Protein corona impact on nanoparticle-cell interactions: toward an energy-based model of endocytosis

Upon incubation of nanoparticles in biological fluids, a new layer called the protein corona is formed on their surface affecting the interactions between nanoparticles and targeted cells during the endocytosis process. In the present study, a mathematical model based on the diffusion of membrane mobile receptors is proposed. Opposing the endocytosis proceeding, membrane bending and tension energies are named as resistant energy. Also, the binding energy and free-energy associated with the configurational entropy are collectively termed promoter energy. Utilizing this model, endocytosis of gold nanoparticle (GNP) is simulated to explore the biological media effect. The results reveal that there exists a nanoparticle size of 60 nm at which, the endocytosis time is at a minimum. It has been illustrated that, although for sufficiently small particles of diameter 30nm, membrane tension has a negligible contribution (<10%) in the resistant energy, it noticeably increases the endocytosis processing time for large particles. Therefore, we report several parametric studies to provide a better insight into the effects of biological media on the ingestion of nanoparticles. Through a detailed analysis of the engulfment of the nanoparticles, it is shown that the nanoparticle radius corresponding to the quickest possible ingestion time is affected in the presence of corona. Moreover, it is found that the formation of this layer does not only affect the endocytosis time but also can lead to incomplete engulfment by decreasing the ligand density on the nanoparticle surface. Use of the proposed model can play a significant role in advancing the design of nanoparticles in targeted drug delivery applications.

Disease-related metabolites affect protein-nanoparticle interactions

Once in biological fluids, the surface of nanoparticles (NPs) is rapidly covered with a layer of biomolecules (i.e., the "protein corona") whose composition strongly determines their biological identity, regulates interactions with biological entities including cells and the immune system, and consequently directs the biological fate and pharmacokinetics of nanoparticles. We recently introduced the concept of a "personalized protein corona" which refers to the formation of different biological identities of the exact same type of NP after being exposed to extract plasmas from individuals who have various types of diseases. As different diseases have distinct metabolomic profiles and metabolites can interact with proteins, it is legitimate to hypothesize that metabolomic profiles in plasma may have the capacity to, at least partially, drive the formation of a personalized protein corona. To test this hypothesis, we employed a multi-scale approach composed of coarse-grained (CG) and all atom (AA) molecular dynamics (MD) simulations to probe the role of glucose and cholesterol (model metabolites in diabetes and hypercholesterolemia patients) in the interaction of fibrinogen protein and polystyrene NPs. Our results revealed that glucose and cholesterol had the capacity to induce substantial changes in the binding site of fibrinogen to the surface of NPs. More specifically, the simulation results demonstrated that increasing the metabolite amount could change the profiles of fibrinogen adsorption and replacement, what is known as the Vroman effect, on the NP surface. In addition, we also found out that metabolites can substantially determine the immune triggering potency of the fibrinogen-NP complex. Our proof-of-concept outcomes further emphasize the need for the development of patient-specific NPs in a disease type-specific manner for high yielding and safe clinical applications.

Nanomechanical properties of MscL α helices: A steered molecular dynamics study

Gating of mechanosensitive (MS) channels is driven by a hierarchical cascade of movements and deformations of transmembrane helices in response to bilayer tension. Determining the intrinsic mechanical properties of the individual transmembrane helices is therefore central to understanding the intricacies of the gating mechanism of MS channels. We used a constant-force steered molecular dynamics (SMD) approach to perform unidirectional pulling tests on all the helices of MscL in M. tuberculosis and E. coli homologs. Using this method, we could overcome the issues encountered with the commonly used constant-velocity SMD simulations, such as low mechanical stability of the helix during stretching and high dependency of the elastic properties on the pulling rate. We estimated Young's moduli of the α-helices of MscL to vary between 0.2 and 12.5 GPa with TM2 helix being the stiffest. We also studied the effect of water on the properties of the pore-lining TM1 helix. In the absence of water, this helix exhibited a much stiffer response. By monitoring the number of hydrogen bonds, it appears that water acts like a 'lubricant' (softener) during TM1 helix elongation. These data shed light on another physical aspect underlying hydrophobic gating of MS channels, in particular MscL.

The Combined Effect of Hydrophobic Mismatch and Bilayer Local Bending on the Regulation of Mechanosensitive Ion Channels

The hydrophobic mismatch between the lipid bilayer and integral membrane proteins has well-defined effect on mechanosensitive (MS) ion channels. Also, membrane local bending is suggested to modulate MS channel activity. Although a number of studies have already shown the significance of each individual factor, the combined effect of these physical factors on MS channel activity have not been investigated. Here using finite element simulation, we study the combined effect of hydrophobic mismatch and local bending on the archetypal mechanosensitive channel MscL. First we show how the local curvature direction impacts on MS channel modulation. In the case of MscL, we show inward (cytoplasmic) bending can more effectively gate the channel compared to outward bending. Then we indicate that in response to a specific local curvature, MscL inserted in a bilayer with the same hydrophobic length is more expanded in the constriction pore region compared to when there is a protein-lipid hydrophobic mismatch. Interestingly in the presence of a negative mismatch (thicker lipids), MscL constriction pore is more expanded than in the presence of positive mismatch (thinner lipids) in response to an identical membrane curvature. These results were confirmed by a parametric energetic calculation provided for MscL gating. These findings have several biophysical consequences for understanding the function of MS channels in response to two major physical stimuli in mechanobiology, namely hydrophobic mismatch and local membrane curvature.

Influence of Global and Local Membrane Curvature on Mechanosensitive Ion Channels: A Finite Element Approach

Mechanosensitive (MS) channels are ubiquitous molecular force sensors that respond to a number of different mechanical stimuli including tensile, compressive and shear stress. MS channels are also proposed to be molecular curvature sensors gating in response to bending in their local environment. One of the main mechanisms to functionally study these channels is the patch clamp technique. However, the patch of membrane surveyed using this methodology is far from physiological. Here we use continuum mechanics to probe the question of how curvature, in a standard patch clamp experiment, at different length scales (global and local) affects a model MS channel. Firstly, to increase the accuracy of the Laplace’s equation in tension estimation in a patch membrane and to be able to more precisely describe the transient phenomena happening during patch clamping, we propose a modified Laplace’s equation. Most importantly, we unambiguously show that the global curvature of a patch, which is visible under the microscope during patch clamp experiments, is of negligible energetic consequence for activation of an MS channel in a model membrane. However, the local curvature (R_L < 50) and the direction of bending are able to cause considerable changes in the stress distribution through the thickness of the membrane. Not only does local bending, in the order of physiologically relevant curvatures, cause a substantial change in the pressure profile but it also significantly modifies the stress distribution in response to force application. Understanding these stress variations in regions of high local bending is essential for a complete understanding of the effects of curvature on MS channels.

The effect of local bending on gating of MscL using a representative volume element and finite element simulation

Many physiological processes such as cell division, endocytosis and exocytosis cause severe local curvature of the cell membrane. Local curvature has been shown experimentally to modulate numerous mechanosensitive (MS) ion channels. In order to quantify the effects of local curvature we introduced a coarse grain representative volume element for the bacterial mechanosensitive ion channel of large conductance (MscL) using continuum elasticity. Our model is designed to be consistent with the channel conformation in the closed and open states to capture its major continuum rheological behavior in response to the local membrane curvature. Herein we show that change in the local curvature of the lipid bilayer can modulate MscL activity considerably by changing both bilayer thickness and lateral pressure profile. Intriguingly, although bending in any direction results in almost the same free-energy cost, inward (cytoplasmic) bending favors channel opening, whereas outward (periplasmic) bending facilitates closing of the narrowest part of the MscL pore. This quantitative study using MscL as a model channel may have wide reaching consequences for the effect of local curvature on the physiological function of other types of prokaryotic and eukaryotic membrane proteins.

Nonlinear membrane model for large amplitude vibration of single layer graphene sheets

The nonlinear vibrational properties of single layer graphene sheets (SLGSs) are investigated using a membrane model. The nonlinear equation of motion is considered for the SLGSs by including the effects of stretching due to large amplitudes. The equation of motion is numerically solved utilizing the finite difference method for SLGSs with different initial and boundary conditions, sizes and pretensions. It is concluded that the nonlinear fundamental frequency of SLGSs increases by increasing the pretension and initial velocity. In addition, it is observed that an increase in the pretension weakens the effects of the initial velocity on the fundamental frequency, such that the fundamental frequency approximately becomes independent of the initial velocity. This is an important feature of the vibrating systems consisting of SLGSs which are used in the nano-electromechanical systems (NEMS), where resonators with a specific fundamental frequency and independent of the initial velocity are of interest.

Nonlinear vibrational analysis of single-layer graphene sheets

Recent experiments have shown the applicability of single-layer graphene sheets (SLGSs) as electromechanical resonators. Existing theoretical models, based on linear continuum or atomistic methods, are limited to the study of linear vibrations of SLGSs. Here we introduce a hybrid atomistic-structural element which is capable of modelling nonlinear behaviour of graphene sheets. This hybrid element is based on an empirical inter-atomic potential function and can model the nonlinear dynamic response of SLGSs. Using this element, nonlinear vibrational analysis of SLGSs is performed. It is shown that the nonlinear vibrational analysis of SLGSs predicts significantly higher fundamental frequencies. Also, the effects of vibration amplitude as well as the geometry of the SLGSs on the fundamental frequency are studied and predictive relations between the fundamental frequency, the SLGS length and the non-dimensional vibration amplitude are presented. The results are verified with experimental observations and are in remarkable agreement.

Vibrational analysis of single-layered graphene sheets

A molecular structural mechanics method has been implemented to investigate the vibrational behavior of single-layered graphene sheets. By adopting this approach, mode shapes and natural frequencies are obtained. Vibrational analysis is performed with different chirality and boundary conditions. Numerical results from the atomistic modeling are employed to develop predictive equations via a statistical nonlinear regression model. With the proposed equations, fundamental frequencies of single-layered graphene sheets with considered boundary conditions can be predicted within 3% difference with respect to the atomistic simulation.