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Marr's three levels for embryonic development: information, dynamical systems, gene networks

David B. Brückner, Gašper Tkačik

TL;DR

The paper frames embryonic development as an information-processing problem solvable via Marr's three levels of analysis, combining normative information-theoretic objectives (e.g., $I(g;c)$ and $I(g;x)$) with algorithmic architectures (layered inputs/outputs and landscape dynamics) and mechanistic realizations (signal transduction, GRNs, and reaction–diffusion/mechano-chemical models). It unifies instructed and self-organized patterning, showing how external inputs, local cellular processing, and intercellular coupling can be organized into hierarchical architectures, including boundary-driven and skip-layer variants, and how Geometric Dynamical Systems provides a minimal, predictive framework. The authors discuss end-to-end multilayer optimization, robustness to natural fluctuations, morphogenesis, and scaling as open questions, arguing that integrating these levels yields a principled bridge from function to mechanism. Overall, the framework offers a coherent, testable roadmap for connecting high-level information objectives to concrete molecular mechanisms across scales, guiding experimental and theoretical work in developmental biology.

Abstract

Developmental patterning comprises processes that range from purely instructed, where external signals specify cell fates, to fully self-organized, where spatial patterns emerge autonomously through cellular interactions. We propose that both extremes -- as well as the continuum of intermediate cases -- can be conceptualized as information processing systems, whose operation can be described using ``Marr's three levels of analysis'': the computational problem being solved, the algorithms employed, and their molecular implementation. At the first level, we argue that normative theories, such as information-theoretic optimization principles, provide a formalization of the computational problem. At the second level, we show how simplified information processing architectures provide a framework for developmental algorithms, which are formalized mathematically using dynamical systems theory. At the third level, the implementation of developmental algorithms is described by mechanistic biophysical and gene regulatory network models.

Marr's three levels for embryonic development: information, dynamical systems, gene networks

TL;DR

The paper frames embryonic development as an information-processing problem solvable via Marr's three levels of analysis, combining normative information-theoretic objectives (e.g., and ) with algorithmic architectures (layered inputs/outputs and landscape dynamics) and mechanistic realizations (signal transduction, GRNs, and reaction–diffusion/mechano-chemical models). It unifies instructed and self-organized patterning, showing how external inputs, local cellular processing, and intercellular coupling can be organized into hierarchical architectures, including boundary-driven and skip-layer variants, and how Geometric Dynamical Systems provides a minimal, predictive framework. The authors discuss end-to-end multilayer optimization, robustness to natural fluctuations, morphogenesis, and scaling as open questions, arguing that integrating these levels yields a principled bridge from function to mechanism. Overall, the framework offers a coherent, testable roadmap for connecting high-level information objectives to concrete molecular mechanisms across scales, guiding experimental and theoretical work in developmental biology.

Abstract

Developmental patterning comprises processes that range from purely instructed, where external signals specify cell fates, to fully self-organized, where spatial patterns emerge autonomously through cellular interactions. We propose that both extremes -- as well as the continuum of intermediate cases -- can be conceptualized as information processing systems, whose operation can be described using ``Marr's three levels of analysis'': the computational problem being solved, the algorithms employed, and their molecular implementation. At the first level, we argue that normative theories, such as information-theoretic optimization principles, provide a formalization of the computational problem. At the second level, we show how simplified information processing architectures provide a framework for developmental algorithms, which are formalized mathematically using dynamical systems theory. At the third level, the implementation of developmental algorithms is described by mechanistic biophysical and gene regulatory network models.

Paper Structure

This paper contains 6 sections, 3 figures, 1 table.

Table of Contents

  1. Marr's first level: Normative theories for development
  2. Marr's second level: Developmental algorithms form an information-processing hierarchy
  3. Marr's third level: Mechanistic implementation of developmental algorithms
  4. Instructed and self-organized development
  5. Open questions
  6. Acknowledgments

Figures (3)

  • Figure 1: Illustration of Marr's three levels for developmental biology. a, The computational problem can be defined using optimization principles such as maximizing information content, which drives patterns to high patterning entropy, high reproducibility states Brueckner2024a. b, The algorithmic level is formalized by dynamical systems theory modeling single and collective cellular states as valleys in a landscape rand_geometry_2021. c, The algorithms are implemented by molecular mechanisms and gene regulatory networks.
  • Figure 2: Developmental information processing architectures. a, Schematic of developmental stages over time, from single fertilized cell to a fully-develped organism. b, A particular developmental process with fixed number of cells $N$ is represented as a two-layer system with inputs $c_i^{\alpha}(t)$ and outputs $g_i^{\beta}(t)$, with cell index $i$, various signals are denoted by indices $\alpha, \beta$, and time by $t$. c-e, Schematics of two-layer systems exhibiting three types of control. Special cases of such systems are feedback from outputs to inputs (f), skip-layer interactions (g), and boundary-driven systems (h).
  • Figure 3: Analyzing instructed and self-organized development across Marr's three levels. a, While instructed development can be formalized as an information transmission problem, the problem of self-organized development can be represented as transforming noise into an output pattern that maximizes self-organized information. Mixed scenarios have not yet been formalized at an information-theoretic level. b, The algorithmic architectures can be arranged along the axis from instructed to self-organized cases along decreasing importance of the input and increasing importance of spatial communication. c, These architectures are implemented by mechanisms that are purely local in instructed scenarios, but allow spatial communication in self-organized scenarios.