Cellular Viability Theory: Models & Mechanisms

Updated 18 November 2025

Theory of Cellular Viability is a rigorous framework that defines how cells maintain life using mathematical, quantum-inspired, and computational models.
It integrates SCOP formalism, lattices, and contradiction-centric approaches to quantify cellular states and model dynamic transitions under various environmental constraints.
The theory employs category theory and information-theoretic criteria to explain multilevel emergence and adaptive behavior from molecular processes to tissue organization.

The theory of cellular viability seeks to rigorously describe the conditions, mechanisms, and formal processes by which living cells maintain, lose, or recover their ability to persist as cohesive, self-organized, and functional entities. It synthesizes insights from information theory, quantum-inspired formalism, contradiction-centric agent models, categorical emergence, and computational frameworks for individuation. The goal is to produce a mathematical, conceptual, and physically interpretable account of how cells achieve and sustain the property of "being alive" amid environmental perturbation, genetic drift, resource constraints, and cooperative or antagonistic agent interactions.

1. Formalisms for Cellular States: SCOP, Lattices, and Quantum-Inspired Models

Modern cellular viability theory employs a suite of mathematical structures to encode cellular states, contexts, and properties. The SCOP (State, Context, Property, Transition, Applicability) formalism models a concept (or cell) as a five-tuple: $(\Sigma,\,\mathcal{M},\,\mathcal{L},\,\mu,\,\nu)$ where $\Sigma$ enumerates possible cellular states (e.g., membrane integrity, metabolic activity), $\mathcal{M}$ denotes relevant contexts (e.g., temperature, pH, signaling environment), $\mathcal{L}$ lists characteristic properties (e.g., gene expression profile, protein folding status), $\nu(p, a)$ quantifies the degree to which property $a$ holds in state $p$ , and $\mu(q, e, p)$ prescribes the probability the system transitions from $p$ to $q$ under context $e$ (Gabora et al., 2010).

Lattices are imposed on $\mathcal{M}$ and $\mathcal{L}$ via a partial order ( $\le$ ), conjunction ( $\wedge$ ), disjunction ( $\vee$ ), and orthocomplement ( $\perp$ ):

Contextual focus (analytic cellular regulation) utilizes sublattices near the top (high abstraction, strongly enforced constraints).
Associative (plastic, adaptive) regulation populates the lattice with atypical or novel cross-context transitions enabled by conjunction and entanglement.

Hilbert and Fock space realizations permit description of aggregated cell states, where entanglement (non-factorizable joint states) captures emergent properties at multicellular or molecular ensemble level.

2. Contradiction-Centric Models of Viability and Behavior

Cellular viability is driven by a set of internal contradictions, each formalized as opposing regulatory aspects with quantified strengths: $c = \langle s^+,\,s^-\rangle, \quad A_c = I_{s^+} - I_{s^-}$ where $A_c \in (-1,1)$ measures the sharpness of dominance between survival-promoting and death-promoting (or adaptation vs. homeostasis, division vs. quiescence) poles (Jiao, 17 Jan 2025, Jiao, 2017). Each contradiction engenders an internal game with explicit payoff matrices, and cell behavior is a dynamic resolution of these tensions, resulting in the observable traits ( $P$ ) and survival utility ( $\mu$ ).

Interactions occur via resource competition and feedback:

Cells contest nutrients, space, or signaling molecules, and shift contradiction strengths accordingly.
Swarm potential $P_n(c)$ aggregates contradiction sharpness over all cells in a tissue, driving either conformity to global homeostasis or antagonistic responses leading to cell death, differentiation, or immune evasion.

Viability manifests as the stable maintenance of contradiction equilibria when $\mu$ is maximized and resource constraints are respected. Failure of equilibria or depletion below energetic thresholds results in viability loss.

3. Categorical Foundation: Emergent Individuals via Category Theory

Category-theoretic approaches recast cellular viability as an emergence property within construct categories ( $A$ ) equipped with structured sets of operations ( $e_A$ ) and generalized underlying functors ( $U_A$ ) (Guardia et al., 2018). Limits and colimits—product, coproduce, pullback, pushout, equalizer—model the assembly, merger, or constraint of cellular subsystems (molecules, organelles, tissues). Homomorphisms encode natural transformations between viability-preserving modules; isomorphisms formalize equivalent cell types or states across biological levels. Representability by atomic blocks models baseline viability and the generation of higher-order multicellular organization.

Stepwise construction of emergent individuals from molecule to organism demonstrates how local viability at the cell level integrates into global systemic persistence.

4. Information-Theoretic and Algorithmic Criteria for Viability

Algorithmic idealism reframes cell viability as informational identity and coherence within computational or physical substrata (Sienicki, 16 Dec 2024). A cell's informational "self-state" $s \in \Sigma$ is viable if its transition trajectory

$(s_0 \rightarrow \ldots \rightarrow s_n)$

minimizes algorithmic cost (Kolmogorov complexity) under sufficiency constraints, preserving identity-invariant features up to tolerance $\varepsilon$ .

Mutual information $I(s : s')$ between successive self-states quantifies robustness of cellular memory and function despite environmental fluctuations. The sufficiency rule ( $K(s'|s) \leq C$ ) prohibits abrupt transitions that compromise viability, such as catastrophic genetic mutations or lethal stress. This perspective formalizes threshold phenomena in apoptosis, necrosis, or reprogramming.

Emergence-focused simulation models instantiate cellular populations with nonlinear genotype, phenotype, and environment dynamics, demonstrating viability as a multilevel phenomenon (Marriott et al., 2015):

Genotype–phenotype divergence can arise when genetic drift in pseudogene regions leaves the phenotype (and thus viability) unaffected.
Gene duplication and neutral drift create genome architectures with robust redundancy, enhancing adaptability under viability pressure.
Agent metabolism and energy balance equations drive survival thresholds; agents/cells survive if $E_{t+1} > 0$ and die otherwise.
Replicator dynamics shape population-level allele frequencies, adaptation, and divergence, revealing viability as both a micro and macro evolutionary property.

Contradiction-centric swarm models and mean-field approaches further reveal collective phase transitions (e.g., all cells cooperate for tissue integrity at high coupling, individualize at low temperature or low interaction strength) (Bertin, 2020).

Models developed for cognitive individuation and LLM-agent communities reveal structural analogues to cellular viability, particularly at multicellular levels:

Mesoscale clusters of mutually reinforcing agents mirror tissue-level homeostasis; "social" emergence of persistent clusters is analogous to specialized cell aggregates (Takata et al., 5 Nov 2024).
Association and coherence thresholds align with percolation models of intercellular connectivity and tissue viability (Gabora et al., 2010).

Such perspectives suggest that computational, cognitive, and agent-based frameworks—when grounded in rigorous mathematical definitions—can illuminate fundamental mechanisms supporting cellular viability and its loss.

7. Synthesis and Open Directions

Cellular viability is best understood as the outcome of coupled dynamical systems—contradiction equilibria, information-theoretic identity, category-theoretic emergence, and resource-driven agent optimization—operating across scales from molecule to organism. Formal thresholds (entropy, percolation, energy, algorithmic complexity) demarcate survival from death, robust function from pathological breakdown. Current idealized models provide a toolkit for exploring the emergence, persistence, and adaptive reconfiguration of viable cells, tissues, and agents. Open directions include rigorous quantification of viability under stochastic perturbations, explicit modeling of context-dependent lattice structures, and development of computational frameworks capable of predicting state transitions across biological and synthetic substrates.