Effect of collagenase–gelatinase ratio on the mechanical properties of a collagen fibril: a combined Monte Carlo–molecular dynamics study

Loading in cartilage is supported primarily by fibrillar collagen, and damage will impair the function of the tissue, leading to pathologies such as osteoarthritis. Damage is initiated by two types of matrix metalloproteinases, collagenase and gelatinase, that cleave and denature the collagen fibrils in the tissue. Experimental and modeling studies have revealed insights into the individual contributions of these two types of MMPs, as well as the mechanical response of intact fibrils and fibrils that have experienced random surface degradation. However, no research has comprehensively examined the combined influences of collagenases and gelatinases on collagen degradation nor studied the mechanical consequences of biological degradation of collagen fibrils. Such preclinical examinations are required to gain insights into understanding, treating, and preventing degradation-related cartilage pathology. To develop these insights, we use sequential Monte Carlo and molecular dynamics simulations to probe the effect of enzymatic degradation on the structure and mechanics of a single collagen fibril. We find that the mechanical response depends on the ratio of collagenase to gelatinase—not just the amount of lost fibril mass—and we provide a possible mechanism underlying this phenomenon. Overall, by characterizing the combined influences of collagenases and gelatinases on fibril degradation and mechanics at the preclinical research stage, we gain insights that may facilitate the development of targeted interventions to prevent the damage and loss of mechanical integrity that can lead to cartilage pathology.

     

Phase behavior of lipid bilayers under tension

Given the proposed importance of membrane tension in regulating cellular functions, we explore the effects of a finite surface tension on phase equilibrium using a molecular theory that captures the quantitative structure of the phase diagram of the tensionless DPPC/DOPC/Cholesterol lipid bilayer. We find that an increase in the surface tension decreases the temperature of the transition from liquid to gel in a pure DPPC system by ～1.0 K/(mN/m), and decreases the liquid-disordered to liquid-ordered transition at constant chemical potentials by approximately the same amount. Our results quantitatively isolate the role of tension in comparison to other thermodynamic factors, such as pressure, in determining the phase behavior of lipid bilayers.     

Structural Effects and Translocation of Doxorubicin in a DPPC/Chol Bilayer: The Role of Cholesterol

We use molecular dynamics simulations to characterize the influence of cholesterol (Chol) on the interaction between the anticancer drug doxorubicin (DOX) and a dipalmitoyl phosphatidylcholine/Chol lipid bilayer. We calculate the potential of mean force, which gives us an estimate of the free energy barrier for DOX translocation across the membrane. We find free energy barriers of 23.1 ± 3.1 k_BT, 36.8 ± 5.1 k_BT, and 54.5 ± 4.7 k_BT for systems composed of 0%, 15%, and 30% Chol, respectively. Our predictions agree with Arrhenius activation energies from experiments using phospholipid membranes, including 20 k_BT for 0% Chol and 37.2 k_BT for 20% Chol. The location of the free energy barrier for translocation across the bilayer is dependent on composition. As Chol concentration increases, this barrier changes from the release of DOX into the water to flip-flop over the membrane center. The drug greatly affects local membrane structure by attracting dipalmitoyl phosphatidylcholine headgroups, curving the membrane, and allowing water penetration. Despite its hydrophobicity, DOX facilitates water transport via its polar groups.     

Kinetics of protein adsorption and desorption on surfaces with grafted polymers

The kinetics of protein adsorption are studied using a generalized diffusion approach which shows that the time-determining step in the adsorption is the crossing of the kinetic barrier presented by the polymers and already adsorbed proteins. The potential of mean-force between the adsorbing protein and the polymer-protein surface changes as a function of time due to the deformation of the polymer layers as the proteins adsorb. Furthermore, the range and strength of the repulsive interaction felt by the approaching proteins increases with grafted polymer molecular weight and surface coverage. The effect of molecular weight on the kinetics is very complex and different than its role on the equilibrium adsorption isotherms. The very large kinetic barriers make the timescale for the adsorption process very long and the computational effort increases with time, thus, an approximate kinetic approach is developed. The kinetic theory is based on the knowledge that the time-determining step is crossing the potential-of-mean-force barrier. Kinetic equations for two states (adsorbed and bulk) are written where the kinetic coefficients are the product of the Boltzmann factor for the free energy of adsorption (desorption) multiplied by a preexponential factor determined from a Kramers-like theory. The predictions from the kinetic approach are in excellent quantitative agreement with the full diffusion equation solutions demonstrating that the two most important physical processes are the crossing of the barrier and the changes in the barrier with time due to the deformation of the polymer layer as the proteins adsorb/desorb. The kinetic coefficients can be calculated a priori allowing for systematic calculations over very long timescales. It is found that, in many cases where the equilibrium adsorption shows a finite value, the kinetics of the process is so slow that the experimental system will show no adsorption. This effect is particularly important at high grafted polymer surface coverage. The construction of guidelines for molecular weight/surface coverage necessary for kinetic prevention of protein adsorption in a desired timescale is shown. The time-dependent desorption is also studied by modeling how adsorbed proteins leave the surface when in contact with a pure water solution. It is found that the kinetics of desorption are very slow and depend in a nonmonotonic way in the polymer chain length. When the polymer layer thickness is shorter than the size of the protein, increasing polymer chain length, at fixed surface coverage, makes the desorption process faster. For polymer layers with thickness larger than the protein size, increases in molecular weight results in a longer time for desorption. This is due to the grafted polymers trapping the adsorbed proteins and slowing down the desorption process. These results offer a possible explanation to some experimental data on adsorption. Limitations and extension of the developed approaches for practical applications are discussed.     

Stability and phase separation in mixed monopolar lipid/bolalipid layers

The phase stability of a fluid lipid layer that is a mixture of conventional monopolar lipids and C20 bipolar bolalipids was studied using a mean field theory that explicitly includes molecular details and configurational properties of the lipid molecules. The effect of changing the fraction of bolalipids, as well as the length of the hydrocarbon chain of the monopolar lipids, was probed. A phase separation between two liquid lipid phases was found when a mismatch exists in the optimal hydrophobic thicknesses of the pure bolalipid and monopolar lipid layers. The lipid mixture phase separates into a thin bolalipid-rich layer and a thicker monopolar-rich layer. The thin membrane phase is mainly composed of transmembrane bolalipid molecules whose polar heads are positioned at opposite membrane-water interfaces. In the monopolar lipid-rich phase, bolalipids are the minor component and most of them assume a looping configuration where both headgroups are present at the same membrane-water interface. For mixed layers that form a single lipid phase across all bolalipid concentrations, the hairpin-transmembrane ratio strongly depends on the hydrocarbon chain length of the monopolar lipid and the bolalipid concentration. The C-D bond order parameters of the different species have been calculated. Our findings suggest that the concentration-dependent phase transition should be experimentally observable by measuring of the order parameters through quadrupolar splitting experiments. The driving force for the phase separation in the monopolar lipid/bolalipid mixture is the packing mismatch between hydrophobic regions of the monopolar lipid hydrocarbon chains and the membrane-spanning bolalipid chains. The results from the molecular theory may be useful in the design of stable lipid layers for integral membrane protein sensing.     

The Role of Solution Conditions in the Bacteriophage PP7 Capsid Charge Regulation

We investigate and quantify the effects of pH and salt concentration on the charge regulation of the bacteriophage PP7 capsid. These effects are found to be extremely important and substantial, introducing qualitative changes in the charge state of the capsid such as a transition from net-positive to net-negative charge depending on the solution pH. The overall charge of the virus capsid arises as a consequence of a complicated balance with the chemical dissociation equilibrium of the amino acids and the electrostatic interaction between them, and the translational entropy of the mobile solution ions, i.e., counterion release. We show that to properly describe and predict the charging equilibrium of viral capsids in general, one needs to include molecular details as exemplified by the acid-base equilibrium of the detailed distribution of amino acids in the proteinaceous capsid shell.     

Interleaflet coupling and domain registry in phase-separated lipid bilayers

There is clear evidence of an interleaflet coupling in model lipid/cholesterol membranes exhibiting liquid-liquid phase separation. The strength of this coupling is quantified by the mismatch free energy, γ. We calculate it using a molecular mean-field model of a phase-separated lipid/cholesterol bilayer and obtain values that increase as the concentration of saturated lipids in the coexisting phases is increased. These values lie in the range 0.01–0.03 k_BT/nm². We clarify the relationship between the interleaflet coupling and the extent of interleaflet alignment of liquid domains by analyzing a statistical mechanical model of coupled fluctuating domain interfaces. The model is solved exactly using the correspondence between statistical mechanics and quantum mechanics, yielding an expression for the characteristic size of fluctuations out of domain registry. This length scale depends only weakly on the strength of the interleaflet coupling and inevitably is only of the order of nanometers, which explains the experimental result that fluctuations out of domain registry have not been observed by optical microscopy.     

The influence of chromosome density variations on the increase in nuclear disorder strength in carcinogenesis

Microscopic structural changes have long been observed in cancer cells and used as a marker in cancer diagnosis. Recent development of an optical technique, partial-wave spectroscopy (PWS), enabled more sensitive detection of nanoscale structural changes in early carcinogenesis in terms of the disorder strength related to density variations. These nanoscale alterations precede the well-known microscopic morphological changes. We investigate the influence of nuclear density variations due to chromosome condensation on changes of disorder strength by computer simulations of model chromosomes. Nuclear configurations with different degrees of chromosome condensation are realized from simulations of decondensing chromosomes and the disorder strength is calculated for these nuclear configurations. We found that the disorder strength increases significantly for configurations with slightly more condensed chromosomes. Coupled with PWS measurements, the simulation results suggest that the chromosome condensation and the resulting spatial density inhomogeneity may represent one of the earliest events in carcinogenesis.     

Phase Separation in Binary Mixtures of Bipolar and Monopolar Lipid Dispersions Revealed by H NMR Spectroscopy, Small Angle X-Ray Scattering, and Molecular Theory

Binary mixtures of C₂₀BAS and POPC membranes were studied by solid-state ²H NMR spectroscopy and small angle x-ray scattering (SAXS) over a wide range of concentrations and at different temperatures. Three specifically deuterated C₂₀BAS derivatives—[1′,1′,20′,20′-²H₄]C₂₀BAS, [2′,2′,19′,19′-²H₄]C₂₀BAS, and [10′,11′-²H₂]C₂₀BAS—combined with protiated 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC), as well as membranes containing POPC-d₃₁ and fully protiated bolalipid, were used in NMR experiments to obtain structural information for the mixtures. The ²H NMR spectra of [10′,11′-²H₂]C₂₀BAS/POPC membrane dispersions reveal that the bolalipid is predominantly in the transmembrane conformation at high bolalipid concentrations (100, 90, and 70 mol %). At ≤50 mol % C₂₀BAS, smaller quadrupolar couplings appear in the spectra, indicating the presence of U-shaped conformers. The proportion of U-shaped bolalipids increases as the amount of POPC in the membrane increases; however, the transmembrane component remains the dominant bolalipid conformation in the membrane even at 45°C and 10 mol % C₂₀BAS, where it accounts for ∼50% of the bolalipid population. The large fraction of C₂₀BAS transmembrane conformers, regardless of the C₂₀BAS/POPC ratio, together with the findings from molecular mean-field theory calculations, suggests the coexistence of phase-separated bolalipid-rich domains and POPC-rich domains. A single lamellar repeat distance was observed in SAXS experiments corresponding to the average repeat spacing expected for C₂₀BAS- and POPC-rich domains. These observations are consistent with the presence of microphase-separated domains in the mixed membrane samples that arise from POPC-C₂₀BAS hydrophobic mismatch.