A microscopic model of enzyme kinetics.

Many in vivo enzymatic processes, such as those of the tissue factor pathway of blood coagulation, occur in environments with facilitated substrate delivery or enzymes bound to cellular or lipid surfaces, which are quite different from the ideal fluid environment for which the Michaelis-Menten equation was derived. To describe the kinetics of such reactions, we propose a microscopic model that focuses on the kinetics of a single-enzyme molecule. This model provides the foundation for macroscopic models of the system kinetics of reactions occurring in both ideal and nonideal environments. For ideal reaction systems, the corresponding macroscopic models thus derived are consistent with the Michaelis-Menten equation. It is shown that the apparent Km is in fact a function of the mechanism of substrate delivery and should be interpreted as the substrate level at which the enzyme vacancy time equals the residence time of ES-complexes; it is suggested that our microscopic model parameters characterize more accurately an enzyme and its catalytic efficiency than does the classical Km. This model can also be incorporated into computer simulations of more complex reactions as an alternative to explicit analytical formulation of a macroscopic model.     

Continuous monitoring of adenosine 5'-triphosphate in the microenvironment of immobilized enzymes by firefly luciferase

The study of enzymes sequestered in artificial or biological systems is generally conducted by indirect methodology with macroscopic measurements of reactants in the bulk medium. This paper describes a new approach with firefly luciferase to monitor ATP concentration directly in the microenvironment of enzymes producing or consuming ATP. Upon addition of ATP to immobilized firefly luciferase, the onset of light production is slower than that observed with the soluble enzyme, due to a slower diffusion of ATP to the immobilized enzyme. With immobilized pyruvate kinase, a relative accumulation of ATP inside the beads is demonstrated, as measured with coimmobilized firefly luciferase. The accumulation of product (ATP) is enhanced when the bead suspension is not stirred. This ATP in the beads is relatively inaccessible to soluble hexokinase added to the bulk medium. Similarly, a rapid ATP depletion in the microenvironment of immobilized hexokinase is demonstrated. This microscopic event is kinetically distinguishable from the slower macroscopic depletion of substrate in the bulk medium. The rate of depletion in the microenvironment depends on the local activity of the immobilized enzyme but not on the total amount of enzyme in suspension, as does the macroscopic phenomenon. The theoretical principles for the interaction of diffusion and catalysis in these systems are briefly summarized and discussed. These results are relevant to various molecular mechanisms proposed for membrane-bound enzyme action and regulation, derived from macroscopic kinetic measurements assuming a negligible diffusion control.     

DC-ELF characterization of random mixtures of piecewise nonlinear media

Biological tissues are ensembles of linear and nonlinear, symmetric and asymmetric constituents. As far as their electromagnetic characterization is concerned, they can be modeled as microscopic mixtures of the corresponding material media. Any medium volume can be properly discretized in a finite number of cells which can be modeled as an equivalent three dimensional network of lumped components, in order to characterize its electromagnetic behavior at wavelengths much longer than the relevant average linear size of the constitutive cells. Therefore, any mixture and the corresponding tissue can be characterized in terms of its effective conductance at extremely low frequency, with respect to a reference set of electrodes (ports of the equivalent network). When the above procedure is implemented for evaluating any of the aforesaid conductances, a resulting nonlinear characteristic should be expected. In reality, it may happen that the effect of the constitutive nonlinearities and the related asymmetries are smeared out by the randomness of the interconnections of the lumped components, leading at a macroscopic level to an isotropic constant equivalent conductance, i.e., to an isotropic constant equivalent conductivity of the mixture. The closed form analysis of a random network of nonlinear (piecewise linear) resistors offers a simple but clear cut example of such a property. This result, if extrapolated to biological media, suggests a new hint for explaining why there is no inconsistency between the typical electric characterization of biological tissues as almost linear macroscopic media, by means of their effective conductivity and permittivity, and the nonlinearities of the biochemical processes occurring in the tissue cells. In fact, the nonlinearities may not be observable by means of macroscopic electrical measurements because of the randomized spatial orientation and location of the processes.     

Fibroblast alignment under interstitial fluid flow using a novel 3-D tissue culture model

Interstitial flow is an important component of the microcirculation and interstitial environment, yet its effects on cell organization and tissue architecture are poorly understood, in part due to the lack of in vitro models. To examine the effects of interstitial flow on cell morphology and matrix remodeling, we developed a tissue culture model that physically supports soft tissue cultures and allows microscopic visualization of cells within the three-dimensional matrix. In addition, pressure-flow relationships can be continuously monitored to evaluate the bulk hydraulic resistance as an indicator of changes in the overall matrix integrity. We observed that cells such as human dermal fibroblasts aligned perpendicular to the direction of interstitial flow. In contrast, fibroblasts in static three-dimensional controls remained randomly oriented, whereas cells subjected to fluid shear as a two-dimensional monolayer regressed. Also, the dynamic measurements of hydraulic conductivity suggest reorganization toward a steady state. These primary findings help establish the importance of interstitial flow on the biology of tissue organization and interstitial fluid balance.     

The effect of media perfusion on three-dimensional cultures of human chondrocytes: integration of experimental and computational approaches

This work examines the effect of perfusion on human mature articular chondrocytes cultured on synthetic biodegradable scaffolds (DegraPol). Human chondrocytes were isolated, seeded on the scaffolds and subjected to perfused culture at a flow rate of 0.5 ml/min, corresponding to an average inlet fluid velocity of 44 microm/s, with flow inversion every 1 minute. The flow was imposed at the construct surface in some constructs, it was forced through the construct thickness in other constructs and was absent in the static controls. We compared cell viability and morphology and we evaluated material properties of the constructs at 1 month of culture. Thickness-perfused constructs showed significantly higher material properties and roughly a two-fold cell viability, when compared both to surface-perfused constructs and to static controls. Chondrocytes maintained a phenotypic morphology in all experiments, probably favoured by a limited cell-scaffold interaction. Biosynthetic activity could be demonstrated only in the bioreactor-cultured constructs. In this experimental model, a bi-directional flow of culture medium was applied to the cells at a macroscopic level and computational modelling was used to quantify the fluid-dynamic environment induced on the cells at a microscopic level. This method may be used to quantify the effects of fluid-dynamic shear on the growth modulation of tissue-engineered cartilage constructs, to potentially enhance tissue growth in vitro.     

Thin sectioning of slice preparations for immunohistochemistry

Many investigations in neuroscience, as well as other disciplines, involve studying small, yet macroscopic pieces or sections of tissue that have been preserved, freshly removed, or excised but kept viable, as in slice preparations of brain tissue. Subsequent microscopic studies of this material can be challenging, as the tissue samples may be difficult to handle. Demonstrated here is a method for obtaining thin cryostat sections of tissue with a thickness that may range from 0.2-5.0 mm. We routinely cut 400 micron thick Vibratome brain slices serially into 5-10 micron coronal cryostat sections. The slices are typically first used for electrophysiology experiments and then require microscopic analysis of the cytoarchitecture of the region from which the recordings were observed. We have constructed a simple device that allows controlled and reproducible preparation and positioning of the tissue slice. This device consists of a cylinder 5 cm in length with a diameter of 1.2 cm, which serves as a freezing stage for the slice. A ring snugly slides over the cylinder providing walls around the slice allowing the tissue to be immersed in freezing compound (e.g., OCT). This is then quickly frozen with crushed dry ice and the resulting wafer can be position easily for cryostat sectioning. Thin sections can be thaw-mounted onto coated slides to allow further studies to be performed, such as various staining methods, in situ hybridization, or immunohistochemistry, as demonstrated here.     

Numerical investigation of non-Newtonian microcirculatory blood flow in hepatic lobule

The circulation in the liver is unique at macroscopic and microscopic levels. At the macroscopic level, there is an unusual presence of portal and arterial inputs rather than a single arterial input. At the microscopic level, a series of microenvironments in the acinar system is essential in controlling the functional characteristics of hepatic parenchymal cells. Since the hemodynamics is much less studied in the multifunctional liver, an attempt is made to study the hepatic hemodynamics in a segment of a hepatic lobular structure, that is made up of high-pressure oxygenated arteriole, low-pressure nutrient-rich portal venule, fenestrated sinusoidal space and hepatic venule. Our goal is to dispel some of the myths of this complex vascular bed by means of finite volume blood flow simulation. Flow features like high-velocity gradients near the fenestrations, flow reversal and Dean vortices in the sinusoidal space are analyzed within the non-Newtonian framework. Since no distinct exact or numerical solutions are available for this complex vascular bed, the present simulated results are compared with the available clinical observations. Results revealed that the pressure plays a key role in hepatic blood flow.     

Micromechanical study of the load transfer in a polycaprolactone–collagen hybrid scaffold when subjected to unconfined and confined compression

Scaffolds are used in diverse tissue engineering applications as hosts for cell proliferation and extracellular matrix formation. One of the most used tissue engineering materials is collagen, which is well known to be a natural biomaterial, also frequently used as cell substrate, given its natural abundance and intrinsic biocompatibility. This study aims to evaluate how the macroscopic biomechanical stimuli applied on a construct made of polycaprolactone scaffold embedded in a collagen substrate translate into microscopic stimuli at the cell level. Eight poro-hyperelastic finite element models of 3D printed hybrid scaffolds from the same batch were created, along with an equivalent model of the idealized geometry of that scaffold. When applying an 8% confined compression at the macroscopic level, local fluid flow of up to 20 \(\upmu \)m/s and octahedral strain levels mostly under 20% were calculated in the collagen substrate. Conversely unconfined compression induced fluid flow of up to 10 \(\upmu \)m/s and octahedral strain from 10 to 35%. No relevant differences were found amongst the scaffold-specific models. Following the mechanoregulation theory based on Prendergast et al. (J Biomech 30:539–548, 1997.  https://doi.org/10.1016/S0021-9290(96)00140-6), those results suggest that mainly cartilage or fibrous tissue formation would be expected to occur under unconfined or confined compression, respectively. This in silico study helps to quantify the microscopic stimuli that are present within the collagen substrate and that will affect cell response under in vitro bioreactor mechanical stimulation or even after implantation.     

Conductance of porous media depends on external electric fields

In obstacle-filled media, such as extracellular or intracellular lumen of brain tissue, effective ion-diffusion permeability is a key determinant of electrogenic reactions. Although this diffusion permeability is thought to depend entirely on structural features of the medium, such as porosity and tortuosity, brain tissue shows prominent nonohmic properties, the origins of which remain poorly understood. Here, we explore Monte Carlo simulations of ion diffusion in a space filled with overlapping spheres to predict that diffusion permeability of such media decreases with stronger external electric fields. This dependence increases with lower medium porosity while decreasing with radial (two-dimensional or three-dimensional) compared with homogenous (one-dimensional) fields. We test our predictions empirically in an electrolyte chamber filled with microscopic glass spheres and find good correspondence with our predictions. A theoretical insight relates this phenomenon to a disproportionately increased dwell time of diffusing ions at potential barriers (or traps) representing geometric obstacles when the field strength increases. The dependence of medium ion-diffusion permeability on electric field could be important for understanding conductivity properties of porous materials, in particular for the accurate interpretation of electric activity recordings in brain tissue.     

Particulate nature of blood determines macroscopic rheology: a 2-D lattice Boltzmann analysis

Historically, predicting macroscopic blood flow characteristics such as viscosity has been an empirical process due to the difficulty in rigorously including the particulate nature of blood in a mathematical representation of blood rheology. Using a two-dimensional lattice Boltzmann approach, we have simulated the flow of red blood cells in a blood vessel to estimate flow resistance at various hematocrits and vessel diameters. By including white blood cells (WBCs) in the flow, we also calculate the increase in resistance due to white cell rolling and adhesion. The model considers the blood as a suspension of particles in plasma, accounting for cell-cell and cell-wall interactions to predict macroscopic blood rheology. The model is able to reproduce the Fahraeus-Lindqvist effect, i.e., the increase in relative apparent viscosity as tube size increases, and the Fahraeus effect, i.e., tube hematocrit is lower than discharge hematocrit. In addition, the model allows direct assessment of the effect of WBCs on blood flow in the microvasculature, reproducing the dramatic increases in flow resistance as WBCs enter short capillary segments. This powerful and flexible model can be used to predict blood flow properties in any vessel geometry and with any blood composition.     

Co-operative dynamics in organelles

Some organelles produce elementary life phenomena which are characterized by the spontaneous formation and/or maintenance of ordered macroscopic dynamics like e.g. the shortening of sarcomeres in striated muscle and the transmission of electrical impulses in an axon. It has been widely accepted that such organelles are organized molecular systems where molecular elements work independently under constraint of a more or less rigid and regular structure of the system. On the other hand, such organelles should be regarded as self-organizing systems if the ordered macroscopic dynamics are self-organized. As the macroscopic dynamics gradually emerge, the microscopic dynamics of its elements become linked to each other through a feedback loop. It is crucial for the feedback loop to operate that the macroscopic dynamics are "free" in their behavior. In the present paper, it is pointed out that the traditional view of independent molecular elements has been obtained from experiments in which, by means of external constraint, the macroscopic dynamics is "clamped". Under such conditions, the self-organizing system may behave as an organized one. Based on synergetics we propose criterions for proving self-organizing systems, and, by applying the criterions, we conclude that skeletal muscle actomysin is a co-operative element in the sense of self-organization.     

A model for diffusion in white matter in the brain

Diffusion of molecules in brain and other tissues is important in a wide range of biological processes and measurements ranging from the delivery of drugs to diffusion-weighted magnetic resonance imaging. Diffusion tensor imaging is a powerful noninvasive method to characterize neuronal tissue in the human brain in vivo. As a first step toward understanding the relationship between the measured macroscopic apparent diffusion tensor and underlying microscopic compartmental geometry and physical properties, we treat a white matter fascicle as an array of identical thick-walled cylindrical tubes arranged periodically in a regular lattice and immersed in an outer medium. Both square and hexagonal arrays are considered. The diffusing molecules may have different diffusion coefficients and concentrations (or densities) in different domains, namely within the tubes' inner core, membrane, myelin sheath, and within the outer medium. Analytical results are used to explore the effects of a large range of microstructural and compositional parameters on the apparent diffusion tensor and the degree of diffusion anisotropy, allowing the characterization of diffusion in normal physiological conditions as well as changes occurring in development, disease, and aging. Implications for diffusion tensor imaging and for the possible in situ estimation of microstructural parameters from diffusion-weighted MR data are discussed in the context of this modeling framework.     

Identification of Medieval Human Soft Tissue Remains in an Advanced State of Decomposition

Naturally preserved human soft tissue remains from mediaeval burials (ll-13th century A. D.) were investigated histologically after azocarmine/aniline alcohol (AZAN) or keratin-prekeratin-mucin (KPM) staining. The tissue remnants were in an advanced state of decomposition; they were completely collapsed and had lost their macroscopic characteristics. After rehydration, thin sectioning, and staining, microscopic properties permitted tissue identification, although differential staining of tissue components did not necessarily correspond with the expected results based on fresh tissue. The techniques and results presented in this paper are relevant for both anthropological and forensic purposes.     

Modified Procedure for the Microscopic and Macroscopic Study of Viral Plaques

A virus plaque method that consistently gives good visual contrast for macroscopic observation and also permits microscopic study is described. Cells are grown in plastic flasks and the gelled overlay medium can be of any desired agar concentration or volume. A fixing solution is used prior to removal of the agar overlay, and dye is added to the fixing solution or staining can follow fixation and agar removal. The bottom of the flask with the fixed monolayer is separated from the rest of the container and handled as a slide. A new mounting medium is described.     

Endothelin-3 induced mesenteric vasoconstriction and PMN infiltration in the rat small intestine: role of endothelin receptors

The objectives of this study were to characterize endothelin (ET)-3-induced alterations in intestinal hemodynamics and to evaluate whether ET-3 administration alters the tissue levels of polymorphonuclear leukocytes (PMNs) and modulates the epithelial barrier function of the small intestine. ET-3 (100 pmol/kg/min) was infused into the superior mesenteric artery (SMA) for 10 min, and tissue samples were obtained 30 min after terminating the infusion. SMA blood flow was significantly decreased throughout the experiment following ET-3 infusion. Pretreatment with bosentan (ET-A and ET-B receptor antagonist), ET-B receptor antagonist BQ-788 or ET-A receptor antagonist BQ-485 completely inhibited the ET-3-induced decrease in the SMA blood flow. Similar results were obtained from the resistance data, in which ET-3-induced increases in SMA resistance were significantly reduced by all ET receptor antagonists. ET-3 administration significantly elevated tissue MPO activity, blood-to-lumen clearance of (51)Cr-EDTA and caused a marked microscopic damage in the intestinal mucosa. ET-3-induced elevations in tissue PMN infiltration and mucosal damage were significantly inhibited by pretreatments with ET-A or ET-B receptor antagonists. Overall, our data indicate that ET-3 causes microscopic damage, PMN infiltration and mucosal dysfunction in the rat small intestine. In addition, ET-3-induced hemodynamic alterations as well as tissue PMN infiltration and mucosal damage are mediated by both ET-A and ET-B receptors.     

The Rapid Manufacture of Uniform Composite Multicellular-Biomaterial Micropellets,Their Assembly into Macroscopic Organized Tissues,and Potential Applications in Cartilage Tissue Engineering

We and others have published on the rapid manufacture of micropellet tissues, typically formed from 100–500 cells each. The micropellet geometry enhances cellular biological properties, and in many cases the micropellets can subsequently be utilized as building blocks to assemble complex macrotissues. Generally, micropellets are formed from cells alone, however when replicating matrix-rich tissues such as cartilage it would be ideal if matrix or biomaterials supplements could be incorporated directly into the micropellet during the manufacturing process. Herein we describe a method to efficiently incorporate donor cartilage matrix into tissue engineered cartilage micropellets. We lyophilized bovine cartilage matrix, and then shattered it into microscopic pieces having average dimensions < 10 μm diameter; we termed this microscopic donor matrix “cartilage dust (CD)”. Using a microwell platform, we show that ~0.83 μg CD can be rapidly and efficiently incorporated into single multicellular aggregates formed from 180 bone marrow mesenchymal stem/stromal cells (MSC) each. The microwell platform enabled the rapid manufacture of thousands of replica composite micropellets, with each micropellet having a material/CD core and a cellular surface. This micropellet organization enabled the rapid bulking up of the micropellet core matrix content, and left an adhesive cellular outer surface. This morphological organization enabled the ready assembly of the composite micropellets into macroscopic tissues. Generically, this is a versatile method that enables the rapid and uniform integration of biomaterials into multicellular micropellets that can then be used as tissue building blocks. In this study, the addition of CD resulted in an approximate 8-fold volume increase in the micropellets, with the donor matrix functioning to contribute to an increase in total cartilage matrix content. Composite micropellets were readily assembled into macroscopic cartilage tissues; the incorporation of CD enhanced tissue size and matrix content, but did not enhance chondrogenic gene expression.     

Analysis of lung parenchyma as a parametric porous medium.

The dynamic behavior of the lung in health and disease depends on its viscoelastic properties. To better understand these properties, several mathematical models have been utilized by many investigators. In the present work, we present a new approach that characterizes the dynamics of gas flow into a viscoelastic porous medium that models the lung structure. This problem is considered in terms of the lung input impedance on a macro level and parenchymal tissue impedance on the level of an alveolar wall. We start from a basic theoretical analysis in which macroscopic tissue deformations are represented in accordance with the linearized Navier-Stokes equations. This approach has strong theoretical underpinnings in other situations but has not been applied to analyze the impedance of the inflated lung. Our analysis provides a theoretical basis for analyzing the interaction between flow into the lungs as a biophysical diffusion process and parenchymal viscoelasticity described phenomenologically, within the frameworks of standard viscoelasticity and structural damping. This lung impedance incorporates parameters of porosity, permeability, and viscoelasticity on micro and macro levels of parenchymal tissue. The analysis shows the theoretical basis of the transformation from the impedance of alveolar walls or isolated tissue strips to that of the intact parenchyma. We also show how the loading impedance at the lung boundary may have a significant impact on the dynamic behavior of whole lung viscoelasticity. Our analysis may be useful in directing specific tests of different models and for analyzing experimental measurements of viscoelastic parameters of lung material under normal and pathological conditions.     

Quantitative analysis of three-dimensional-resolved fiber architecture in heterogeneous skeletal muscle tissue using nmr and optical imaging methods

The determination of principal fiber directions in structurally heterogeneous biological tissue substantially contributes to an understanding of its mechanical function in vivo. In this study we have depicted structural heterogeneity through the model of the mammalian tongue, a tissue comprised of a network of highly interwoven fibers responsible for producing numerous variations of shape and position. In order to characterize the three-dimensional-resolved microscopic myoarchitecture of the intrinsic musculature of the tongue, we viewed its fiber orientation at microscopic and macroscopic length scales using NMR (diffusion tensor MRI) and optical (two-photon microscopy) imaging methods. Diffusion tensor imaging (DTI) of the excised core region of the porcine tongue resulted in an array of 3D diffusion tensors, in which the leading eigenvector corresponded to the principal fiber orientation at each location in the tissue. Excised axially oriented lingual core tissues (fresh or paraffin-embedded) were also imaged with a mode-locked Ti-Sapphire laser, (76 MHz repetition rate, 150 femtosecond pulse width), allowing for the visualization of individual myofibers at in situ orientation. Fiber orientation was assessed by computing the 3D autocorrelation of discrete image volumes, and deriving the minimal eigenvector of the center voxel Hessian matrix. DTI of the fibers, comprising the intrinsic core of the tongue, demonstrated directional heterogeneity, with two distinct populations of fibers oriented orthogonal to each other and in-plane to the axial perspective. Microscopic analysis defined this structural heterogeneity as discrete regions of in-plane parallel fibers, with an angular separation of ~80 degrees, thereby recapitulating the macroscopic angular relationship. This analysis, conceived at two different length scales, demonstrates that the lingual core is a spatially complex tissue, composed of repeating orthogonally oriented and in-plane fiber patches, which are capable of jointly producing hydrostatic elongation and displacement.     

Microscopic-macroscopic interface in biological information processing

Recent experimental work suggests that chemical messengers associated with the neuron membrane serve as a link between macroscopic and microscopic information processes in the brain. Arguments based on the physical limits of computing, on computational parallelism, and on evolution theory suggest that microphysical computing processes enormously enhance the brain's computing power. A number of models are briefly sketched which illustrate how molecular switching processes could be recruited for useful biological functions. The flow of information between microscopic and macroscopic forms is suggestive of processes which occur in a measuring apparatus, and the implications of this analogy are considered.