Extended compartmental model for modeling COVID-19 epidemic in Slovenia.

In the absence of a systematic approach to epidemiological modeling in Slovenia, various isolated mathematical epidemiological models emerged shortly after the outbreak of the COVID-19 epidemic. We present an epidemiological model adapted to the COVID-19 situation in Slovenia. The standard SEIR model was extended to distinguish between age groups, symptomatic or asymptomatic disease progression, and vaccinated or unvaccinated populations. Evaluation of the model forecasts for 2021 showed the expected behavior of epidemiological modeling: our model adequately predicts the situation up to 4 weeks in advance; the changes in epidemiologic dynamics due to the emergence of a new viral variant in the population or the introduction of new interventions cannot be predicted by the model, but when the new situation is incorporated into the model, the forecasts are again reliable. Comparison with ensemble forecasts for 2022 within the European Covid-19 Forecast Hub showed better performance of our model, which can be explained by a model architecture better adapted to the situation in Slovenia, in particular a refined structure for vaccination, and better parameter tuning enabled by the more comprehensive data for Slovenia. Our model proved to be flexible, agile, and, despite the limitations of its compartmental structure, heterogeneous enough to provide reasonable and prompt short-term forecasts and possible scenarios for various public health strategies. The model has been fully operational on a daily basis since April 2020, served as one of the models for decision-making during the COVID-19 epidemic in Slovenia, and is part of the European Covid-19 Forecast Hub.

Key Challenges in Modelling an Epidemic - What have we Learned from the COVID-19 Epidemic so Far.

Mathematical modelling can be useful for predicting how infectious diseases progress, enabling us to show the likely outcome of an epidemic and help inform public health interventions. Different modelling techniques have been used to predict and simulate the spread of COVID-19, but they have not always been useful for epidemiologists and decision-makers. To improve the reliability of the modelling results, it is very important to critically evaluate the data used and to check whether or not due regard has been paid to the different ways in which the disease spreads through the population. As building an epidemiological model that is reliable enough and suits the current epidemiological situation within a country or region, certain criteria must be met in the modelling process. It might be necessary to use a combination of two or more different types of models in order to cover all aspects of epidemic modelling. If we want epidemiological models to be a useful tool in combating the epidemic, we need to engage experts from epidemiology, data science and statistics.

Cell confinement reveals a branched-actin independent circuit for neutrophil polarity.

Migratory cells use distinct motility modes to navigate different microenvironments, but it is unclear whether these modes rely on the same core set of polarity components. To investigate this, we disrupted actin-related protein 2/3 (Arp2/3) and the WASP-family verprolin homologous protein (WAVE) complex, which assemble branched actin networks that are essential for neutrophil polarity and motility in standard adherent conditions. Surprisingly, confinement rescues polarity and movement of neutrophils lacking these components, revealing a processive bleb-based protrusion program that is mechanistically distinct from the branched actin-based protrusion program but shares some of the same core components and underlying molecular logic. We further find that the restriction of protrusion growth to one site does not always respond to membrane tension directly, as previously thought, but may rely on closely linked properties such as local membrane curvature. Our work reveals a hidden circuit for neutrophil polarity and indicates that cells have distinct molecular mechanisms for polarization that dominate in different microenvironments.

Theoretical study of vesicle shapes driven by coupling curved proteins and active cytoskeletal forces.

Eukaryote cells have a flexible shape, which dynamically changes according to the function performed by the cell. One mechanism for deforming the cell membrane into the desired shape is through the expression of curved membrane proteins. Furthermore, these curved membrane proteins are often associated with the recruitment of the cytoskeleton, which then applies active forces that deform the membrane. This coupling between curvature and activity was previously explored theoretically in the linear limit of small deformations, and low dimensionality. Here we explore the unrestricted shapes of vesicles that contain active curved membrane proteins, in three-dimensions, using Monte-Carlo numerical simulations. The activity of the proteins is in the form of protrusive forces that push the membrane outwards, as may arise from the cytoskeleton of the cell due to actin or microtubule polymerization occurring near the membrane. For proteins that have an isotropic convex shape, the additional protrusive force enhances their tendency to aggregate and form membrane protrusions (buds). In addition, we find another transition from deformed spheres with necklace type aggregates, to flat pancake-shaped vesicles, where the curved proteins line the outer rim. This second transition is driven by the active forces, coupled to the spontaneous curvature, and the resulting configurations may shed light on the formation of sheet-like protrusions and lamellipodia of adhered and motile cells.

On the role of external force of actin filaments in the formation of tubular protrusions of closed membrane shapes with anisotropic membrane components.

Biological membranes are composed of different components and there is no a priori reason to assume that all components are isotropic. It was previously shown that the anisotropic properties of membrane components may explain the stability of membrane tubular protrusions even without the application of external force. Our theoretical study focuses on the role of anisotropic membrane components in the stability of membrane tubular structures generated or stabilized by actin filaments. We show that the growth of the actin cytoskeleton inside the vesicle can induce the partial lateral segregation of different membrane components. The entropy of mixing of membrane components hinders the total lateral segregation of the anisotropic and isotropic membrane components. Self-assembled aggregates formed by anisotropic membrane components facilitate the growth of long membrane tubular protrusions. Protrusive force generated by actin filaments favors strong segregation of membrane components by diminishing the opposing effect of mixing entropy.

Bending elasticity of vesicle membranes studied by Monte Carlo simulations of vesicle thermal shape fluctuations.

The membrane bending stiffness of nearly spherical lipid vesicles can be deduced from the analysis of their thermal shape fluctuations. The theoretical basis of this analysis [Milner and Safran, Phys. Rev. A: At., Mol., Opt. Phys., 1987, 36, 4371-4379] uses the mean field approximation. In this work we apply Monte Carlo simulations and estimate the error in the determination of the bending stiffness due to the approximations applied in the theory. It is less than 10%. The method presented in this work can also be used to determine the changes of the bending stiffness of biological membranes due to their chemical and/or structural modifications.

Determination of the strength of adhesion between lipid vesicles.

A commonly used method to determine the strength of adhesion between adhering lipid vesicles is measuring their effective contact angle from experimental images. The aim of this paper is to estimate the interobserver variations in vesicles effective contact angle measurements and to propose a new method for estimating the strength of membrane vesicle adhesion. Theoretical model shows for the old and for the new measure a monotonic dependence on the strength of adhesion. Results obtained by both measuring techniques show statistically significant correlation and high interobserver reliability for both methods. Therefore the conventional method of measuring the effective contact angle gives qualitatively relevant results as the measure of the lipid vesicle adhesion. However, the new measuring technique provides a lower variation of the measured values than the conventional measures using the effective contact angle. Moreover, obtaining the adhesion angle can be automatized more easily than obtaining the effective contact angle.

Fusion pore stability of peptidergic vesicles.

It is believed that in regulated exocytosis the vesicle membrane fuses with the plasma membrane in response to a physiological stimulus. However, in the absence of stimulation, repetitive transient fusion events are also observed, reflecting a stable state. The mechanisms by which the initial fusion pore attains stability are poorly understood. We modelled energetic stability of the fusion pore by taking into account the anisotropic, intrinsic shape of the membrane constituents and their in-plane ordering in the local curvature of the membrane. We used cell-attached membrane capacitance techniques to monitor the appearance and conductance of single fusion pore events in cultured rat lactotrophs. The results revealed a bell-shaped distribution of the fusion pore conductance with a modal value of 25 pS. The experimentally observed increase of the fusion pore stability with decreasing fusion pore radius agrees well with the theoretical predictions. Moreover, the results revealed a correlation between the amplitude of transient capacitance increases and the fusion pore conductance, indicating that larger vesicles may attain a stable fusion pore with larger fusion pore diameters.

On the role of anisotropy of membrane constituents in formation of a membrane neck during budding of a multicomponent membrane.

The expression for the isotropic membrane bending energy was generalized for the case of a multicomponent membrane where the membrane constituents (single molecules or small complexes of molecules-membrane inclusions) were assumed to be anisotropic. Using this generalized expression for the membrane energy it was shown that the change of intrinsic shape of membrane components may induce first-order-like shape transitions leading to the formation of a membrane neck. The predicted discontinuous membrane shape transition and the concomitant lateral segregation of membrane components were applied to study membrane budding. Based on the results presented we conclude that the budding process might be driven by accumulation of anisotropic membrane components in the necks connecting the bud and the parent membrane, and by accumulation of isotropic (conical) membrane components on the bud. Both processes may strongly depend on the intrinsic shape of membrane components and on the direct interactions between them.

Shape variation of bilayer membrane daughter vesicles induced by anisotropic membrane inclusions.

A theoretical model of a two-component bilayer membrane was used in order to describe the influence of anisotropic membrane inclusions on shapes of membrane daughter micro and nano vesicles. It was shown that for weakly anisotropic inclusions the stable vesicle shapes are only slightly out-of-round. In contrast, for strongly anisotropic inclusions the stable vesicle shapes may significantly differ from spheres, i.e. they have a flattened oblate shape at small numbers of inclusions in the membrane, and an elongated cigar-like prolate shape at high numbers of inclusions in the vesicle membrane.

Influence of rigid inclusions on the bending elasticity of a lipid membrane.

We model the influence of rigid inclusions on the curvature elasticity of a lipid membrane. Our focus is on conelike transmembrane inclusions that are able to induce long-range deformations in the host bilayer membrane. The elastic properties of the membrane are described in terms of curvature and tilt elasticity. The latter adds an additional degree of freedom that allows the membrane to accommodate an inclusion not only through a curvature deformation but also via changes in lipid tilt. Using a (mean-field level) cell model for homogeneously distributed inclusions in a small membrane segment of prescribed (mesoscopic-scale) spherical shape, we calculate the optimal microscopic-scale deviation of the membrane shape around the intercalated inclusions and the corresponding free energy, analytically. We show that the lipid tilt degree of freedom can lead to local softening of the inclusion-containing lipid bilayer segment. The predicted softening requires a sufficiently small value of the tilt modulus; its origin lies in the reduction of the excess membrane-inclusion interaction energy. We compare our results to the case of suppressed microscopic shape relaxation. Here, too, local softening of the membrane is possible.

The influence of anisotropic membrane inclusions on curvature elastic properties of lipid membranes.

A membrane inclusion can be defined as a complex of protein or peptide and the surrounding significantly distorted lipids. We suggest a theoretical model that allows for the estimation of the influence of membrane inclusions on the curvature elastic properties of lipid membranes. Our treatment includes anisotropic inclusions whose energetics depends on their in-plane orientation within the membrane. On the basis of continuum elasticity theory, we calculate the inclusion-membrane interaction energy that reflects the protein or peptide-induced short-ranged elastic deformation of a bent lipid layer. A numerical estimate of the corresponding interaction constants indicates the ability of inclusions to sense membrane bending and to accumulate at regions of favorable curvature, matching the effective shape of the inclusions. Strongly anisotropic inclusions interact favorably with lipid layers that adopt saddlelike curvature; such structures may be stabilized energetically. We explore this possibility for the case of vesicle budding where we consider a shape sequence of closed, axisymmetric vesicles that form a (saddle-curvature adopting) membrane neck. It appears that not only isotropic but also strongly anisotropic inclusions can significantly contribute to the budding energetics, a finding that we discuss in terms of recent experiments.

Endovesicle formation and membrane perturbation induced by polyoxyethyleneglycolalkylethers in human erythrocytes.

Polyoxyethyleneglycolalkylether (CmEn, m=12, n=8) can induce a large torocyte-like endovesicle in human erythrocytes. The present study aimed to examine how variations in the molecular structure of CmEn (m=10,12,14,16,18; n=1-10,23) affect the occurrence of torocyte endovesicles. Our results show that torocytes occur most frequently when m=12,14 and n=8,9. At this molecular configuration the detergents induce inward membrane bending (stomatocytic S1-S2 shapes) resulting in the formation of a large membrane invagination. These detergents have a strong membrane perturbing, i.e., haemolytic, effect. Theoretical calculations indicate that a torocyte-shaped inside-out membrane vesicle can be created from a large membrane invagination due to the impact of laterally mobile anisotropic membrane inclusions. Such inclusions may be detergent-membrane component complexes or unanchored integral membrane proteins. It is shown that a nonhomogeneous lateral distribution of anisotropic membrane inclusions may stabilise the torocyte endovesicle shape, characterised by having opposite membranes in the thin central region of the vesicles separated by a certain distance. Tubular, conical or inverted conical isotropic inclusions cannot do so.

Coupling between vesicle shape and the non-homogeneous lateral distribution of membrane constituents in Golgi bodies.

In this work, a hypothesis is presented that could explain the non-homogeneous lateral distribution of membrane components in Golgi vesicles. It is shown that the non-homogeneous lateral distribution of membrane components and the specific flattened shape of Golgi vesicles are strongly coupled. In agreement with experimental evidence, it is indicated that some of the membrane components may be concentrated mainly on the curved bulbous rims of the Golgi vesicles, while the other components are distributed predominantly in their flat central part.

Spherocyte shape transformation and release of tubular nanovesicles in human erythrocytes.

We have studied dodecylmaltoside-induced echinocyte-spheroechincyte-spherocyte shape transformation and membrane vesiculation using transmission electron microscopy (TEM) on freeze-fracture replicas. It is indicated that spherical erythrocyte shape at higher dodecylmaltoside concentration is formed due to loss of membrane in the process where small, mostly tubular nanovesicles are released predominantly from the top of echinocyte and spheroechinocyte spicules.

A possible origin of the torocyte-like shape of vesicles derived from the transverse tubule in the triad junction of skeletal muscle.

The origin of characteristic torocyte-like shape of vesicles derived from transverse tubule in triad junction of skeletal muscles is studied theoretically. Two possible mechanisms are suggested. The first is the minimization of membrane bending energy where the special intermediate molecular structures in the central region of the vesicle is assumed to protect the opposing bilayers to come in the direct contact. The second mechanism is based on the assumption that the characteristic shape of the vesicles may be explained by non-homogenous lateral distribution of anisotropic membrane components.