Information content and optimization of self-organized developmental systems

Abstract: A key feature of many developmental systems is their ability to self-organize spatial patterns of functionally distinct cell fates. To ensure proper biological function, such patterns must be established reproducibly, by controlling and even harnessing intrinsic and extrinsic fluctuations. While the relevant molecular processes are increasingly well understood, we lack a principled framework to quantify the performance of such stochastic self-organizing systems. To that end, we introduce a new information-theoretic measure for self-organized fate specification during embryonic development. We show that the proposed measure assesses the total information content of fate patterns, and decomposes it into interpretable contributions corresponding to the positional and correlational information. By optimizing the proposed measure, our framework provides a normative theory for developmental circuits, which we demonstrate on lateral inhibition, cell type proportioning, and reaction-diffusion models of self-organization. This paves a way towards a classification of developmental systems based on a common information-theoretic language, thereby organizing the zoo of implicated chemical and mechanical signaling processes.

• The paper introduces an information-theoretic framework that quantifies self-organization in developmental systems using patterning and reproducibility entropy.
• It decomposes informational measures into positional and correlational data to evaluate models like lateral inhibition, cell sorting, and reaction-diffusion dynamics.
• The methodology offers actionable insights for designing robust biological patterns, with notable implications for synthetic biology and developmental research.

Information Content and Optimization of Self-Organized Developmental Systems

The paper "Information Content and Optimization of Self-Organized Developmental Systems" introduces a novel framework for assessing the efficacy of self-organizing biological systems that dictate cell fate during embryonic development. The research seeks to bridge the gap between well-known molecular processes and a quantitative measure of their organizational performance through an information-theoretic approach.

Self-organization in developmental biology refers to the ability of biological systems to autonomously form spatial patterns of cell fates. These systems are inherently stochastic due to intrinsic and extrinsic fluctuations, yet they aim to achieve consistent and reproducible patterns necessary for proper biological functions. The authors introduce a utility function comprised of two entropic components: the patterning entropy, which describes diversity in cell types, and the reproducibility entropy, which measures the similarity across replicates. The utility function optimally favors systems minimizing the latter while maximizing the former, thereby creating a comprehensive metric for analyzing self-organization efficacy.

The researchers expand upon this utility by dissecting the information into positional information (PI) and correlational information (CI). PI quantifies the order of cell fates relative to position, indicative of spatially structured patterns, whereas CI measures non-local correlations that enhance reproducibility but don't necessarily correspond to positional order.

Three paradigmatic models of self-organized patterning are evaluated within this framework: lateral inhibition signaling (LIS), cell-type proportioning and sorting, and reaction-diffusion (RD) dynamics. Lateral inhibition is explored first, utilizing a minimal model with a delta-notch pathway to establish an alternating cell fate pattern. Analysis reveals a range of parameter space conducive to optimal reproducibility and information content, yet susceptible to noise levels, demonstrating graded vs. bistable dynamics' relative advantages.

In the second model, the concept of cell-type proportioning is examined, wherein an ideal state is characterized by a specific distribution of cell types. The model's efficacy is demonstrated by its ability to consistently achieve these proportions despite stochastic variations and external noise, revealing that optimizing for CI can stabilize proportions even when PI is low.

The paper's final exemplar, reaction-diffusion systems, leverages activator-inhibitor interactions to pattern cell fates. Intrinsic noise and extrinsic variability are examined, with supplemental regulatory expansions such as fast-diffusing species suggested to bolster the system's robustness against spatial variances.

The proposed framework holds significant implications for understanding and engineering developmental systems. In addition to optimizing existing biological processes, it proposes a pathway for synthetic biology applications aiming to design systems with robust patterning capabilities. By aligning theoretical measures with experimental data, future work could further quantify developmental mechanisms, providing a standardized classification across different biological systems based on information content. This work serves as a foundation for integrating statistical descriptions into the complex choreography of cellular self-organization, offering insights into potential evolutionary advantages of specific regulatory motifs in developmental biology.