Probabilistic, Thermodynamic, and Information-Theoretic Constraints on De Novo Protein Assembly

The emergence of functional, sequence-specific biopolymers from prebiotic chemistry remains one of the most significant unresolved challenges in molecular biology and biophysics. Functional proteins require highly specific linear arrangements of homochiral amino acids linked exclusively by α-peptide bonds to achieve stable tertiary folds capable of enzymatic catalysis. This article reviews the empirical mathematical probabilities, stereochemical constraints, and thermodynamic barriers governing unguided de novo polypeptide assembly. Quantitative analysis of sequence space demonstrates that the probability of generating a single functional 150-residue protein through purely random molecular interactions is approximately 10−164 to 10−167 per trial—a figure that exceeds the probabilistic resources of the observable universe across a 5-billion-year timeframe. Furthermore, aqueous thermodynamic equilibria and error-catastrophe thresholds present formidable physical barriers to spontaneous polymerization. The implications of these empirical constraints on origin-of-life models and teleological inferences in biological systems are examined.