A three dimensional model of multicellular aggregate compression.

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics, which has been demonstrated to play a crucial role in many physiological and pathological processes. In this paper, we propose a three-dimensional mechanical model and apply it to the uniaxial compression of a multicellular aggregate in a realistic biological setting. In particular, we consider an aggregate of initially spherical shape and describe both its elastic deformations and the reorganisation of the cells forming the spheroid. The latter phenomenon, understood as remodelling, is accounted for by assuming that the aggregate undergoes plastic-like distortions. The study of the compression of the spheroid, achieved by means of two parallel, compressive plates, needs the formulation of a contact problem between the living spheroid itself and the plates, and is solved with the aid of the augmented Lagrangian method. The results of the performed numerical simulations are in qualitative agreement with the biological observations reported in the literature and can also be used to estimate quantitatively some fundamental aggregate mechanical parameters.

Non-linear model for compression tests on articular cartilage.

Hydrated soft tissues, such as articular cartilage, are often modeled as biphasic systems with individually incompressible solid and fluid phases, and biphasic models are employed to fit experimental data in order to determine the mechanical and hydraulic properties of the tissues. Two of the most common experimental setups are confined and unconfined compression. Analytical solutions exist for the unconfined case with the linear, isotropic, homogeneous model of articular cartilage, and for the confined case with the non-linear, isotropic, homogeneous model. The aim of this contribution is to provide an easily implementable numerical tool to determine a solution to the governing differential equations of (homogeneous and isotropic) unconfined and (inhomogeneous and isotropic) confined compression under large deformations. The large-deformation governing equations are reduced to equivalent diffusive equations, which are then solved by means of finite difference (FD) methods. The solution strategy proposed here could be used to generate benchmark tests for validating complex user-defined material models within finite element (FE) implementations, and for determining the tissue's mechanical and hydraulic properties from experimental data.

Raman Fingerprints of SARS-CoV-2 Omicron Subvariants: Molecular Roots of Virological Characteristics and Evolutionary Directions.

The latest RNA genomic mutation of SARS-CoV-2 virus, termed the Omicron variant, has generated a stream of highly contagious and antibody-resistant strains, which in turn led to classifying Omicron as a variant of concern. We systematically collected Raman spectra from six Omicron subvariants available in Japan (i.e., BA.1.18, BA.2, BA.4, BA.5, XE, and BA.2.75) and applied machine-learning algorithms to decrypt their structural characteristics at the molecular scale. Unique Raman fingerprints of sulfur-containing amino acid rotamers, RNA purines and pyrimidines, tyrosine phenol ring configurations, and secondary protein structures clearly differentiated the six Omicron subvariants. These spectral characteristics, which were linked to infectiousness, transmissibility, and propensity for immune evasion, revealed evolutionary motifs to be compared with the outputs of genomic studies. The availability of a Raman "metabolomic snapshot", which was then translated into a barcode to enable a prompt subvariant identification, opened the way to rationalize in real-time SARS-CoV-2 activity and variability. As a proof of concept, we applied the Raman barcode procedure to a nasal swab sample retrieved from a SARS-CoV-2 patient and identified its Omicron subvariant by coupling a commercially available magnetic bead technology with our newly developed Raman analyses.

Fluorescence recovery after photobleaching: direct measurement of diffusion anisotropy.

Fluorescence recovery after photobleaching (FRAP) is a widely used technique for studying diffusion in biological tissues. Most of the existing approaches for the analysis of FRAP experiments assume isotropic diffusion, while only a few account for anisotropic diffusion. In fibrous tissues, such as articular cartilage, tendons and ligaments, diffusion, the main mechanism for molecular transport, is anisotropic and depends on the fibre alignment. In this work, we solve the general diffusion equation governing a FRAP test, assuming an anisotropic diffusivity tensor and using a general initial condition for the case of an elliptical (thereby including the case of a circular) bleaching profile. We introduce a closed-form solution in the spatial coordinates, which can be applied directly to FRAP tests to extract the diffusivity tensor. We validate the approach by measuring the diffusivity tensor of [Formula: see text] FITC-Dextran in porcine medial collateral ligaments. The measured diffusion anisotropy was [Formula: see text] (SE), which is in agreement with that reported in the literature. The limitations of the approach, such as the size of the bleached region and the intensity of the bleaching, are studied using COMSOL simulations.

Advanced Hepatitis C Virus Replication PDE Models within a Realistic Intracellular Geometric Environment.

The hepatitis C virus (HCV) RNA replication cycle is a dynamic intracellular process occurring in three-dimensional space (3D), which is difficult both to capture experimentally and to visualize conceptually. HCV-generated replication factories are housed within virus-induced intracellular structures termed membranous webs (MW), which are derived from the Endoplasmatic Reticulum (ER). Recently, we published 3D spatiotemporal resolved diffusion⁻reaction models of the HCV RNA replication cycle by means of surface partial differential equation (sPDE) descriptions. We distinguished between the basic components of the HCV RNA replication cycle, namely HCV RNA, non-structural viral proteins (NSPs), and a host factor. In particular, we evaluated the sPDE models upon realistic reconstructed intracellular compartments (ER/MW). In this paper, we propose a significant extension of the model based upon two additional parameters: different aggregate states of HCV RNA and NSPs, and population dynamics inspired diffusion and reaction coefficients instead of multilinear ones. The combination of both aspects enables realistic modeling of viral replication at all scales. Specifically, we describe a replication complex state consisting of HCV RNA together with a defined amount of NSPs. As a result of the combination of spatial resolution and different aggregate states, the new model mimics a cis requirement for HCV RNA replication. We used heuristic parameters for our simulations, which were run only on a subsection of the ER. Nevertheless, this was sufficient to allow the fitting of core aspects of virus reproduction, at least qualitatively. Our findings should help stimulate new model approaches and experimental directions for virology.

3D Spatially Resolved Models of the Intracellular Dynamics of the Hepatitis C Genome Replication Cycle.

Mathematical models of virus dynamics have not previously acknowledged spatial resolution at the intracellular level despite substantial arguments that favor the consideration of intracellular spatial dependence. The replication of the hepatitis C virus (HCV) viral RNA (vRNA) occurs within special replication complexes formed from membranes derived from endoplasmatic reticulum (ER). These regions, termed membranous webs, are generated primarily through specific interactions between nonstructural virus-encoded proteins (NSPs) and host cellular factors. The NSPs are responsible for the replication of the vRNA and their movement is restricted to the ER surface. Therefore, in this study we developed fully spatio-temporal resolved models of the vRNA replication cycle of HCV. Our simulations are performed upon realistic reconstructed cell structures-namely the ER surface and the membranous webs-based on data derived from immunostained cells replicating HCV vRNA. We visualized 3D simulations that reproduced dynamics resulting from interplay of the different components of our models (vRNA, NSPs, and a host factor), and we present an evaluation of the concentrations for the components within different regions of the cell. Thus far, our model is restricted to an internal portion of a hepatocyte and is qualitative more than quantitative. For a quantitative adaption to complete cells, various additional parameters will have to be determined through further in vitro cell biology experiments, which can be stimulated by the results deccribed in the present study.

A transversely isotropic, transversely homogeneous microstructural-statistical model of articular cartilage.

Articular cartilage is a multi-phasic, composite, fibre-reinforced material. Therefore, its mechanical properties are determined by the tissue microstructure. The presence of cells (chondrocytes) and collagen fibres within the proteoglycan matrix influences, at a local and a global level, the material symmetries. The volumetric concentration and shape of chondrocytes, and the volumetric concentration and spatial arrangement of collagen fibres have been observed to change as a function of depth in articular cartilage. In particular, collagen fibres are perpendicular to the bone-cartilage interface in the deep zone, their orientation is almost random in the middle zone, and they are parallel to the surface in the superficial zone. The aim of this work is to develop a model of elastic properties of articular cartilage based on its microstructure. In previous work, we addressed this problem based on Piola's notation for fourth-order tensors. Here, mathematical tools initially developed for transversely isotropic composite materials comprised of a statistical orientation of spheroidal inclusions are extended to articular cartilage, while taking into account the dependence of the elastic properties on cartilage depth. The resulting model is transversely isotropic and transversely homogeneous (TITH), the transverse plane being parallel to the bone-cartilage interface and the articular surface. Our results demonstrate that the axial elastic modulus decreases from the deep zone to the articular surface, a result that is in good agreement with experimental findings. Finite element simulations were carried out, in order to explore the TITH model's behaviour in articular cartilage compression tests. The force response, fluid flow and displacement fields obtained with the TITH model were compared with the classical linear elastic, isotropic, homogeneous (IH) model, showing that the IH model is unable to predict the non-uniform behaviour of the tissue. Based on considerations that the mechanical stability of the tissue depends on its topological and microstructural properties, our long-term goal is to clearly understand the stability conditions in topological terms, and the relationship with the growth and remodelling mechanisms in the healthy and diseased tissue.

Synaptic bouton properties are tuned to best fit the prevailing firing pattern.

The morphology of presynaptic specializations can vary greatly ranging from classical single-release-site boutons in the central nervous system to boutons of various sizes harboring multiple vesicle release sites. Multi-release-site boutons can be found in several neural contexts, for example at the neuromuscular junction (NMJ) of body wall muscles of Drosophila larvae. These NMJs are built by two motor neurons forming two types of glutamatergic multi-release-site boutons with two typical diameters. However, it is unknown why these distinct nerve terminal configurations are used on the same postsynaptic muscle fiber. To systematically dissect the biophysical properties of these boutons we developed a full three-dimensional model of such boutons, their release sites and transmitter-harboring vesicles and analyzed the local vesicle dynamics of various configurations during stimulation. Here we show that the rate of transmission of a bouton is primarily limited by diffusion-based vesicle movements and that the probability of vesicle release and the size of a bouton affect bouton-performance in distinct temporal domains allowing for an optimal transmission of the neural signals at different time scales. A comparison of our in silico simulations with in vivo recordings of the natural motor pattern of both neurons revealed that the bouton properties resemble a well-tuned cooperation of the parameters release probability and bouton size, enabling a reliable transmission of the prevailing firing-pattern at diffusion-limited boutons. Our findings indicate that the prevailing firing-pattern of a neuron may determine the physiological and morphological parameters required for its synaptic terminals.

Do two-phase biogas plants separate anaerobic digestion phases? - a mathematical model for the distribution of anaerobic digestion phases among reactor stages.

In this article a mathematical model is introduced, which estimates the distribution of the four anaerobic digestion phases (hydrolysis, acidogenesis, acetogenesis and methanogenesis) that occur among the leach bed reactor and the anaerobic filter of a biogas plant. It is shown that only the hydrolysis takes place in the first stage (leach bed reactor), while all other anaerobic digestion phases take place in both reactor stages. It turns out that, besides the usually measured raw materials of the acetogenesis and the methanogenesis phases (organic acids), it is also necessary to analyze the process liquid for raw materials of the acidogenesis phase, i.e., sugars, fatty acids, amino acids, etc. The introduced model can be used to monitor the inhibition of the anaerobic digestion phases in reactor stages and can, thus, help to improve the control system of biogas plants.

Mathematical modeling of process liquid flow and acetoclastic methanogenesis under mesophilic conditions in a two-phase biogas reactor.

Acetoclastic methanogenesis in the second stage of a two-phase biogas reactor is investigated. A mathematical model coupling chemical reactions with transport of process liquid and with the variation of population of the microorganisms living on the plastic tower packing of the reactor is proposed. The evolution of the liquid is described by an advection-diffusion-reaction equation, while a monod-type kinetic is used for the reactions. Moreover, a new inhibition factor MO(max) is introduced, which hinders the growth of microorganisms when the plastic tower packing is overpopulated. After estimating the reaction parameters, the acetate outflow measured experimentally is in good agreement with that predicted by simulations. For coupling liquid transport with reaction processes, a spatial discretization of the reactor is performed. This yields essential information about the distribution of acetate and the production of methane in the reactor. This information allows for defining a measure of the effectiveness of the reactor.