arXiv subjects

Laurent Kreplak

Publications and source records attributed to Laurent Kreplak.

11 recordsLinked to original sources

arXiv2026

Polarization controlled second harmonic generation imaging of stretched collagen fibrils reveals collagen deformation pathway in situ

The tensile properties of single collagen fibrils, the building block of load-bearing tissues, have been studied extensively by nanomechanical techniques and molecular dynamics simulation. However, the deformation pathway of collagen molecules within fibrils has not yet been observed experimentally. In addition, the role played by divalent and trivalent enzymatic crosslinks in modulating this deformation pathway is poorly understood. Here we used polarization controlled second harmonic generation (SHG) imaging combined with atomic force microscopy (AFM) to characterize the molecular state of collagen triple helices within stretched single collagen fibrils. The fibrils were extracted from a pair of bovine leg tendons from the same animal in order to compare fibrils with a high amount of immature divalent crosslinks to fibrils with a high amount of mature trivalent crosslinks. By selecting fibrils with a large SHG intensity gradient along their length and then imaging the same fibrils by AFM we were able to link the observed intensity gradient with a gradient in D-band strain and a gradient in molecular strain as estimated from the SHG anisotropy parameter rho. In contrast to previous studies at the tendon scale, we observed that the SHG molecular strain is always larger than the D-band strain for all fibrils with this difference being largest for fibrils rich in divalent crosslinks. By analyzing the behavior of the relative density of SHG emitters as a function of molecular strain, we observe a two-state transition from an SHG producing to a non SHG producing state with a free energy barrier between 6 and 10 kBT that we propose corresponds to the local untwisting of the collagen triple helix superhelical twist which likely preceded bond rupture and loss of the SHG signal. We also show that trivalent crosslinks tend to delay the transition onset compared to divalent crosslinks.

q-bio.QM↗

arXiv2025

Super-resolution Radial Fluctuations Enables Polarization-resolved Nonlinear Optical Nanoscopy

Second harmonic generation microscopy (SHG) is a powerful imaging modality which has found applications in investigating both biological and synthetic nanostructures. Like all optical microscopy techniques, the resolution of SHG is limited to approximately half the wavelength of the excitation light. Because of this several groups have proposed techniques to enable super-resolution SHG imaging. However, these techniques often involve quite complicated optical setups compared to standard SHG microscopes, a major impediment towards more widespread utilization. Here we apply super-resolution radial fluctuations (SRRF), a commonly used technique for super-resolution fluorescence imaging, to enable super-resolution SHG microscopy. By imaging individual nanostructures, we demonstrate that SRRF can provide resolution enhancement of up to 3x compared to a laser scanning SHG microscope, which is comparable to the best resolution enhancement reported in the literature. Additionally, we show that SRRF maintains the polarization dependence of SHG, therefore enabling super-resolution polarization SHG imaging. Finally, we perform SRRF processing on third harmonic generation images to demonstrate the significant potential of SRRF for other super-resolution nonlinear optical microscopy. Importantly, since SRRF can achieve super-resolution purely through image processing, the technique demonstrated here could be used to enhance the resolution of images obtained using a wide variety of nonlinear optical microscopy setups including both laser scanning and widefield configurations.

physics.optics↗

arXiv2023

Anisotropic swelling due to hydration constrains anisotropic elasticity in biomaterial fibers

Naturally occurring protein fibers often undergo anisotropic swelling when hydrated. Within a tendon, a hydrated collagen fibril's radius expands by 40% but its length only increases by 5%. The same effect, with a similar relative magnitude, is observed for single hair shafts. Fiber hydration is known to affect elastic properties. Here we show that anisotropic swelling constrains the anisotropic linear elastic properties of fibers. First we show, using data from disparate previously reported studies, that anisotropic swelling can be described as an approximately linear function of water content. Then, under the observation that the elastic energy of swelling can be minimized by the anisotropic shape, we relate swelling anisotropy to elastic anisotropy -- assuming radial (transverse) symmetry within a cylindrical geometry. We find an upper bound for the commonly measured axial Poisson ratio $\nu_{zx}<1/2$. This is significantly below recently estimated values for collagen fibrils extracted from tissue-level measurements, but is consistent with both single hair shaft and single collagen fibril mechanical and hydration studies. Using $\nu_{zx}$, we can then constrain the product $\gamma \equiv (1-\nu_{xy}) E_z/E_x$ -- where $\nu_{xy}$ is the seldom measured transverse Poisson ratio and $E_z/E_x$ is the ratio of axial to radial Young's moduli.

cond-mat.soft↗

arXiv2023

Torsion and Bistability of Double-Twist Elastomers

We investigate the elastic properties of anisotropic elastomers with a double-twist director field, which is a model for collagen fibrils or blue phases. We observe a significant Poynting-like effect, coupling torsion (fibril twist) and extension. For freely-rotating boundary conditions, we identify a structural bistability at very small extensional strains which undergoes a saddle-node bifurcation at a critical strain -- at approximately 1% strain for a parameterization appropriate for collagen fibrils. With clamped boundary conditions appropriate for many experimental setups, the bifurcation is not present. We expect significant helical shape effects when fixed torsion does not equal the equilibrium torsion of freely-rotating boundary conditions, due to residual torques.

cond-mat.soft↗

arXiv2021

D-band strain underestimates fibril strain for twisted collagen fibrils at low strains

Collagen fibrils are the main structural component of load-bearing tissues such as tendons, ligaments, skin, the cornea of the eye, and the heart. The D-band of collagen fibrils is an axial periodic density modulation that can be easily characterized by tissue-level X-ray scattering. During mechanical testing, D-band strain is often used as a proxy for fibril strain. However, this approach ignores the coupling between strain and molecular tilt. We examine the validity of this approximation using an elastomeric collagen fibril model that includes both the D-band and a molecular tilt field. In the low strain regime, we show that the D-band strain substantially underestimates fibril strain for strongly twisted collagen fibrils -- such as fibrils from skin or corneal tissue.

physics.bio-ph↗

arXiv2021

Chiral phase-coexistence in compressed double-twist elastomers

We adapt the theory of anisotropic rubber elasticity to model cross-linked double-twist liquid crystal cylinders such as exhibited in biological systems. In mechanical extension we recover strain-straightening, but with an exact expression in the small twist-angle limit. In compression, we observe coexistence between high and low twist phases. Coexistence begins at small compressive strains and is robustly observed for any anisotropic cross-links and for general double-twist functions -- but disappears at large twist angles. Within the coexistence region, significant compression of double-twist cylinders is allowed at constant stress. Our results are qualitatively consistent with previous observations of swollen or compressed collagen fibrils, indicating that this phenomenon may be readily accessible experimentally.

physics.bio-ph↗

arXiv2020

Non-equilibrium Growth and Twist of Cross-Linked Collagen Fibrils

The lysyl oxidase (LOX) enzyme that catalyses cross-link formation during the assembly of collagen fibrils in vivo is too large to diffuse within assembled fibrils, and so is incompatible with a fully equilibrium mechanism for fibril formation. We propose that enzymatic cross-links are formed at the fibril surface during the growth of collagen fibrils; as a consequence no significant reorientation of previously cross-linked collagen molecules occurs inside collagen fibrils during fibril growth in vivo. By imposing local equilibrium only at the fibril surface, we develop a coarse-grained quantitative model of in vivo fibril structure that incorporates a double-twist orientation of collagen molecules and a periodic D-band density modulation along the fibril axis. Radial growth is controlled by the density of available collagen molecules around the fibril. In contrast with earlier equilibrium models of fibril structure, we find that all fibrils can exhibit a core-shell structure that is controlled only by the fibril radius. At small radii a core is developed with a linear double-twist structure as a function of radius. Within the core the double-twist structure is largely independent of the D-band. Within the shell at larger radii, the structure approaches a constant twist configuration that is strongly coupled with the D-band. We suggest a stable radius control mechanism that corneal fibrils can exploit near the edge of the linear core regime; while larger tendon fibrils can use a cruder version of growth control that does not select a preferred radius.

physics.bio-ph↗

arXiv2020

Phase-field collagen fibrils: Coupling chirality and density modulations

To describe the interaction between longitudinal density modulations along collagen fibrils (the D-band) with the radial twist-field of molecular orientation (double-twist), we couple phase-field-crystal (PFC) with liquid-crystalline free-energies to obtain a hybrid model of equilibrium collagen fibril structure. We numerically compute the resulting axial and radial structure. We find two distinct fibrillar phases, `L' and `C', with a coexistence line that ends in an Ising-like critical point. We propose that coexistence between these phases can explain the bimodal distribution of fibril radii that has been widely reported within tendon tissues. Tensile strain applied to our model fibrils straightens the average fibrillar twist and flattens the D-band modulation. Our PFC approach should apply directly to other longitudinally-modulated chiral filaments, such as fibrin and intermediate filaments.

cond-mat.soft↗

arXiv2018

Polymorphism of stable collagen fibrils

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 \textit{in vitro} or anatomical location \textit{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 $ k_{24}/K_{22}$ and the ratio of surface tension to chiral strength $\hatγ \equiv γ/(K_{22}q)$, 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, $\hatγ \lesssim 0.2$. 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 ($19^{\text{o}}$). Our results are compatible with corneal collagen fibrils, and we show how the large surface twist is needed to 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.

cond-mat.soft↗

arXiv2016

Uniform spatial distribution of collagen fibril radii within tendon implies local activation of pC-collagen at individual fibrils

Collagen fibril cross-sectional radii show no systematic variation between the interior and the periphery of fibril bundles, indicating an effectively constant rate of collagen incorporation into fibrils throughout the bundle. Such spatially homogeneous incorporation constrains the extracellular diffusion of collagen precursors from sources at the bundle boundary to sinks at the growing fibrils. With a coarse-grained diffusion equation we determine stringent bounds, using parameters extracted from published experimental measurements of tendon development. From the lack of new fibril formation after birth, we further require that the concentration of diffusing precursors stays below the critical concentration for fibril nucleation. We find that the combination of the diffusive bound, which requires larger concentrations to ensure homogeneous fibril radii, and lack of nucleation, which requires lower concentrations, is only marginally consistent with fully-processed collagen using conservative bounds. More realistic bounds may leave no consistent concentrations. Therefore, we propose that unprocessed pC-collagen diffuses from the bundle periphery followed by local C-proteinase activity and subsequent collagen incorporation at each fibril. We suggest that C-proteinase is localized within bundles, at fibril surfaces, during radial fibrillar growth. The much greater critical concentration of pC-collagen, as compared to fully-processed collagen, then provides broad consistency between homogeneous fibril radii and the lack of fibril nucleation during fibril growth.

q-bio.TO↗

arXiv2014

An equilibrium double-twist model for the radial structure of collagen fibrils

Mammalian tissues contain networks and ordered arrays of collagen fibrils originating from the periodic self-assembly of helical 300 nm long tropocollagen complexes. The fibril radius is typically between 25 to 250 nm, and tropocollagen at the surface appears to exhibit a characteristic twist-angle with respect to the fibril axis. Similar fibril radii and twist-angles at the surface are observed in vitro, suggesting that these features are controlled by a similar self-assembly process. In this work, we propose a physical mechanism of equilibrium radius control for collagen fibrils based on a radially varying double-twist alignment of tropocollagen within a collagen fibril. The free-energy of alignment is similar to that of liquid crystalline blue phases, and we employ an analytic Euler-Lagrange and numerical free energy minimization to determine the twist-angle between the molecular axis and the fibril axis along the radial direction. Competition between the different elastic energy components, together with a surface energy, determines the equilibrium radius and twist-angle at the fibril surface. A simplified model with a twist-angle that is linear with radius is a reasonable approximation in some parameter regimes, and explains a power-law dependence of radius and twist-angle at the surface as parameters are varied. Fibril radius and twist-angle at the surface corresponding to an equilibrium free-energy minimum are consistent with existing experimental measurements of collagen fibrils. Remarkably, in the experimental regime, all of our model parameters are important for controlling equilibrium structural parameters of collagen fibrils.

physics.bio-ph↗