Toward a mathematical model of the assembly and disassembly of membrane microdomains: comparison with experimental models

Coupling of mitochondrial population evolution to microtubule dynamics in fission yeast cells: a kinetic Monte Carlo study

Mitochondrial populations in cells are maintained by cycles of fission and fusion events. Perturbation of this balance has been observed in several diseases such as cancer and neurodegeneration. In fission yeast cells, the association of mitochondria with microtubules inhibits mitochondrial fission [Mehta et al., J. Biol. Chem., 2019, 294, 3385], illustrating the intricate coupling between mitochondria and the dynamic population of microtubules within the cell. In order to understand this coupling, we carried out kinetic Monte Carlo (KMC) simulations to predict the evolution of mitochondrial size distributions for different cases; wild-type cells, cells with short and long microtubules, and cells without microtubules. Comparisons are made with mitochondrial distributions reported in experiments with fission yeast cells. Using experimentally determined mitochondrial fission and fusion frequencies, simulations implemented without the coupling of microtubule dynamics predicted an increase in the mean number of mitochondria, equilibrating within 50 s. The mitochondrial length distribution in these models also showed a higher occurrence of shorter mitochondria, implying a greater tendency for fission, similar to the scenario observed in the absence of microtubules and cells with short microtubules. Interestingly, this resulted in overestimating the mean number of mitochondria and underestimating mitochondrial lengths in cells with wild-type and long microtubules. However, coupling mitochondria's fission and fusion events to the microtubule dynamics effectively captured the mitochondrial number and size distributions in wild-type and cells with long microtubules. Thus, the model provides greater physical insight into the temporal evolution of mitochondrial populations in different microtubule environments, allowing one to study both the short-time evolution as observed in the experiments (<5 minutes) as well as their transition towards a steady-state (>15 minutes). Our study illustrates the critical role of microtubules in mitochondrial dynamics and coupling microtubule growth and shrinkage dynamics is critical to predicting the evolution of mitochondrial populations within the cell.

Development of a Simple Kinetic Mathematical Model of Aggregation of Particles or Clustering of Receptors

The process of clustering of plasma membrane receptors in response to their agonist is the first step in signal transduction. The rate of the clustering process and the size of the clusters determine further cell responses. Here we aim to demonstrate that a simple 2-differential equation mathematical model is capable of quantitative description of the kinetics of 2D or 3D cluster formation in various processes. Three mathematical models based on mass action kinetics were considered and compared with each other by their ability to describe experimental data on GPVI or CR3 receptor clustering (2D) and albumin or platelet aggregation (3D) in response to activation. The models were able to successfully describe experimental data without losing accuracy after switching between complex and simple models. However, additional restrictions on parameter values are required to match a single set of parameters for the given experimental data. The extended clustering model captured several properties of the kinetics of cluster formation, such as the existence of only three typical steady states for this system: unclustered receptors, receptor dimers, and clusters. Therefore, a simple kinetic mass-action-law-based model could be utilized to adequately describe clustering in response to activation both in 2D and in 3D.

The Roles of Signaling in Cytoskeletal Changes, Random Movement, Direction-Sensing and Polarization of Eukaryotic Cells

Movement of cells and tissues is essential at various stages during the lifetime of an organism, including morphogenesis in early development, in the immune response to pathogens, and during wound-healing and tissue regeneration. Individual cells are able to move in a variety of microenvironments (MEs) (A glossary of the acronyms used herein is given at the end) by suitably adapting both their shape and how they transmit force to the ME, but how cells translate environmental signals into the forces that shape them and enable them to move is poorly understood. While many of the networks involved in signal detection, transduction and movement have been characterized, how intracellular signals control re-building of the cyctoskeleton to enable movement is not understood. In this review we discuss recent advances in our understanding of signal transduction networks related to direction-sensing and movement, and some of the problems that remain to be solved.

Quantitative dynamics of reversible platelet aggregation: mathematical modelling and experiments

Although reversible platelet aggregation observed in response to ADP stimulation in the presence of calcium is a well-known phenomenon, its mechanisms are not entirely clear. To study them, we developed a simple kinetic mass-action-law-based mathematical model to use it in combination with experiments. Light transmission platelet aggregometry (LTA) induced by ADP was performed for platelet-rich plasma or washed platelets using both conventional light transmission and aggregate size monitoring method based on optical density fluctuations. Parameter values of the model were determined by means of parameter estimation techniques implemented in COPASI software. The mathematical model was able to describe reversible platelet aggregation LTA curves without assuming changes in platelet aggregation parameters over time, but with the assumption that platelet can enter the aggregate only once. In the model, the mean size of platelet aggregates correlated with the solution transparency. This corresponded with flow cytometry analysis and with optical density fluctuations data on aggregate size. The predicted values of model parameters correlated with ADP concentration used in experiments. These data suggest that, at the start of the aggregation, when platelet integrins switch “on”, large unstable platelet aggregates are rapidly formed, which leads to an increase in light transmission. However, upon fragmentation of these aggregates, the probability of the post-aggregate platelets’ attachment to each other decreases preventing new aggregation and resulting in the reversible aggregation phenomenon.

Lipid Raft Size and Lipid Mobility in Non-raft Domains Increase during Aging and Are Exacerbated in APP/PS1 Mice Model of Alzheimer's Disease. Predictions from an Agent-Based Mathematical Model

A connection between lipid rafts and Alzheimer's disease has been studied during the last decades. Mathematical modeling approaches have recently been used to correlate the effects of lipid composition changes in the physicochemical properties of raft-like membranes. Here we propose an agent based model to assess the effect of lipid changes in lipid rafts on the evolution and progression of Alzheimer's disease using lipid profile data obtained in an established model of familial Alzheimer's disease. We have observed that lipid raft size and lipid mobility in non-raft domains are two main factors that increase during age and are accelerated in the transgenic Alzheimer's disease mouse model. The consequences of these changes are discussed in the context of neurotoxic amyloid β production. Our agent based model predicts that increasing sterols (mainly cholesterol) and long-chain polyunsaturated fatty acids (LCPUFA) (mainly DHA, docosahexaenoic acid) proportions in the membrane composition might delay the onset and progression of the disease.

The interactions of squalene, alkanes and other mineral oils with model membranes; effects on membrane heterogeneity and function

Droplet interface bilayers (DIBs) offer many favourable facets as an artificial membrane system but the influence of any residual oil that remains in the bilayer following preparation is ill-defined. In this study the fluorescent membrane probes di-8-butyl-amino-naphthyl-ethylene-pyridinium-propyl-sulfonate (Di-8-ANEPPS) and Fluoresceinphosphatidylethanolamine (FPE) were used to help understand the nature of the phospholipid-oil interaction and to examine any structural and functional consequences of such interactions on membrane bilayer properties. Concentration-dependent modifications of the membrane dipole potential were found to occur in phospholipid vesicles exposed to a variety of different oils. Incorporation of oil into the lipid bilayer was shown to have no significant effect on the movement of fatty acids across the lipid bilayer. Changes in membrane heterogeneity were, however, demonstrated with increased microdomain formation being visible in the bilayer following exposure to mineral oil, pentadecane and squalene. As it is important that artificial systems provide an accurate representation of the membrane environment, careful consideration should be taken prior to the application of DIBs in studies of membrane structure and organisation.

Receptor-independent interaction of bacterial lipopolysaccharide with lipid and lymphocyte membranes; the role of cholesterol

Lipopolysaccharide (LPS) is a major constituent of bacterial outer membranes where it makes up the bulk of the outer leaflet and plays a key role as determinant of bacterial interactions with the host. Membrane-free LPS is known to activate T-lymphocytes through interactions with Toll-like receptor 4 via multiprotein complexes. In the present study, we investigate the role of cholesterol and membrane heterogeneities as facilitators of receptor-independent LPS binding and insertion, which underpin bacterial interactions with the host in symbiosis, pathogenesis and cell invasion. We use fluorescence spectroscopy to investigate the interactions of membrane-free LPS from intestinal Gram-negative organisms with cholesterol-containing model membranes and with T-lymphocytes. LPS preparations from Klebsiella pneumoniae and Salmonella enterica were found to bind preferentially to mixed lipid membranes by comparison to pure PC bilayers. The same was observed for LPS from the symbiote Escherichia coli but with an order of magnitude higher dissociation constant. Insertion of LPS into model membranes confirmed the preference for sphimgomyelin/cholesterol-containing systems. LPS insertion into Jurkat T-lymphocyte membranes reveals that they have a significantly greater LPS-binding capacity by comparison to methyl-β-cyclodextrin cholesterol-depleted lymphocyte membranes, albeit at slightly lower binding rates.

Mathematical modeling of K-Ras nanocluster formation on the plasma membrane

K-Ras functions as a critical node in the mitogen-activated protein kinase (MAPK) pathway that regulates key cellular functions including proliferation, differentiation, and apoptosis. Following growth factor receptor activation K-Ras.GTP forms nanoclusters on the plasma membrane through interaction with the scaffold protein galectin-3. The generation of nanoclusters is essential for high fidelity signal transduction via the MAPK pathway. To explore the mechanisms underlying K-Ras.GTP nanocluster formation, we developed a mathematical model of K-Ras-galectin-3 interactions. We designed a computational method to calculate protein collision rates based on experimentally determined protein diffusion rates and diffusion mechanisms and used a genetic algorithm to search the values of key model parameters. The optimal estimated model parameters were validated using experimental data. The resulting model accurately replicates critical features of K-Ras nanoclustering, including a fixed ratio of clustered K-Ras.GTP to monomeric K-Ras.GTP that is independent of the concentration of K-Ras.GTP. The model reproduces experimental results showing that the cytosolic level of galectin-3 determines the magnitude of the K-Ras.GTP clustered fraction and illustrates that nanoclustering is regulated by key nonequilibrium processes. Our kinetic model identifies a potential biophysical mechanism for K-Ras nanoclustering and suggests general principles that may be relevant for other plasma-membrane-localized proteins.

The interaction of N-acylhomoserine lactone quorum sensing signaling molecules with biological membranes: implications for inter-kingdom signaling

Background

The long chain N-acylhomoserine lactone (AHL) quorum sensing signal molecules released by Pseudomonas aeruginosa have long been known to elicit immunomodulatory effects through a process termed inter-kingdom signaling. However, to date very little is known regarding the exact mechanism of action of these compounds on their eukaryotic targets.

Methodology/Principal Findings

The use of the membrane dipole fluorescent sensor di-8-ANEPPS to characterise the interactions of AHL quorum sensing signal molecules, N-(3-oxotetradecanoyl)-L-homoserine lactone (3-oxo-C14-HSL), N-(3-oxododecanoyl)homoserine-L-lactone (3-oxo-C12-HSL) and N-(3-oxodecanoyl) homoserine-L-lactone (3-oxo-C10 HSL) produced by Pseudomonas aeruginosa with model and cellular membranes is reported. The interactions of these AHLs with artificial membranes reveal that each of the compounds is capable of membrane interaction in the micromolar concentration range causing significant modulation of the membrane dipole potential. These interactions fit simple hyperbolic binding models with membrane affinity increasing with acyl chain length. Similar results were obtained with T-lymphocytes providing the evidence that AHLs are capable of direct interaction with the plasma membrane. 3-oxo-C12-HSL interacts with lymphocytes via a cooperative binding model therefore implying the existence of an AHL membrane receptor. The role of cholesterol in the interactions of AHLs with membranes, the significance of modulating cellular dipole potential for receptor conformation and the implications for immune modulation are discussed.

Conclusions/ Significance

Our observations support previous findings that increasing AHL lipophilicity increases the immunomodulatory activity of these quorum compounds, while providing evidence to suggest membrane interaction plays an important role in quorum sensing and implies a role for membrane microdomains in this process. Finally, our results suggest the existence of a eukaryotic membrane-located system that acts as an AHL receptor.

Functional imaging of microdomains in cell membranes

The presence of microdomains or rafts within cell membranes is a topic of intense study and debate. The role of these structures in cell physiology, however, is also not yet fully understood with many outstanding problems. This problem is partly based on the small size of raft structures that presents significant problems to their in vivo study, i.e., within live cell membranes. But the structure and dynamics as well as the factors that control the assembly and disassembly of rafts are also of major interest. In this review we outline some of the problems that the study of rafts in cell membranes present as well as describing some views of what are considered the generalised functions of membrane rafts. We point to the possibility that there may be several different 'types' of membrane raft in cell membranes and consider the factors that affect raft assembly and disassembly, particularly, as some researchers suggest that the lifetimes of rafts in cell membranes may be sub-second. We attempt to review some of the methods that offer the ability to interrogate rafts directly as well as describing factors that appear to affect their functionality. The former include both near-field and far-field optical approaches as well as scanning probe techniques. Some of the advantages and disadvantages of these techniques are outlined. Finally, we describe our own views of raft functionality and properties, particularly, concerning the membrane dipole potential, and describe briefly some of the imaging strategies we have developed for their study.