Bacterial adhesion kinetics and thermodynamics: A stochastic model integrating pili, fimbriae, and surface roughness into extended DLVO theory

The thermodynamic and kinetic modeling of prokaryotic interfacial deposition provides significant insights into the beginning stages of biofilm formation. While classical Derjaguin–Landau–Verwey–Overbeek (DLVO) formalisms establish a foundational continuum framework, accurate reconciliation of theoretical interaction potentials with experimental deposition rates necessitates the integration of cell envelope ultrastructure, specifically the discrete geometry of pili, fimbriae, and glycocalyx brush layers. DLVO and XDLVO models are inherently two-body formalisms which predict whether a single isolated bacterium will deposit but cannot predict how the deposited bacterium on substrates evolves in time, how cell organization occurs laterally, or how interactions modulated in the late-stage coverage. This study advances a stochastic "hairy bacterium" interaction model, parameterizing the cell surface via spherical Fourier modes with periodic gap modulation (p, q bands) to represent nanoscale appendage heterogeneity. Utilizing a dynamic Metropolis–Hastings Monte Carlo framework coupled with Surface Element Integration (SEI), we compute trajectory-dependent potentials incorporating retarded Lifshitz–van der Waals attraction, linearized Poisson–Boltzmann electrostatics, and Hookean elastic deformation. Parametric analysis reveals that increasing substrate root-mean-square roughness (R q ) from 2 nm to 40 nm, together with appendage elongation (ε from 0 to 50 nm), significantly attenuates the primary activation energy barrier from ∼ 10 3 k B T (smooth sphere DLVO) to ∼1 – 10 k B T representing a 10 3 fold reduction in the Boltzmann weighted barrier crossing penalty thereby enhancing the thermodynamic favorability of irreversible capture. Temporal evolution, calibrated via Stokes–Einstein diffusivity, reproduces sigmoidal adsorption kinetics with saturation timescales approaching 10 5 seconds, quantitatively consistent with parallel-plate flow cell data for S. auerus on silanized substrates. Microstructural interrogation via the radial distribution function, g(r), identifies a characteristic nearest-neighbor clustering peak at ∼1 μm, consistent with steric cell-to-cell spacing. Steady-state surface coverage analysis yields a saturation limit of 31.6%, dominated by monolayer configuration (Φ mono ≈ 0.316) and microcolony consolidation (Φ colony ≈ 0.106), with a negligible contribution from multilayer stacking (Φ multi ≈ 0), which demonstrates that the thermodynamic and steric landscape strongly disfavors vertical stacking during initial adhesion in favor of lateral microcolony consolidation. Traditional DLVO/XDLVO models resolve the single-particle, dilute regime question of whether a bacterium will deposit on a substrate, whereas our Monte Carlo simulation resolves the many-body, finite-coverage question of how the deposited population organizes spatially with specific characterization to bacterial microcolony, monolayer, multilayer partitioning, and temporal saturation kinetics. These findings demonstrate that nanoscale topographic commensurability and appendage-mediated barrier attenuation are major factors governing bacterial adhesion and should be incorporated into predictive models to achieve quantitative agreement with experimental deposition kinetics.