Kinetics of cancer metastasis.

The formation of metastases during cancer is now considered to be induced by migrating metastatic stem cells (MetSCs) in preexisting niches or niches induced by MetSCs or tumor-derived exosomes (TDEs). I propose and compare two simplest generic models describing these two scenarios. The number of tumors is predicted (i) to increase exponentially in the case of preexisting niches and (ii) to diverge during a finite time interval in the case of induced niches. The latter prediction is novel and of interest because rapid collapse in the end of a finite time interval is a well-known feature of the cancer metastasis. Two advanced models describing the two scenarios of cancer metastasis have been scrutinized as well. These models clarify the likely role of various specific factors in the metastasis. In particular, the equations derived in the framework of the advanced model with preexisting niches have been solved analytically allowing (i) to clarify the factors determining the duration of the period from the initiation of the primary tumor to the phase when the metastases start to dominate, (ii) to estimate the number of metastases in the end of this period, and (iii) to explains why the use of chemotherapy typically results in the improvement of the patient state only for a relatively short period. The equations derived in the framework of the advanced model with induced niches have no analytical solution, and their analysis merits additional attention.

Label-free quantification of protein binding to lipid vesicles using transparent waveguide evanescent-field scattering microscopy with liquid control.

Recent innovations in microscopy techniques are paving the way for label-free studies of single nanoscopic biological entities such as viruses, lipid-nanoparticle drug carriers, and even proteins. One such technique is waveguide evanescent-field microscopy, which offers a relatively simple, yet sensitive, way of achieving label-free light scattering-based imaging of nanoparticles on surfaces. Herein, we extend the application of this technique by incorporating microfluidic liquid control and adapting the design for use with inverted microscopes by fabricating a waveguide on a transparent substrate. We furthermore formulate analytical models describing scattering and fluorescence intensities from single spherical and shell-like objects interacting with evanescent fields. The models are then applied to analyze scattering and fluorescence intensities from adsorbed polystyrene beads and to temporally resolve cholera-toxin B (CTB) binding to individual surface-immobilized glycosphingolipid GM1 containing vesicles. We also propose a self-consistent means to quantify the thickness of the CTB layer, revealing that protein-binding to individual vesicles can be characterized with sub-nm precision in a time-resolved manner.

Release of molecules from nanocarriers.

Release of drugs or vaccine molecules from macro-, micro-, and nano-sized carriers is usually considered to be limited by diffusion and/or carrier dissolution and/or erosion. The corresponding experimentally observed kinetics are customarily fitted by using the empirical Weibull and Korsemeyer-Peppas expressions. With decreasing size of carriers down to about 100 nm, the timescale of diffusion decreases, and accordingly the release can be kinetically limited, i.e., controlled by jumps of molecules located near the carrier-solution interface. In addition, nanocarriers (e.g., lipid nanoparticles) are often structurally heterogeneous so that the absorption of molecules there can be interpreted in terms of energetic heterogeneity, i.e., distribution of energies corresponding to binding sites and activation barriers for release. Herein, I present a general kinetic model aimed at such situations. For illustration, the deviation of the molecule binding energy from the maximum value was considered to be about 4-8 kcal mol-1. With this physically reasonable (for non-covalent interaction) scale of energetic heterogeneity, the predicted kinetics (i) are linear in the very beginning and then, with increasing time, become logarithmic and (ii) can be nearly perfectly fitted by employing the Weibull or Korsmeyer-Peppas expressions with the exponent in the range from 0.6 to 0.75. Such values of the exponent are often obtained in experiments and customarily associated with non-Fickian diffusion. My analysis shows that the energetic heterogeneity can be operative here as well.

Extracellular interplay of amyloid fibrils and neural cells.

Some neurological disorders such e.g. as Alzheimer disease are accompanied by the appearance of amyloid fibrils inside and outside cells. Herein, I present a generic coarse-grained kinetic mean-field model describing at the extracellular level the interplay of fibrils and cells. It includes the formation and degradation of fibrils, activation of healthy cells with respect to the fabrication of fibrils, and death of activated cells. The corresponding analysis indicates that the disease development can occur in two qualitatively different regimes. The first one is controlled primarily by the intrinsic factors resulting in slow increase of fibril production inside cells. The second one implies faster self-promoted growth of the fibril population by analogy with explosion. This prediction reported as a hypothesis is of interest for conceptual understanding of the neurological disorders.

pH-Modulated Nanoarchitectonics for Enhancement of Multivalency-Induced Vesicle Shape Deformation at Receptor-Presenting Lipid Membrane Interfaces.

Multivalent ligand-receptor interactions between receptor-presenting lipid membranes and ligand-modified biological and biomimetic nanoparticles influence cellular entry and fusion processes. Environmental pH changes can drive these membrane-related interactions by affecting membrane nanomechanical properties. Quantitatively, however, the corresponding effects on high-curvature, sub-100 nm lipid vesicles are scarcely understood, especially in the multivalent binding context. Herein, we employed the label-free localized surface plasmon resonance (LSPR) sensing technique to track the multivalent attachment kinetics, shape deformation, and surface coverage of biotin ligand-functionalized, zwitterionic lipid vesicles with different ligand densities on a streptavidin receptor-coated supported lipid bilayer under varying pH conditions (4.5, 6, 7.5). Our results demonstrate that more extensive multivalent interactions caused greater vesicle shape deformation across the tested pH conditions, which affected vesicle surface packing as well. Notably, there were also pH-specific differences, i.e., a higher degree of vesicle shape deformation was triggered at a lower multivalent binding energy in pH 4.5 than in pH 6 and 7.5 conditions. These findings support that the nanomechanical properties of high-curvature lipid membranes, especially the membrane bending energy and the corresponding responsiveness to multivalent binding interactions, are sensitive to solution pH, and indicate that multivalency-induced vesicle shape deformation occurs slightly more readily in acidic pH conditions relevant to biological environments.

Ionizable lipids in bio-inspired nanocarriers.

In applications of bio-inspired nanoparticles (NPs), their composition is often optimised by including ionizable lipids. I use a generic statistical model to describe the charge and potential distributions in lipid nanoparticles (LNPs) containing such lipids. The LNP structure is considered to contain the biophase regions separated by narrow interphase boundaries with water. Ionizable lipids are uniformly distributed at the biophase-water boundaries. The potential is there described at the mean-filed level combining the Langmuir-Stern equation for ionizable lipids and the Poisson-Boltzmann equation for other charges in water. The latter equation is used outside a LNP as well. With physiologically reasonable parameters, the model predicts the scale of the potential in a LNP to be rather low, smaller or about [Formula: see text], and to change primarily near the LNP-solution interface or, more precisely, inside an NP near this interface because the charge of ionizable lipids becomes rapidly neutralized along the coordinate towards the center of a LNP. The extent of dissociation-mediated neutralization of ionizable lipids along this coordinate increases but only slightly. Thus, the neutralization is primarily due to the negative and positive ions related to the ionic strength in solution and located inside a LNP.

Unraveling How Cholesterol Affects Multivalency-Induced Membrane Deformation of Sub-100 nm Lipid Vesicles.

Cholesterol plays a critical role in modulating the lipid membrane properties of biological and biomimetic systems and recent attention has focused on its role in the functions of sub-100 nm lipid vesicles and lipid nanoparticles. These functions often rely on multivalent ligand-receptor interactions involving membrane attachment and dynamic shape transformations while the extent to which cholesterol can influence such interaction processes is largely unknown. To address this question, herein, we investigated the attachment of sub-100 nm lipid vesicles containing varying cholesterol fractions (0-45 mol %) to membrane-mimicking supported lipid bilayer (SLB) platforms. Biotinylated lipids and streptavidin proteins were used as model ligands and receptors, respectively, while the localized surface plasmon resonance sensing technique was employed to track vesicle attachment kinetics in combination with analytical modeling of vesicle shape changes. Across various conditions mimicking low and high multivalency, our findings revealed that cholesterol-containing vesicles could bind to receptor-functionalized membranes but underwent appreciably less multivalency-induced shape deformation than vesicles without cholesterol, which can be explained by a cholesterol-mediated increase in membrane bending rigidity. Interestingly, the extent of vesicle deformation that occurred in response to increasingly strong multivalent interactions was less pronounced for vesicles with greater cholesterol fraction. The latter trend was rationalized by taking into account the strong dependence of the membrane bending energy on the area of the vesicle-SLB contact region and such insights can aid the engineering of membrane-enveloped nanoparticles with tailored biophysical properties.

Interaction Kinetics of Individual mRNA-Containing Lipid Nanoparticles with an Endosomal Membrane Mimic: Dependence on pH, Protein Corona Formation, and Lipoprotein Depletion.

Lipid nanoparticles (LNPs) have emerged as potent carriers for mRNA delivery, but several challenges remain before this approach can offer broad clinical translation of mRNA therapeutics. To improve their efficacy, a better understanding is required regarding how LNPs are trapped and processed at the anionic endosomal membrane prior to mRNA release. We used surface-sensitive fluorescence microscopy with single LNP resolution to investigate the pH dependency of the binding kinetics of ionizable lipid-containing LNPs to a supported endosomal model membrane. A sharp increase of LNP binding was observed when the pH was lowered from 6 to 5, accompanied by stepwise large-scale LNP disintegration. For LNPs preincubated in serum, protein corona formation shifted the onset of LNP binding and subsequent disintegration to lower pH, an effect that was less pronounced for lipoprotein-depleted serum. The LNP binding to the endosomal membrane mimic was observed to eventually become severely limited by suppression of the driving force for the formation of multivalent bonds during LNP attachment or, more specifically, by charge neutralization of anionic lipids in the model membrane due to their association with cationic lipids from earlier attached LNPs upon their disintegration. Cell uptake experiments demonstrated marginal differences in LNP uptake in untreated and lipoprotein-depleted serum, whereas lipoprotein-depleted serum increased mRNA-controlled protein (eGFP) production substantially. This complies with model membrane data and suggests that protein corona formation on the surface of the LNPs influences the nature of the interaction between LNPs and endosomal membranes.

Comment on "Real-time atomistic simulation of the Ostwald ripening of TiO2 supported Au nanoparticles" by B. Zhu, R. Qi, L. Yuan and Y. Gao, Nanoscale, 2020, 12, 19142.

Using Monte Carlo simulations (MCS) in combination with an analytical model for the metal-metal interaction with the parameters based on density functional theory (DFT), Zhu, Qi, Yuan, and Gao predicted that the Ostwald ripening of Au nanoparticles on TiO2 occurs primarily via the detachment and attachment of Au dimers. I show that this and some other predictions are not properly validated because the parameters employed in the analytical model in order to describe the Au-Au interaction are in fact inconsistent both with DFT and experimental thermodynamical data.

Time-Resolved Thickness and Shape-Change Quantification using a Dual-Band Nanoplasmonic Ruler with Sub-Nanometer Resolution.

Time-resolved measurements of changes in the size and shape of nanobiological objects and layers are crucial to understand their properties and optimize their performance. Optical sensing is particularly attractive with high throughput and sensitivity, and label-free operation. However, most state-of-the-art solutions require intricate modeling or multiparameter measurements to disentangle conformational or thickness changes of biomolecular layers from complex interfacial refractive index variations. Here, we present a dual-band nanoplasmonic ruler comprising mixed arrays of plasmonic nanoparticles with spectrally separated resonance peaks. As electrodynamic simulations and model experiments show, the ruler enables real-time simultaneous measurements of thickness and refractive index variations in uniform and heterogeneous layers with sub-nanometer resolution. Additionally, nanostructure shape changes can be tracked, as demonstrated by quantifying the degree of lipid vesicle deformation at the critical coverage prior to rupture and supported lipid bilayer formation. In a broader context, the presented nanofabrication approach constitutes a generic route for multimodal nanoplasmonic optical sensing.

Lipid nanoparticles with ionizable lipids: Statistical aspects.

Lipid nanoparticles (LNPs) with size ∼100 nm are now used for fabrication of a new generation of drugs and antiviral vaccines. To optimize their function or, more specifically, interaction with cell membranes, their composition often includes ionizable lipids which are neutral or cationic (after association with H^{+}). Physically, such LNPs represent an interesting example of mesoscopic nanosystems with complex and far from understood properties. Experimentally, they can be studied at cell-membrane mimics. Herein, I analyze theoretically three related aspects. (i) I describe how the extent of protonation of ionizable lipids located at the surface of LNPs depends on the H^{+} concentration by using the phenomenological Langmuir-Stern and Poisson-Boltzmann models with continuum distribution of charges and the dipole model with discrete charges. In these frameworks, the H^{+} adsorption isotherms are predicted to be close to Langmuirian provided the fraction of ionizable lipids is smaller than 0.5. (ii) I scrutinize the interaction between charged LNPs and their interaction with a supported lipid bilayer (SLB) by using the phenomenological theory and lattice-gas model. The long-term association or attachment is predicted provided the charges are opposite. The models make it possible to estimate the size of the contact region (provided a LNP is not deformed) and the number of lipid-lipid bonds in this region. (iii) I briefly discuss denaturation of a LNP during interaction with the SLB and argue that it may occur via a few stepwise transitions.

Multivalency-Induced Shape Deformation of Nanoscale Lipid Vesicles: Size-Dependent Membrane Bending Effects.

The size of membrane-enveloped virus particles, exosomes, and lipid vesicles strongly impacts functional properties in biological and applied contexts. Multivalent ligand-receptor interactions involving nanoparticle shape deformation are critical to such functions, yet the corresponding effect of nanoparticle size remains largely elusive. Herein, using an indirect nanoplasmonic sensing approach, we investigated how the nanoscale size properties of ligand-modified lipid vesicles affect real-time binding interactions, especially vesicle deformation processes, with a receptor-modified, cell membrane-mimicking platform. Together with theoretical analyses, our findings reveal a pronounced, size-dependent transition in the membrane bending properties of nanoscale lipid vesicles between 60 and 180 nm in diameter. For smaller vesicles, a large membrane bending energy enhanced vesicle stiffness while the osmotic pressure energy was the dominant modulating factor for larger, less stiff vesicles. These findings advance our fundamental understanding of how nanoparticle size affects multivalency-induced nanoparticle shape deformation and can provide guidance for the design of biomimetic nanoparticles with tailored nanomechanical properties.

Late stage of the formation of a protein corona around nanoparticles in biofluids.

In biofluids containing various proteins, nanoparticles rapidly come to be surrounded by a nanometer-thick protein layer referred to as a protein corona. The late stage of this process occurs via replacement of proteins already bound to a nanoparticle by new ones. In the available kinetic models, this process is considered to include independent acts of protein detachment and attachment. It can, however, occur also at the level of protein pairs via exchange, i.e., concerted replacement of an attached protein by a newly arrived one. I argue that the exchange channel can be more important than the conventional one. To illustrate the likely specifics of the exchange channel, I present a kinetic model focused exclusively on this channel and based on the Evans-Polanyi-type relation between the activation energies of the protein-exchange steps and the protein binding energies. The corresponding kinetics were calculated for three qualitatively different distributions of proteins in solution over binding energy (with a maximum or monotonously decreasing or increasing, respectively) and are found to be similar, with relatively rapid replacement of weakly bound proteins and slow redistribution of strongly bound proteins. The ratio of the timescales characterizing the evolution of weakly and strongly bound proteins is found to depend on the type of the binding-energy distribution.

Dissimilar Deformation of Fluid- and Gel-Phase Liposomes upon Multivalent Interaction with Cell Membrane Mimics Revealed Using Dual-Wavelength Surface Plasmon Resonance.

The mechanical properties of biological nanoparticles play a crucial role in their interaction with the cellular membrane, in particular for cellular uptake. This has significant implications for the design of pharmaceutical carrier particles. In this context, liposomes have become increasingly popular, among other reasons due to their customizability and easily varied physicochemical properties. With currently available methods, it is, however, not trivial to characterize the mechanical properties of nanoscopic liposomes especially with respect to the level of deformation induced upon their ligand-receptor-mediated interaction with laterally fluid cellular membranes. Here, we utilize the sensitivity of dual-wavelength surface plasmon resonance to probe the size and shape of bound liposomes (∼100 nm in diameter) as a means to quantify receptor-induced deformation during their interaction with a supported cell membrane mimic. By comparing biotinylated liposomes in gel and fluid phases, we demonstrate that fluid-phase liposomes are more prone to deformation than their gel-phase counterparts upon binding to the cell membrane mimic and that, as expected, the degree of deformation depends on the number of ligand-receptor pairs that are engaged in the multivalent binding.

Interplay of Cellular mRNA, miRNA and Viral miRNA during Infection of a Cell.

The understanding of the kinetics of gene expression in cells infected by viruses is currently limited. As a rule, the corresponding models do not take viral microRNAs (miRNAs) into account. Such RNAs are, however, operative during the replication of some viruses, including, e.g., herpesvirus. To clarify the kinetics of this category (with emphasis on the information available for herpesvirus), I introduce a generic model describing the transient interplay of cellular mRNA, protein, miRNA and viral miRNA. In the absence of viral miRNA, the cellular miRNA is considered to suppress the populations of mRNA and protein due to association with mRNA and subsequent degradation. During infection, the viral miRNA suppresses the population of cellular miRNA and via this pathway makes the mRNA and protein populations larger. This effect becomes appreciable with the progress of intracellular viral replication. Using biologically reasonable parameters, I investigate the corresponding mean-field kinetics and show the scale of the effect of viral miRNAs on cellular miRNA and mRNA. The scale of fluctuations of the populations of these species is illustrated as well by employing Monte Carlo simulations.

How nanoparticles can induce dimerization and aggregation of cells in blood or lymph.

By analogy with virions, the binding of biologically-inspired nanoparticles (NPs) with ligands to the cellular membrane containing receptors depends on the multivalent ligand-receptor interaction, membrane bending, and cytoskeleton deformation. The interplay of these factors results in the existence of the potential minimum and activation barrier on the pathway towards full absorption of a NP. Herein, I hypothesize and show theoretically that the interaction of a NP, bound to one cell, with another cell can stabilize the potential minimum and increase the corresponding activation barrier, i.e., NPs can mediate the formation of long-living pairs of cells and aggregates containing a few cells inside blood and lymphatic vessels.

Grain-growth mediated hydrogen sorption kinetics and compensation effect in single Pd nanoparticles.

Grains constitute the building blocks of polycrystalline materials and their boundaries determine bulk physical properties like electrical conductivity, diffusivity and ductility. However, the structure and evolution of grains in nanostructured materials and the role of grain boundaries in reaction or phase transformation kinetics are poorly understood, despite likely importance in catalysis, batteries and hydrogen energy technology applications. Here we report an investigation of the kinetics of (de)hydriding phase transformations in individual Pd nanoparticles. We find dramatic evolution of single particle grain morphology upon cyclic exposure to hydrogen, which we identify as the reason for the observed rapidly slowing sorption kinetics, and as the origin of the observed kinetic compensation effect. These results shed light on the impact of grain growth on kinetic processes occurring inside nanoparticles, and provide mechanistic insight in the observed kinetic compensation effect.

Diffusion of Lipid Nanovesicles Bound to a Lipid Membrane Is Associated with the Partial-Slip Boundary Condition.

During diffusion of nanoparticles bound to a cellular membrane by ligand-receptor pairs, the distance to the laterally mobile interface is sufficiently short for their motion to depend not only on the membrane-mediated diffusivity of the tethers but also in a not yet fully understood manner on nanoparticle size and interfacial hydrodynamics. By quantifying diffusivity, velocity, and size of individual membrane-bound liposomes subjected to a hydrodynamic shear flow, we have successfully separated the diffusivity contributions from particle size and number of tethers. The obtained diffusion-size relations for synthetic and extracellular lipid vesicles are not well-described by the conventional no-slip boundary condition, suggesting partial slip as well as a significant diffusivity dependence on the distance to the lipid bilayer. These insights, extending the understanding of diffusion of biological nanoparticles at lipid bilayers, are of relevance for processes such as cellular uptake of viruses and lipid nanoparticles or labeling of cell-membrane-residing molecules.

Unraveling How Multivalency Triggers Shape Deformation of Sub-100 nm Lipid Vesicles.

Multivalent ligand-receptor interactions are critical to the function of membrane-enveloped biological and biomimetic nanoparticles, yet resulting nanoparticle shape changes are rarely investigated. Using the localized surface plasmon resonance (LSPR) sensing technique, we tracked the attachment of biotinylated, sub-100 nm lipid vesicles to a streptavidin-functionalized supported lipid bilayer (SLB) and developed an analytical model to extract quantitative details about the vesicle-SLB contact region. The experimental results were supported by theoretical analyses of biotin-streptavidin complex formation and corresponding structural and energetic aspects of vesicle deformation. Our findings reveal how varying the surface densities of streptavidin receptors in the SLB and biotin ligands in the vesicles affects the extent of nanometer-scale vesicle deformation. We also identify conditions, i.e., a critical ligand density, at which appreciable vesicle deformation began, which provides insight into how the membrane bending energy partially counterposes the multivalent binding interaction energy. These findings are generalizable to various multivalent ligand-receptor systems.

Kinetic aspects of virus targeting by nanoparticles in vivo.

One of the suggested ways of the use of nanoparticles in virology implies their association with and subsequent deactivation of virions. The conditions determining the efficiency of this approach in vivo are now not clear. Herein, I propose the first kinetic model describing the corresponding processes and clarifying these conditions. My analysis indicates that nanoparticles can decrease concentration of infected cells by a factor of one order of magnitude, but this decrease itself (without feedback of the immune system) is insufficient for full eradication of infection. It can, however, induce delay in the progress of infection, and this delay can help to form sufficient feedback of the immune system.