Statistical Teleodynamics of Hexapeptide Energy Landscapes: Rugged Barrier Topology, Kinetic Networks, and Graph-Theoretic Analysis

Abstract

Small sequence changes can reshape the slow dynamics of disordered biomolecular motifs that help drive liquid--liquid phase separation (LLPS) and can also bias condensates toward aging and pathological aggregation in disorders such as ALS and frontotemporal dementia. This thesis asks if and when that sequence-dependent kinetic structure is already visible in explicit peptide energy landscapes and if and when it survives principled compression into smaller stochastic models. We develop a new framework linking explicit energy landscapes of LLPS-relevant hexapeptides to validated MFPT-preserving coarse-grained Markov models and observable-specific graph learning. We study 30 unique hexapeptide monomer sequences and one yyggyy dimer benchmark in the Mpipi coarse-grained model. At T=300K, the quantitative monomer analysis comprises 43 kinetic-network realizations, with 36 supporting direct microscopic-to-coarse validation and 35 entering the final graph-level machine-learning panel. Stationary-point databases built with GMIN and OPTIM/LAMMPS are converted into reversible continuous-time Markov chains and then reduced by mean-first-passage-time-preserving graph transformation. Despite a median 90.3% reduction in state-space size, the reduced models preserve endpoint mean first-passage times with median relative errors below 0.00000001 in both directions. On these validated coarse networks, interpretable graph descriptors recover statistically significant cross-sequence variation in mean first-passage times and the leading relaxation time, but not in the finer spectral ratio. A complementary node-level analysis shows that committor probabilities are strongly recoverable from nonlinear baselines on local node descriptors, whereas sparse message-passing graph neural networks remain much weaker. Together, these results show that LLPS-relevant peptide motifs already encode real mesoscale kinetic structure, but that its recoverability depends on the observable and the representation. In statistical-teleodynamic terms, the results support a bounded form of organization emerging from constrained stochastic flow rather than a fully compressible global order. The thesis therefore establishes a validated multiscale workflow for stochastic model reduction and clarifies what can and cannot be compressed into graph-level structure in minimal peptide systems.