Intent Field Theory of Biology:

A Lagrangian Framework Linking Genome Architecture, Epigenetic Memory and Phenotypic Dynamics

Abstract

Biological systems integrate genomic information, epigenetic states and environmental inputs to generate coherent phenotypes across multiple spatial and temporal scales. Despite extensive molecular characterization, a unifying theoretical framework that connects these layers through dynamical laws remains lacking. Here we propose Intent Field Theory of Biology (IFTB), a field-theoretic formulation in which biological decision dynamics are represented by a scalar field defined over biological spacetime. The dynamics of this field are derived from a Lagrangian density that integrates genomic architecture, epigenetic memory and environmental forcing. The resulting equation of motion is a nonlinear Klein–Gordon–type field equation whose attractor landscape determines stable phenotypic states. We further propose a computational framework combining genome language models and physics-informed neural operators to simulate the evolution of the Intent field in virtual populations. The theory generates quantitative, falsifiable predictions linking genomic GC/AT architecture to dynamical coupling constants, predicting specific perturbation outcomes under CRISPR editing, and forecasting transgenerational inheritance of behavioural phenotypes through epigenetic memory. Together, this framework suggests that biological phenotypes may emerge from the dynamics of an information field shaped by genome architecture and environmental history.

Introduction

Living systems transform genetic information into coherent phenotypes through complex regulatory networks spanning molecular, cellular and organismal scales. Modern genomics has revealed extensive layers of regulation including transcriptional control, chromatin modification, epigenetic inheritance and environmental responsiveness. However, the absence of a unifying theoretical framework has limited our ability to describe how these components jointly generate dynamical biological behaviour.

In physics, complex phenomena often emerge from simple dynamical fields governed by variational principles. Scalar fields, for example, provide the foundation of theories ranging from condensed matter phase transitions to particle physics. In biological contexts, reaction–diffusion models and dynamical systems have successfully described morphogenesis and pattern formation. Yet these approaches rarely incorporate genome architecture directly into their governing equations.

Here we propose Intent Field Theory of Biology (IFTB), a field-theoretic model in which biological decision processes are described by a scalar field representing the instantaneous state of biological intent. In this formulation, genomic architecture, epigenetic state and environmental context act as sources and modifiers of the field dynamics. The resulting framework unifies multiple regulatory layers within a single variational principle.

Theoretical Framework

Intent Field

We define a scalar field

latex I(x^\mu)

where

latex x^\mu = (t, \mathbf{x})

represents biological spacetime.

The field represents the instantaneous regulatory configuration of a biological system, capturing the integrated influence of genomic, epigenetic and environmental factors.

Lagrangian Density

The dynamics of the Intent field are defined by the Lagrangian density

latex \mathcal{L}_{IFTB} = \frac{1}{2}(\partial_\mu I)(\partial^\mu I) - V(I) + \mathcal{L}_{int}(I,G,M,E) + \mathcal{L}_{source}

where

represents genomic architecture
represents epigenetic state
represents environmental forcing

Potential Landscape

To capture attractor states in biological systems we define

latex V(I)=\frac{\lambda}{4}(I^2-I_0^2)^2

This double-well potential generates two stable attractor states corresponding to alternative phenotypic or behavioural outcomes.

Interaction Terms

Coupling between regulatory layers is defined as

latex \mathcal{L}_{int} = -\frac{g_1}{2}G(x)I^2 - \frac{g_2}{2}M(x,t)I^2 - g_3E(x,t)I

where

are coupling constants representing the strength of genomic, epigenetic and environmental influence on the Intent field.

Genomic Source Terms

Genomic base composition provides additional source terms

latex \mathcal{L}_{source} = J_{AT}(x)I(x)+J_{CG}(x)I(x)

where

and represent the spatial densities of AT- and GC-rich genomic regions.

Equation of Motion

Applying the Euler–Lagrange equation yields

latex \partial_\mu \partial^\mu I + \lambda (I^2-I_0^2)I + (g_1G+g_2M)I = -g_3E + (J_{AT}+J_{CG})

In explicit form

latex \frac{\partial^2 I}{\partial t^2} - D\nabla^2 I + \lambda(I^2-I_0^2)I + (g_1G+g_2M)I = -g_3E + (J_{AT}+J_{CG})

This nonlinear field equation describes the evolution of biological intent across space and time.

Simulation Framework

Direct analytical solutions of the field equation are generally intractable for realistic genomes. We therefore propose a computational simulation framework combining genome language models with differentiable physics simulators.

Genome Encoding

Whole-genome sequences are transformed into functional embeddings using genome language models such as DNABERT or Nucleotide Transformer.

Each genome is mapped to

latex z_i \in \mathbb{R}^d

representing regulatory potential.

Neural PDE Solver

The field dynamics are approximated using a physics-informed neural operator

latex I(t+\Delta t) = \mathcal{F}(I(t),z_i,M(t),E(t))

allowing differentiable simulation of large virtual populations.

Virtual Population

A digital population of individuals is simulated, each characterized by

genome embedding
epigenetic state
Intent field

Phenotypes are generated through mapping functions

latex P_i = f(I_i)

Testable Predictions

Prediction 1: Genomic architecture and coupling constants

IFTB predicts a strong correlation between GC content in regulatory regions and the inferred genomic coupling constant .

Failure to detect this relationship would falsify the theory.

Prediction 2: CRISPR perturbation

Targeted edits in GC-rich regulatory regions should alter behavioural attractor states without affecting morphology, whereas mutations in AT-rich structural regions should alter morphology without behavioural change.

Prediction 3: Transgenerational intent memory

Environmental perturbations can generate hysteresis in the Intent field mediated by epigenetic state , producing measurable transgenerational inheritance of behavioural phenotypes.

Discussion

Intent Field Theory proposes that biological systems may be described by dynamical information fields whose attractor landscapes determine phenotypic outcomes. By integrating genome architecture, epigenetic memory and environmental forcing within a Lagrangian framework, the theory offers a unified mathematical description of biological decision processes.

The computational framework presented here enables large-scale simulation of these dynamics using modern genome language models and differentiable physics solvers. If experimentally validated, this approach may provide a new paradigm for understanding how genomic information shapes organismal behaviour and evolution.

Methods (Conceptual)

Genome embeddings were generated using pretrained nucleotide language models. Field dynamics were simulated using physics-informed neural operators implemented in PyTorch. Parameter inference was performed through gradient-based optimization minimizing phenotype prediction error.

References (example style)

Turing A. (1952) The chemical basis of morphogenesis. Levin M. (2022) Bioelectric networks in morphogenesis. Ji Y. et al. (2021) DNABERT: pre-trained transformer for genomic sequences.

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