Morphological computational capacity of Physarum polycephalum

TL;DR

This study establishes a quantitative framework to bound the computational capacity of Physarum polycephalum, an aneural organism, by linking its morphology to information processing through the macroscopic Margolus–Levitin limit. By analyzing time-series growth data, the authors derive four distinct capacity bounds—hydrodynamical, chemical ATP, kinetic energy, and quantum optical—each tied to specific biophysical processes and supporting a comparative, condition-dependent view of computation in living matter. The work shows that chemical ATP bounds dominate in magnitude, while hydrodynamic and quantum-optical channels are orders of magnitude smaller but still informative, and that scaling with area and fractal boundary structure governs long-time behavior. The results offer a principled, physically grounded way to compare computational capacities across strains, ages, and environmental conditions, and lay groundwork for extending morphological computation bounds to other living and reservoir-like systems. Overall, the paper provides a rigorous, multi-degree-of-freedom framework to quantify how morphology enables information processing in a life form without a nervous system, with potential implications for bio-inspired and reservoir-computing architectures.

Abstract

While computational capacity limits of the universe and carbon-based life have been estimated, a stricter bound for aneural organisms has not been established. Physarum polycephalum, a unicellular, multinucleated amoeba, is capable of complex problem-solving despite lacking neurons. By analyzing growth dynamics in two distinct Physarum strains under diverse biological conditions, we map morphological evolution to information processing. As the Margolus-Levitin theorem constrains maximum computation rates by accessible energies, we analyze high-throughput time-series data of Physarum's morphology--quantified through area, perimeter, circularity, and fractal dimension-to determine upper bounds on the number of logical operations achievable through its hydromechanical, chemical, kinetic, and quantum-optical degrees of freedom. Based on spatial distribution of ATP and explored areas, Physarum can perform up to ~$10^{36}$ logical operations in 24 hours, scaling linearly in the non-equilibrium steady state. This framework enables comparison of the computational capacities of life, exploiting either classical or quantum degrees of freedom.

Figures (13)

• Figure 1: Hydrodynamic cytosol oscillations, distribution of ATP across Physarum’s body, kinetic motion of the advancing perimeter, and theoretically predicted superradiant states in actin bundles provide the organism with distinct computational capabilities, enabling determination of their respective upper bounds---a first-ever quantification in an aneural organism. The figure illustrates with histological stains (DAPI for DNA, phalloidin for actin filaments) the biophysical processes that confer on Physarum distinct zones of computational power: (a) Oscillating branches (width $\sim$0.45 mm) act as individual hydrodynamic oscillators. (b) Dividing nuclei localized at the advancing front mirror the spatial distribution of ATP, as shown by experiments in hirose1980changesueda1987patterns. (c) The rate of perimeter expansion, $v(t)=\dot{P}(t)$, characterizes the growth of the organism’s advancing front. (d) Actin filament bundles with organized tryptophan networks (shown in red) have been theoretically predicted to maintain photoexcited superradiant states patwa2024quantum, with lifetimes of tens of picoseconds for ultrafast information processing.
• Figure 2: The morphological circularity of a Physarum body---proportional to the ratio of its area to its perimeter squared---exhibits a similar decay across the younger strains, with an earlier peak in their fractal dimensions while exploring a 2D agar surface. (a) Time-lapse snapshots of Physarum growth shown at $\sim$5-hours intervals over the first $\sim$20 hours for three young strains (age since revival from sclerotia$\leq$ 29 days) : Japanese (top row), Carolina (middle row), and starved Japanese (bottom row). (b) area, (c) perimeter, (d) circularity, and (e) fractal dimension as a function of time averaged across replicates in each group.
• Figure 3: The young Japanese group exhibits rapid, protuberant initial growth with early peaks in its fractal dimension, whereas the old Japanese group grows more slowly and equiradially at the outset but eventually stabilizes at a higher fractal dimension. (a) Time-lapse snapshots shown at $\sim$5-hour intervals over the first $\sim$20 hours for young (top row, age since revival from sclerotia $\leq$27 days) and old (bottom row, age since revival from sclerotia $\geq$49 days) Japanese strains. Averaged (b) area, (c) perimeter, (d) circularity, and (e) fractal dimension for the young (age since revival from sclerotia $\leq$ 27 days) and old (age since revival from sclerotia $\geq$ 49 days) Japanese samples. The blue and orange bars indicate the earliest point at which the organism touches the boundary of the dish for young and old Japanese groups, respectively, with the width of each bar representing the standard error across samples in the corresponding group.
• Figure 4: The vein network-connected Japanese Physarum group initially exhibits higher circularity and lower fractal dimension values compared to the vein network-disrupted group, before gradually transitioning to lower circularity and slightly higher fractal dimension as they explore larger area and perimeter values over time. (a) Time-lapse snapshots shown at $\sim$10-hours intervals over the first $\sim$40 hours for two old Japanese samples (age since revival from sclerotia $\geq$49 days): vein network connected (top row) and vein network disrupted (bottom row). Averaged (b) circularity and (c) fractal dimension for ten biomass ranges for vein network-disrupted group. Averaged (d) area, (e) perimeter, (f) circularity, and (g) fractal dimension across all biomasses for both vein network-connected and -disrupted groups.
• Figure 5: The hydrodynamic bound obtained over a 24-hour interval is higher in the more active young Japanese groups compared to the old Japanese and Carolina groups, closely mirroring their perimeter growth trends shown in Fig. \ref{['Various_strains']}c. The figure shows (a) the hydrodynamic bound for each group, averaged across all group samples, over a 24-hour interval, with the tail fitted using a linear function to capture long-time behavior. The vertical dotted line indicates the NESS, defined from area stabilization, which precedes the onset of the long-time linear regime of the hydrodynamic bound defined from perimeter stabilization. The $x$–axis intercepts of the late-time fits mark the inflection points of the perimeter sigmoids in Fig. S6b of the Supplementary Material, yielding values close to the $\theta$ estimates in Table S1, except for the Carolina subgroup ($N = 63$) extending to 48 h, where the intercept lies at a weighted average of the two inflection points of the perimeter bi-sigmoid. The plot is shown extended to 72 hours in panel (b) for the old Japanese group and to 48 hours in panel (c) for the Carolina strain subgroup ($N = 63$). The transition to the NESS in the old Japanese group occurs well beyond 24 hours.