Peer reviewe

Vector Field Embryogeny

We present a novel approach toward evolving artificial embryogenies, which omits the graph representation of gene regulatory networks and directly shapes the dynamics of a system, i.e., its phase space. We show the feasibility of the approach by evolving cellular differentiation, a basic feature of both biological and artificial development. We demonstrate how a spatial hierarchy formulation can be integrated into the framework and investigate the evolution of a hierarchical system. Finally, we show how the framework allows the investigation of allometry, a biological phenomenon, and its role for evolution. We find that direct evolution of allometric change, i.e., the evolutionary adaptation of the speed of system states on transient trajectories in phase space, is advantageous for a cellular differentiation task

The Role of Criticality of Gene Regulatory Networks on Emergent Properties of Biological Systems

The relationship between criticality of gene regulatory networks (GRNs) and dynamics of GRNs at a single cell level has been vigorously studied. However, the relationship between the criticality of GRNs and properties of multicellular organisms at a higher level has not been fully explored. Here we aim at revealing potential roles of the criticality of GRNs at a multicellular and hierarchical level, using a random Boolean network as a GRN. We perform three studies. Firstly, we propose a GRN-based morphogenetic model, and delve into the role of the criticality of GRNs in morphogenesis at a multicellular level. Secondly, we include an evolutionary context in our morphogenetic model by introducing genetic perturbations (e.g., mutations) to GRNs, and examine whether the role of the criticality of GRNs can be maintained even in the presence of the evolutionary perturbations. Also, we look into what the resulting morphologies are like and what kind of biological implications they have from the epigenetic viewpoint in morphology. Lastly, we present multilayer GRNs consisting of an intercellular layer and an intracellular layer. A network in an intercellular layer represents interactions between cells, and a network in an intracellular layer means interactions between genes. All the nodes of an intercellular network have identical intracellular GRNs. We investigate how the criticality of GRNs affects the robustness and evolvability of the multilayer GRNs at a hierarchical level, depending on cellular topologies and the number of links of an intercellular network. From the three studies, we found that the criticality of GRNs facilitated the formation of nontrivial morphologies at a multicellular level, and generated robust and evolvable multilayer GRNs most frequently at a hierarchical level. Our findings indicate that the roles of the criticality of GRNs are hard to be discovered through the single-cell-level studies. It justifies the value of our research on the relationship between criticality of GRNs and properties of organisms in the context of multicellular settings

Information Driven Self-Organization of Agents and Agent Collectives

From a visual standpoint it is often easy to point out whether a system is considered to be self-organizing or not, though a quantitative approach would be more helpful. Information theory, as introduced by Shannon, provides the right tools not only quantify self-organization, but also to investigate it in relation to the information processing performed by individual agents within a collective. This thesis sets out to introduce methods to quantify spatial self-organization in collective systems in the continuous domain as a means to investigate morphogenetic processes. In biology, morphogenesis denotes the development of shapes and form, for example embryos, organs or limbs. Here, I will introduce methods to quantitatively investigate shape formation in stochastic particle systems. In living organisms, self-organization, like the development of an embryo, is a guided process, predetermined by the genetic code, but executed in an autonomous decentralized fashion. Information is processed by the individual agents (e.g. cells) engaged in this process. Hence, information theory can be deployed to study such processes and connect self-organization and information processing. The existing concepts of observer based self-organization and relevant information will be used to devise a framework for the investigation of guided spatial self-organization. Furthermore, local information transfer plays an important role for processes of self-organization. In this context, the concept of synergy has been getting a lot attention lately. Synergy is a formalization of the idea that for some systems the whole is more than the sum of its parts and it is assumed that it plays an important role in self-organization, learning and decision making processes. In this thesis, a novel measure of synergy will be introduced, that addresses some of the theoretical problems that earlier approaches posed

Chemotaxis-based spatial self-organization algorithms

Self-organization is a process that increases the order of a system as a result of local interactions among low-level, simple components, without the guidance of an outside source. Spatial self-organization is a process in which shapes and structures emerge at a global level from collective movements of low level shape primitives. Spatial self-organization is a stochastic process, and the outcome of the aggregation cannot necessarily be guaranteed. Despite the inherent ambiguity, self-organizing complex systems arise everywhere in nature. Motivated by the ability of living cells to form specific shapes and structures, we develop two self-organizing systems towards the ultimate goal of directing the spatial self-organizing process. We first develop a self-sorting system composed of a mixture of cells. The system consistently produces a sorted structure. We then extend the sorting system to a general shape formation system. To do so, we introduce morphogenetic primitives (MP), defined as software agents, which enable self-organizing shape formation of user-defined structures through a chemotaxis paradigm. One challenge that arises from the shape formation process is that the process may form two or more stable final configurations. In order to direct the self-organizing process, we find a way to characterize the macroscopic configuration of the MP swarm. We demonstrate that statistical moments of the primitives' locations can successfully capture the macroscopic structure of the aggregated shape. We do so by predicting the final configurations produced by our spatial self-organization system at an early stage in the process using features based on the statistical moments. At the next stage, we focus on developing a technique to control the outcome of bifurcating aggregations. We identify thresholds of the moments and generate biased initial conditions whose statistical moments meet the thresholds. By starting simulations with biased, random initial configurations, we successfully control the aggregation for a number of swarms produced by the agent-based shape formation system. This thesis demonstrates that chemotaxis can be used as a paradigm to create an agent- based spatial self-organization system. Furthermore, statistical moments of the swarm can be used to robustly predict and control the outcomes of the aggregation process.Ph.D., Computer Science -- Drexel University, 201