Polymorphism of stable collagen fibrils

Abstract

Collagen fibrils are versatile self-assembled structures that provide mechanical integrity within mammalian tissues. The radius of collagen fibrils vary widely depending on experimental conditions in vitro or anatomical location in vivo. Here we explore the variety of thermodynamically stable fibril configurations that are available. We use a liquid crystal model of radial collagen fibril structure with a double-twist director field. Using a numerical relaxation method we show that two dimensionless parameters, the ratio of saddle-splay to twist elastic constants k24/K22 and the ratio of surface tension to chiral strength [small gamma, Greek, tilde] ≡ γ/(K22q), largely specify both the scaled fibril radius and the associated surface twist of equilibrium fibrils. We find that collagen fibrils are the stable phase with respect to the cholesteric phase only when the reduced surface tension is small, [small gamma, Greek, tilde] ⪅ 0.2. Within this stable regime, collagen fibrils can access a wide range of radii and associated surface twists. Remarkably, we find a maximal equilibrium surface twist of 0.33 rad (19°). Our results are compatible with corneal collagen fibrils, and we show how the large surface twist can explain the narrow distribution of corneal fibril radii. Conversely, we show how small surface twist is required for the thermodynamic stability of tendon fibrils in the face of considerable polydispersity of radius.

Phase-field collagen fibrils: Coupling chirality and density modulations

“…The Dband modulation leads to a co-existence line (indicated by the thick black line) between qualitatively distinct fibril phases, which ends at a critical point at γ c = 0.0348, k c 24 = 0.2554. This coexistence line, along which the fibril radius and twist-field changes discontinuously, is not observed without the PFC terms [13].…”

“…The chiral nature of collagen fibrils is evident in the tilted alignment of individual molecules with respect to the fibril axis [9][10][11][12][13]. This "twist" angle ψ can be as large as 17 • at the surface of corneal fibrils, and is approximately 5 • in tendon fibrils [2,14].…”

“…However, a simple geometrical interpretation of the Hodge-Petruska model also locally implies a D-band period d ∝ cos ψ(r) within an individual fibril [2], whereas only a single D-band period is observed in experiment. One previous model of both D-band and double-twist therefore assumes a radially constant twist [19], though this is energetically unfavourable for the double-twist field [13]. A second model has an approximately constant twist gradient [9], which is energetically preferable for the double-twist but implies local stretch-ing or compression of the D-band [2].…”

Chiral and achiral mechanisms of self-limiting assembly of twisted bundles

“…Increasing chirality at fixed χ −1 increases the stability range of finite bundles for both twist-stable and twistunstable bundles, consistent with the σ max ∼ Q 2/3 scaling for large Q in eqs. (22) and (23). This derives simply from the fact that higher chirality generically increases the free energy difference between locally twisted and untwisted assembly.…”

Revealing the Assembly of Filamentous Proteins with Scanning Transmission Electron Microscopy

“…The differences have been attributed to fibril curvature and twisting or to the coexistence of ordered and less-ordered domains along the fibril axis. 33,34 However, all of these explanations remain speculative, and are mostly supported by theoretical models of molecular packing, without clear experimental evidence.…”