Konstantinov and Konstantinova (2020) showed by large-scale simulation (~65,000 coupled rate equations for 20 amino acids and peptides up to length 3, with randomly assigned catalytic pairs) that aggregate chiral symmetry breaking occurs only inside bounded windows of two statistical parameters: the abundance parameter (how scarce catalytic pairs are) and the similarity parameter (how broadly each catalyst acts across related reactions). Too many catalysts makes enantioselectivities average out by the central limit theorem; too few leaves no nonlinearity. Coexisting catalytic synthesis and destruction channels enlarge the window beyond what independent channels would give. All of these results rest on severe truncations — peptide length capped at 3, a fixed small reaction menu, discretized ±0.95 enantioselectivity, 50-model ensembles — and no later work is known to have tested any of the extension directions the source itself enumerates. The open problem is to determine whether the window picture and the cooperative-channel enhancement survive longer chains, additional reaction classes, and general statistical laws, to establish whether the cooperative-channel hypothesis holds, and to assess whether surviving windows are compatible with plausible prebiotic peptide chemistry.

Background

A central puzzle about the origin of life is homochirality: biology uses almost exclusively one mirror-image form (enantiomer) of each chiral molecule — left-handed amino acids and right-handed sugars. The classical explanation, due to Frank (1953), combines autocatalytic production of each enantiomer with mutual inhibition between them, which destabilizes the racemic (equal left/right) state so that a small fluctuation tips the system toward one hand. Sandars (2003) recast this idea as a tractable polymerization model in which chiral monomers join into chains, enantiomeric cross-inhibition poisons mixed chains, and the homochiral state emerges through a bifurcation. Such models, however, involve only a handful of species and hand-picked rate constants. Konstantinov and Konstantinova (2018, 2020) asked instead whether chiral symmetry breaking can occur at all in a chemically large prebiotic system with 20 amino acids (both enantiomers) and their peptides, where thousands of potential chiral catalysts act simultaneously with random properties. Here enantioselectivity denotes the fractional preference of a catalyst for producing (or destroying) one enantiomer over the other; if many catalysts with randomly handed preferences act on the same substrate, the central limit theorem makes their effects average out, which suppresses symmetry breaking. The 2020 model is a far-from-equilibrium system of roughly 65,000 coupled ordinary differential equations covering irreversible synthesis and catalytic synthesis of amino acids from a food source, all-to-all peptide ligation, and destruction and catalytic destruction of amino acids with waste recycling to conserve total mass. Which (amino acid, catalyst) pairs are catalytic is randomized, controlled by the abundance parameter aa — the probability that a random pair is catalytic, i.e. how scarce organic catalysts are — and the similarity parameter ss — the expected fraction of additional amino acids on which a chosen catalytic pair acts with the same rates. For tractability, enantioselectivity took the discrete values ±0.95\pm 0.95 with equal probability, similar reactions shared identical rates, and each parameter point was estimated from ensembles of 50 randomized networks with Wilson score confidence intervals (a standard confidence interval for a proportion from a finite number of trials). Peptide length was truncated at 3, since in the source's scaling estimate for a hypothetical primordial soup containing 50 amino acids the number of potential catalysts grows from (2×50)3=106(2\times 50)^3 = 10^6 at length 3 to 101010^{10} at length 5 — the estimated number of possible catalysts, after multiplying by a catalytic probability of 10−610^{-6}–10−510^{-5}, rising from order 10010^0–10110^1 to 10410^4–10510^5 — while concentrations of individual peptides fall steeply with length. In the source, symmetry breaking in a randomized network is identified with a sustained nonzero enantiomeric excess of amino-acid concentrations over the simulation time course, the evolution time being chosen so that symmetry breaking can occur if it can occur at all; reported window percentages are Wilson-interval estimates of the fraction of ensemble runs in which symmetry breaking was observed. Within this truncated setting the study found that symmetry breaking occurs only inside bounded windows of the (a,s)(a,s) plane: too few catalysts and the system is effectively linear (no symmetry breaking); too many, and central-limit averaging of enantioselectivity destroys it, with a=200×10−6a=200\times10^{-6} apparently near the too-large threshold. Models with both catalytic synthesis and catalytic destruction channels (DS models) broke symmetry substantially more often than the statistical superposition of single-channel models, leading to the authors' cooperative multi-channel hypothesis. When symmetry breaking occurred, amino-acid concentrations themselves split into cooperative and competing groups. The question is whether this window picture and the cooperative-channel effect are artifacts of the truncations or robust features of large peptide systems.

Problem Statement

Determine whether aggregate chiral symmetry breaking in large peptide systems remains confined to bounded abundance-similarity windows — and whether the cooperative enhancement from coexisting catalytic synthesis and destruction channels persists — once the model of Konstantinov and Konstantinova (2020) is extended beyond the setting in which those results were established. Concretely, the source leaves open: (i) how the symmetry-breaking regions in the (abundance, similarity) parameter plane scale when peptides grow beyond length 3, given that individual-peptide concentrations fall roughly exponentially with chain length while the number of potential catalysts rises (in the source's 50-amino-acid scaling estimate) from order 10610^6 at length 3 toward 101010^{10} at length 5, so that longer chains both dilute concentrations and introduce additional catalytic motifs; (ii) how the omitted reaction classes — catalytic ligation, racemization and catalytic racemization, and more realistic sedimentation/precipitation of waste — shift, shrink, or destroy these windows; (iii) whether the windows are robust to replacing the discretized enantioselectivity law (bi-delta ±0.95\pm 0.95), the identical rates assigned to similar reactions, and the tractability-motivated coefficient distributions by general statistical laws for catalytic rates and enantioselectivity, at statistical resolution beyond the 50-network ensembles, including the under-resolved high-abundance regime near a=200×10−6a=200\times10^{-6}; (iv) whether the hypothesis that multiple coupled nonlinear channels (coexisting catalytic synthesis and destruction) cooperatively enlarge the symmetry-breaking region beyond the superposition of independent channels — a hypothesis explicitly labeled as such in the source — is established or refuted; and (v) whether the surviving windows correspond to parameter magnitudes — catalyst scarcity, breadth of catalytic action, enantioselectivity distributions — that are plausible for prebiotic peptide chemistry, judged against measurements of peptide catalytic promiscuity and enantioselectivity where such data exist. The reaction classes listed in (ii) and the replacement axes listed in (iii) are each in scope as independently refutable sub-claims — all of them must be assessed and settling one resolves that part; 'general statistical laws' in (iii) means continuous distributions on the enantioselectivity range [−1,1][-1,1] together with general catalytic-rate distributions sampled across their spread, rather than only the two-point bi-delta law and the identical-rate assignment. Items (i)-(iv) jointly serve one objective — establishing the robustness of the window picture and of the cooperative-channel enhancement beyond the truncations — and are independently refutable sub-questions: a result that settles one of them resolves that part of the objective while the remaining sub-questions stay open. Item (v) is an optional interpretive add-on to the same objective, assessing whether the surviving windows are compatible with plausible prebiotic peptide chemistry; it is not required to establish the robustness objective.

References

  1. K. K. Konstantinov and A. F. Konstantinova (2020), 'Chiral Symmetry Breaking in Large Peptide Systems', Origins of Life and Evolution of Biospheres 50(3-4):99-120, DOI 10.1007/s11084-020-09600-1, https://doi.org/10.1007/s11084-020-09600-1
  2. K. K. Konstantinov and A. F. Konstantinova (2018), 'Chiral Symmetry Breaking in Peptide Systems During Formation of Life on Earth', Origins of Life and Evolution of Biospheres 48(1):93-122, DOI 10.1007/s11084-017-9551-4, https://doi.org/10.1007/s11084-017-9551-4 (predecessor study)
  3. P. C. Diniz, J. A. D. Wattis and F. P. da Costa (2022), 'Mathematical Models of Chiral Symmetry-breaking – A Review of General Theories, and Adiabatic Approximations of the APED System', Origins of Life and Evolution of Biospheres 52(4):183-204, DOI 10.1007/s11084-022-09631-w, https://doi.org/10.1007/s11084-022-09631-w
  4. K. K. Konstantinov and A. F. Konstantinova (2022), 'Evolutionary Approach to Biological Homochirality', Origins of Life and Evolution of Biospheres 52(4):205-232, DOI 10.1007/s11084-022-09632-9, https://doi.org/10.1007/s11084-022-09632-9
  5. K. K. Konstantinov and A. F. Konstantinova (2025), 'Chiral symmetry breaking and information accumulation in pre-biological protocell evolution', Scientific Reports 15:12806, DOI 10.1038/s41598-025-97319-2, https://doi.org/10.1038/s41598-025-97319-2
  6. A. D'Elia and S. Longo (2026), 'Symmetry Breaking on a Chessboard: 50 Years After Eigen's and Winkler's "Laws of the Game"', Symmetry 18(1):205, DOI 10.3390/sym18010205, https://doi.org/10.3390/sym18010205
  7. T. Buhse and J.-C. Micheau (2022), 'Spontaneous Emergence of Transient Chirality in Closed, Reversible Frank-like Deterministic Models', Origins of Life and Evolution of Biospheres 52(1-3):3-20, DOI 10.1007/s11084-022-09621-y, https://doi.org/10.1007/s11084-022-09621-y
  8. A. Brandenburg (2021), 'Chirality in Astrophysics', arXiv:2110.08117, https://arxiv.org/abs/2110.08117 (also published as a chapter in 'Chiral Matter', World Scientific, 2023, DOI 10.1142/9789811265068_0002)
  9. F. C. Frank (1953), 'On spontaneous asymmetric synthesis', Biochimica et Biophysica Acta 11:459-463, DOI 10.1016/0006-3002(53)90082-1, https://doi.org/10.1016/0006-3002(53)90082-1
  10. P. G. H. Sandars (2003), 'A Toy Model for the Generation of Homochirality during Polymerization', Origins of Life and Evolution of the Biosphere 33(6):575-587, DOI 10.1023/A:1025705401769, https://doi.org/10.1023/A:1025705401769