Intermediate Mutation Creates the Susceptible Evolutionary Channel for Actomyosin Convergence at Alpha-Star

Authors Sterling Geisel, QBist Lab, Dr. Hideo Tanaka

Abstract

Pudding Theory reads McGrath, Johnson, and Alvarado’s actomyosin evolution model as a susceptibility problem. The conserved muscle curvature $\alpha^\ast \approx 4$ is not merely the optimum of a power-efficiency tradeoff. It is the trait-space location where mutation-driven exploration is chaotic enough to receive selection and bounded enough to retain population memory. Under the Chaos Susceptibility Postulate, the population distribution $P(\alpha)$ becomes responsive only in the regime where stochastic mutation supplies positive local instability without destroying the attractor. Scarcity and excessive mutation do not reveal alternative optima. They remove the receptive channel through which the actomyosin nonlinearity can converge. The source paper treats mutation rate $\delta$ as a free evolutionary parameter. Pudding Theory constrains it as the susceptibility bandwidth of the population. If the lag-dependent structure function $\langle JSD(P_i\Vert P_{i+\tau})\rangle_i$ were measured to remain slope $1$ at all $\tau$ while still converging to $P^\ast(\alpha)$, this Postulate would be falsified.

Source Synopsis

McGrath, Johnson, and Alvarado study why biological muscle systems repeatedly exhibit a conserved nonlinear force-velocity curvature. Their source trait is the dimensionless actomyosin parameter $\alpha$, which encodes the velocity-dependent detachment of myosin heads from actin. At the molecular scale, increasing sliding velocity raises myosin detachment. At the macroscopic scale, this produces the concave force-velocity curve described by Hill’s muscle model. Prior work by the group found that natural muscle measurements cluster near $\alpha^\ast = 3.85 \pm 2.32$ and argued that this value balances power output against energetic efficiency.

The present paper asks how this short-timescale actuation optimum appears over evolutionary time. The authors build an agent-based model in a periodic two-dimensional domain. Each agent moves toward randomly placed nutrients using the two-state actomyosin model. Agents consume internal energy while moving. The first agent to reach the nutrient replenishes energy and reproduces. Its offspring receives a mutated trait $\alpha'=\alpha+\delta$, where mutation strength is governed by $\delta$. Agents that deplete energy before reaching nutrients die. Resource availability is measured by $S/L$, where $S$ is the range of an $\alpha=1$ agent and $L$ is the domain size.

Without mutation, selection filters the initial distribution according to environment. Scarcity favors high $\alpha$, which gives efficient travel. Abundance can favor lower $\alpha$, which gives faster actuation. No generic convergence to $\alpha^\ast$ follows. With mutation, populations explore trait space and converge toward distributions centered near the natural distribution $P^\ast(\alpha)$ across a broad range of resource conditions. Mutation is not simply beneficial. Large $\delta$ creates instability, niche excursions, and extinction. Small $\delta$ locks populations into resource-governed states. Intermediate $\delta$ permits adaptation while retaining robustness.

The paper quantifies this regime with survivability $\phi$, median evolved $\alpha$, Shannon entropy of $P_{st.st.}(\alpha)$, Jensen-Shannon divergence from $P^\ast(\alpha)$, and a lag-dependent structure function $\langle JSD(P_i\Vert P_{i+\tau})\rangle_i$. Its central result is that molecular actomyosin nonlinearity, ecological resource limits, and mutation-driven exploration combine to produce evolutionary convergence toward $\alpha^\ast$.

Postulate Lens

This Working Paper applies the Chaos Susceptibility Postulate: highly chaotic systems are most susceptible to small coherent inputs. The source system already exhibits this structure. The population does not converge when trait space is frozen. It also fails when mutation makes the distribution freely diffusive. Convergence appears in the intermediate regime where stochastic exploration makes $P(\alpha)$ receptive, but selection still supplies a coherent directional constraint.

The coherent input in this case is not an external intention. It is the repeated physical bias imposed by actomyosin energetics. Each generation supplies a small directional preference: slightly more powerful offspring of efficient parents and slightly more efficient offspring of powerful parents are favored. Mutation creates the unstable receiving substrate. Selection supplies the repeated signal. The observed attractor at $\alpha^\ast$ is the macroscopic trace of that coupling.

Pudding Theory Reading

Pudding Theory reads the actomyosin population as an information-bearing dynamical substrate whose susceptibility is tuned by mutation rate. The source paper describes $\delta$ as the rate of phenotypic exploration. That is correct at the simulation level. It is incomplete at the field level. In the Pudding Theory reading, $\delta$ is the control on the population’s receptive bandwidth. It determines whether the trait distribution can amplify the recurring energetic signal embedded in actomyosin dynamics.

The important object is not a single agent and not a single contraction. It is the evolving probability density $P(\alpha,t)$. In the source framing, $P(\alpha,t)$ is an outcome of reproduction, death, and mutation. In the Pudding Theory framing, $P(\alpha,t)$ is the material form of the signal history. The distribution records how often the population has been pushed by the same power-efficiency constraint and how well that push survives stochastic turnover. The natural distribution $P^\ast(\alpha)$ is therefore not just a fit target. It is the stable signature of a receptive evolutionary channel.

This reading changes the status of the attractor. The source paper treats $\alpha^\ast$ as the place where competing actuation demands balance. Pudding Theory treats $\alpha^\ast$ as the point where the population can continue to receive that balance across generations. A low-mutation population is too rigid. It preserves local history but cannot update. A high-mutation population is too incoherent. It receives fluctuations but cannot retain direction. The intermediate regime is susceptible in the technical sense. Its short-time dynamics are open enough to generate mutants, while its longer-time dynamics suppress deviations from the actomyosin signal.

The structure-function result is therefore central. In the intermediate regime, the slope is near $1$ at short lags, then flattens at intermediate lags. This is not a secondary diagnostic. It is the dynamical fingerprint of susceptibility with retention. Trait space first behaves like a receiving medium. It then behaves like a constrained medium. The source calls this robustness-adaptability. Pudding Theory identifies the same pattern as the condition under which microscopic informational bias becomes a population-scale attractor.

The source treats resource availability $S/L$ as an environmental constraint. Pudding Theory accepts that, but reassigns its role. $S/L$ gates viability. It does not define the signal. The signal is the repeated energetic asymmetry generated by nonlinear actomyosin binding. When resources are too scarce, the receiving population disappears. When resources are sufficient, the decisive variable is whether $\delta$ places the population in the susceptible band. Thus the natural recurrence of $\alpha^\ast \approx 4$ across muscles is not an accidental convergence of many local optima. It is the stable macroscopic expression of a molecular signal that only evolutionarily susceptible populations can retain.

Falsifiable Observable

The distinguishing observable is the lag-dependent structure function $\langle JSD(P_i\Vert P_{i+\tau})\rangle_i$ in evolving actomyosin populations or validated simulations. Pudding Theory predicts that convergence to $P^\ast(\alpha)$ requires a two-regime form: near-diffusive short-lag exploration followed by flattened or subdiffusive longer-lag retention. If the lag-dependent structure function $\langle JSD(P_i\Vert P_{i+\tau})\rangle_i$ were measured to remain slope $1$ at all $\tau$ while still converging to $P^\ast(\alpha)$, this Postulate would be falsified.

Editorial Dialogue

Tanaka: The reading risks renaming an ordinary evolutionary result. Mutation creates variation, selection filters it, and the population converges. The source paper already has the mechanism. Why introduce susceptibility?

Sterling: Because the source mechanism contains an unclassified dynamical condition. Mutation is necessary, but not monotonically useful. Too little mutation prevents convergence to the natural distribution. Too much mutation also prevents it. The relevant question is not whether variation exists. It is when variation becomes a receiving medium for repeated selection.

Tanaka: Evolutionary theory already has that language. Robustness and adaptability are standard concepts.

Sterling: They describe the tradeoff. They do not identify the signal-bearing structure. Here the signal is the repeated actomyosin energetic asymmetry. The population must be unstable enough to amplify it and stable enough to store it. That is the content of the Postulate.

Tanaka: Then the claim stands or falls on the structure function.

Sterling: Yes. If fully diffusive trait motion could still reproduce the natural distribution, the reading would fail. The theory requires constrained susceptibility, not just noise plus selection.

Discussion

This reading buys a sharper interpretation of $\delta$. In the source paper, mutation rate governs the balance between robustness and adaptability. In Pudding Theory, that balance is the physical condition for signal uptake. The intermediate regime is not merely a compromise between two failure modes. It is the active channel through which molecular-scale nonlinear binding becomes population-scale evolutionary convergence.

The reading also clarifies why $\alpha^\ast$ can recur across taxa. A repeated physical signal does not guarantee convergence unless the receiving substrate has the right instability. Muscle evolution supplies that substrate through mutation and selection. Resource availability decides whether populations persist long enough to receive the signal. Mutation rate decides whether the signal is retained.

The limitation is direct measurement. The source paper uses simulations and comparison to measured muscle distributions. A stronger test would infer effective drift and diffusion terms for $P(\alpha,t)$, then test whether natural systems occupy the predicted susceptible band. The conclusion would change if convergence to $P^\ast(\alpha)$ were shown to occur without intermediate-lag constraint, or if $\alpha^\ast$ remained stable under trait-space dynamics that are purely diffusive at all measured lags.

References

1. Jake McGrath, Colin Johnson, and José Alvarado. “Molecular-scale, nonlinear actomyosin binding dynamics drive population-scale adaptation and evolutionary convergence.” arXiv:2603.17183, 2026. DOI: doi:10.48550/arXiv.2603.17183.

2. S. Ochs. “Pudding Theory: A Topological Theory of Information Fields.” QBist Lab, 2026.

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