The osmotic migration of cells in a solute gradient.

The effect of a nonuniform solute concentration on the osmotic transport of water through the boundaries of a simple model cell is investigated. A system of two ordinary differential equations is derived for the motion of a single cell in the limit of a fast solute diffusion, and an analytic solution is obtained for one special case. A two-dimensional finite element model has been developed to simulate the more general case (finite diffusion rates, solute gradient induced by a solidification front). It is shown that the cell moves to regions of lower solute concentration due to the uneven flux of water through the cell boundaries. This mechanism has apparently not been discussed previously. The magnitude of this effect is small for red blood cells, the case in which all of the relevant parameters are known. We show, however, that it increases with cell size and membrane permeability, so this effect could be important for larger cells. The finite element model presented should also have other applications in the study of the response of cells to an osmotic stress and for the interaction of cells and solidification fronts. Such investigations are of major relevance for the optimization of cryopreservation processes.     

On the cyclotron resonance model of ion transport.

The cyclotron-resonance model, which has been suggested as an explanation of a purported enhancement of transport of ions through the membranes of cells exposed to weak, low-frequency-modulated RF fields, is shown to be inconsistent with basic physical principles. Under the conditions of the model, in which the ions are presumed to circulate under the constraint of the earth's magnetic field, the radii of gyration of the ions would approximate 50 m and, thus, are much larger than the cells. Moreover, from general considerations, the collision-damping time of such ions is expected to be less than 10(-10) s, much smaller than the times of the order of 10(-2) s, shown to be necessary if the conditions for low-frequency resonance are to be satisfied.     

A new analysis of allogeneic interactions.

Allogeneic reactions have conventionally been considered as typical immune responses by one population of cells to antigens present on the other. This view is inadequate, since it does not explain many features of these reactions, among which are: (1) reactivity is much higher between different strains within a species than between species, in spite of the much greater antigenic disparity in the second case; (2) a very high proportion of cells may respond to allogeneic stimuli; (3) major histocompatibility differences are not essential for vigorous allogeneic reactions; (4) the responding population need not be immunologically competent to respond to antigens of the stimulating population; (5) the stimulating population must be both metabolically active and immunocompetent. We have tried to produce a model of cell interaction which will account for these and other anomalies, which at the same time explaining both normal antigenic stimulation (through cell-cell cooperation) and allogeneic interactions as examples of the same basic mechanisms. The model is based on the Bretscher-Cohn scheme of cell interaction. An allogeneic reaction is seen as having two stages: (1) Cells come together when antibody receptors on cells of one population combine with antigens on cells of the other. To this extent, our model is the same as the conventional one. It need not be the responding population which has the receptors, however. (2) A species-specific proliferation signal passes between the cells. This is the same signal as is involved in normal antibody induction. Even antigen-receptor bonds which are very weak may result in effective stimulation of one or both partners because of enhancing effect of this signal, and because the antigens involved are probably repeated over the cell surface, enabling multipoint binding. This explains the very proportions of cells which proliferate. The exact outcome of any allogeneic interaction will depend on which of the two populations have antibody receptors for antigens on the other, which can produce the proliferative stimulus, and which can respond to either the proliferative signal alone or to this stimulus plus antigen.     

Impedance analysis of MDCK cells measured by electric cell-substrate impedance sensing.

Transepithelial impedance of Madin-Darby canine kidney cell layers is measured by a new instrumental method, referred to as electric cell-substrate impedance sensing. In this method, cells are cultured on small evaporated gold electrodes, and the impedance is measured in the frequency range 20-50,000 Hz by a small probing current. A model for impedance analysis of epithelial cells measured by this method is developed. The model considers three different pathways for the current flowing from the electrode through the cell layer: (1) in through the basal and out through the apical membrane, (2) in through the lateral and out through the apical membrane, and (3) between the cells through the paracellular space. By comparing model calculation with experimental impedance data, several morphological and cellular parameters can be determined: (1) the resistivity of the cell layer, (2) the average distance between the basal cell surface and substratum, and (3) the capacitance of apical, basal, and lateral cell membranes. This model is used to analyze impedance changes on removal of Ca2+ from confluent Mardin-Darby canine kidney cell layers. The method shows that reduction of Ca2+ concentration causes junction resistance between cells to drop and the distance between the basal cell surface and substratum to increase.     

Modulation of differentiation in vitro. I. Influence of the attachment surface on myogenesis

Myogenic cells of the L6 line proliferate and fuse in culture to form myotubes that actively synthesize muscle-specific proteins such as myosin. We show that the expression of the differentiated phenotype can be influenced by the electrical charges of the substratum on which the cells were grown. Negatively charged surfaces did not influence the developmental program of the cells although positively charged ones interfered with myogenesis. The interaction operates primarily by interfering with the mitotic cycle, which is slowed down, with fusion which is blocked, and with myosin synthesis, which is reduced. Our results show that growth of the cells on positively charged surfaces prevents the switching of a large fraction of the population from a proliferative state to a differentiating program. We postulate that this interference might operate through the slowdown in DNA replication. The cell culture method described represents a good model for studying the different steps involved in the differentiation of L6 cells.     

Intercellular communication in a positional field. Ultrastructural correlates and tracer analysis of communication between insect epidermal cells.

The junctional membrane in the epidermal cells of the larval beetle (Tenebrio molitor L.) is comprised of macular gap junctions embedded in septate junctions. Ultrastructural and morphometric analysis of the distribution of gap junctions within the segmental epidermis suggests that this junction alone could account for the high electrotonic coupling recorded for the epidermal sheet. Analysis of the lanthanum-impregnated septate junction makes it doubtful that this junction serves as a communicating channel between beetle cells. A new model for the septate junction is presented in which pleated septa, less than 30 A thick, connect adjacent plasma membranes; the septa themselves are interconnected by two interseptal platforms that are coplanar with the plasma membranes. Iontophoretic injection of organic tracers into single epidermal cells suggests that only molecules of less than MW 1000 can transfer between cells through low-resistance junctions.     

Matrix simulation of duodenal crypt cell kinetics. I. The steady state.

Steady state crypt cell kinetics have been simulated using matrix algebra. The model crypt cell population is distributed through two proliferation compartments (P1 and P2) and a quiescent state (Q). Under steady state conditions half the daughter cells produced on completion of P1 enter G1 of P2 and half enter G1 of P1. Both P2 daughter cells enter Q. Cells in Q are non-dividing but retain the potential to divide. On completion of Q, cells lose the potential to divide and move up onto the villi. The model has been developed by simultaneously simulating the following biological data: (1) the per cent labeled mitosis (PML) curve, (2) the number of labeled cells per crypt as a function of time following an injection of 3H-thymidine, and (3) the total number of cells per crypt.     

Effect of syncytium structure of receptor systems on stochastic resonance induced by chaotic potential fluctuation.

To study a role of syncytium structure of sensory receptor systems in the detection of weak signals through stochastic resonance, we present a model of a receptor system with syncytium structure in which receptor cells are interconnected by gap junctions. The apical membrane of each cell includes two kinds of ion channels whose gating processes are described by the deterministic model. The membrane potential of each cell fluctuates chaotically or periodically, depending on the dynamical state of collective channel gating. The chaotic fluctuation of membrane potential acts as internal noise for the stochastic resonance. The detection ability of the system increases as the electric conductance between adjacent cells generated by the gap junction increases. This effect of gap junctions arises mainly from the fact that the synchronization of chaotic fluctuation of membrane potential between the receptor cells is strengthened as the density of gap junctions is increased.     

Model for a self-repairing system of non-articulated coralline algae.

We propose a perspective for living systems, emphasizing that living systems are organized through the recognition of themselves and their surroundings. Oscillator functions in Brownian Algebra are introduced, supposing that the oscillation can be regarded as metabolism of the living state. We illustrate the idea of the self-repairing model in non-articulated coralline algae. Since various cells of this plant are assumed to be identified with the periodic sequence of oscillations, the individual periodic sequence characterizing a cell is supposed to be determined by a local-interaction rule which can be regarded as the process of self-organization through the recognition of local shape. Owing to accidental injury the rule characterizing a cell's own state can be transformed, and it entails another periodic sequence. We express the oscillator as state flow diagrams, and analyze the relationship between the transformation of the period and the injury which is represented by the removal of transient in flow diagrams.     

The alternative migratory pathways of the Drosophila tracheal cells are associated with distinct subsets of mesodermal cells

The Drosophila tracheal system is a model for the study of the mechanisms that guide cell migration. The general conclusion from many studies is that migration of tracheal cells relies on directional cues provided by nearby cells. However, very little is known about which paths are followed by the migrating tracheal cells and what kind of interactions they establish to move in the appropriate direction. Here we analyze how tracheal cells migrate relative to their surroundings and which tissues participate in tracheal cell migration. We find that cells in different branches exploit different strategies for their migration; while some migrate through preexisting grooves, others make their way through homogeneous cell populations. We also find that alternative migratory pathways of tracheal cells are associated with distinct subsets of mesodermal cells and propose a model for the allocation of groups of tracheal cells to different branches. These results show how adjacent tissues influence morphogenesis of the tracheal system and offer a model for understanding how organ formation is determined by its genetic program and by the surrounding topological constraints.     

Modelling the internalization of labelled cells in tumour spheroids

In this paper a mathematical model is developed to describe the migration of labelled particles within a multicell spheroid. In the model, spatial variations in cell proliferation and death create an internal velocity field which leads to redistribution of the labelled and unlabelled cells. By applying a range of numerical and analytical techniques to the model equations, it is possible to show that, whilst the speed with which the labelled cells migrate through the tumour is independent of the type of cells that are labelled, their limiting distribution depends crucially on whether inert polystyrene microspheres or live tumour cells are labelled. These predictions are shown to be in good qualitative agreement with independent experimental results.     

Ephaptic coupling of cardiac cells through the junctional electric potential

Cardiac cells are electrically coupled through gap junction channels, which allow ionic current to spread intercellularly from one cell to the next. In addition, it is possible that cardiac cells are coupled through the electric potential in the junctional cleft space between neighboring cells. We develop and analyze a mathematical model of two cells coupled through a common junctional cleft potential. Consistent with more detailed models, we find that the coupling mechanism is highly parameter dependent. Analysis of our model reveals that there are two time scales involved, and the dynamics of the slow subsystem provide new mathematical insight into how the coupling mechanism works. We find that there are two distinct types of propagation failure and we are able to characterize parameter space into regions of propagation success and the two different types of propagation failure.     

Immunocompetence of chimeric rabbits. III. Serial passage and persistence of B-lymphocyte memory

In a model consisting of noninbred rabbits matched for major histocompatibility antigens and mismatched for immunoglobulin allotypes, using cell donors and recipients unrelated to each other, B-cell memory has been demonstrated to persist through three successive transfers for a period approaching 2 years. Memory cells from the original donor are shown to dominate specific antibody responses of the primary and secondary recipients. Vigorous antibody responses by donor-derived cells are obtained even when antigenic stimulation is delayed by several months. The data suggest that B memory cells may be particularly efficient in the colonization of recipients, and the potential significance of these findings for adoptive immunization of human bone marrow recipients is discussed.     

The cyclic AMP control system in the development of Dictyostelium discoideum. I. Cellular dynamics.

A model for the synthesis and release of cyclic AMP in aggregating cells of Dictyostelium discoideum is developed. The model shows transitions from low level steady release of cAMP to excitable pulsatile release and then to autonomous periodic pulsatile release of cAMP as starvation proceeds. Finally, there is a transition to high level continuous release of cAMP. A detailed correspondence is drawn between these transitions and the phenomena that are observed to appear sequentially during the aggregation phase, specifically: cloud formation, relaying competence, autonomous competence, and tip activity. The only assumptions necessary to the model are that there is a autocatalytic mechanism for cAMP synthesis, a negative feedback regulation of cAMP through another variable C, and a source term for C that declines with starvation. By analogy with other systems across the phylogenetic scale, in which cAMP activates catabolic pathways and catabolites depress cAMP levels, C is tentatively identified as some measure of the level of energy-yielding catabolites in the cell and the source term for C, as a measure of the cells stored reserves. Starvation for C induces catabolism of stored reserves S through a rise in cAMP. As S, the source term for C declines, the feedback regulation through C can no longer maintain homeostosis and the control loop may be destabilised by small perturbations, i.e. it becomes excitable. A further decline in S can produce limit cycle oscillations in the catabolite-cAMP feedback loop. As S declines even further, continuous steady release of cAMP may ensue.In addition to incorporating the four developmental transitions observed during the aggregation phase as direct consequences of starvation, the model features a super-exponential emergence of relaying competence, phase shifts and acceleration of development by cAMP pulses, and a decreasing refractory period that becomes less than the period of an autonomous cell. All these features closely parallel experimental findings. Finally, the model suggests further experiments critical to an understanding of the dynamics underlying aggregation.     

Periodicity of DNA folding in higher order chromatin structures.

Each level of DNA folding in cells corresponds to a distinct chromatin structure. The basic chromatin units, nucleosomes, are arranged into solenoids which form chromatin loops. To characterize better the loop organization of chromatin we have assumed that the accessibility of DNA inside these structures is lower than on the outside and examined the size distribution of high mol. wt DNA fragments obtained from cells and isolated nuclei after digestion with endogenous nuclease or topoisomerase II. The largest discrete fragments obtained contain 300 kbp of DNA. Their further degradation proceeds through another discrete size step of 50 kbp. This suggests that chromatin loops contain approximately 50 kbp of DNA and that they are grouped into hexameric rosettes at the next higher level of chromatin structure. Based upon these observations a model by which the 30 nm chromatin fibre can be folded up into compact metaphase chromosomes is also described.     

Transcytosis of pancreatic bile salt-dependent lipase through human Int407 intestinal cells.

In previous studies, we have shown that the bile-salt-dependent-lipase (BSDL), secreted by pancreatic acinar cells and secreted into the duodenal lumen, can be transcytosed through intestinal cells up to the lamina propria. In this study, we used an in vitro system to provide insights into the apical to basolateral transport of BSDL, across the intestinal barrier. The Int407 human epithelial cell line, grown under conditions that optimize polarity, was used as a tight epithelium model. We attempted to delineate uptake mechanisms and the transcytotic pathway followed by this pancreatic enzyme within the intestinal Int407 cells, which do not produce BSDL. When added to the apical reservoir of Transwell-grown Int407 cells, BSDL was shown to first interact with the apical membrane. Further, BSDL forms clusters that are internalized via clathrin-coated pits. Following endocytosis, BSDL is directed to a nocodazole- and colchicin-sensitive multivesicular compartment. Interestingly, this protein transits through the Golgi apparatus, where it was found to colocalize with the KDEL retrieval-receptor. Finally, enzymatically active intact BSDL was released at the basolateral membrane level. This is the first demonstration for an apical-to-basolateral transcytotic pathway of a secreted pancreatic digestive enzyme through polarized intestinal cells.     

Alternative mechanisms for homeostatic regulation of mammalian cell populations

A model for homeostatic regulation in mammalian tissues is analyzed. The model treats resting and active dividing cells, immature and mature non-dividing cells as separate populations. In the model, regulation is accomplished through control of the proportion of newly-formed cells that will become non-dividers. Four possible regulating substances, produced by dividing cells, non-dividing cells, mature non-dividing cells, and newly-formed cells respectively, are considered. Stability theorems are provided. System behavior in each instance depends on the relative values of the rate at which cells divide and the rate at which non-dividers die.     

Assessment of the symmetry of stem-cell mitoses.

A model of Paneth-cell renewal in the small intestinal epithelium is used to estimate the probability that epithelial stem-cell mitoses are symmetric in the sense that they produce two cells of the same type. I found that counts of the number of Paneth cells per crypt (Paneth cells are terminally differentiated cells derived from small intestinal epithelial stem cells) support a model in which most, if not all, stem-cell mitoses are symmetric.     

The physico-chemical mechanism of mediated transport. I. Facilitated diffusion

On the basis of the currently accepted model for the cell membrane structure, a physico-chemical model for mediated transport is developed and solved for the case of polar non-electrolyte migration through the cell membrane. The model considers the interstitial space defined by the transport protein subunits to be the migration pathway for polar solutes. A Langmuir-type adsorption equilibrium is assumed at the interfaces and a multicomponent diffusion mechanism of solute and water is postulated within the migration pathway, where the polar residues of the transport protein represent another component of the system. Membrane selectivity is governed by the adsorption constants, which are shown to affect strongly the kinetics of transport. Isosmotic transport and the volume change of the cell are important features incorporated in the model, which is shown to fulfill the peculiar properties of facilitated diffusion systems. It is concluded that the same type of pathway can be used for the transport of other polar solutes through existing or induced hydrophilic channels, for which a similar approach is suggested.     

Frequency domain impedance measurements of erythrocytes. Constant phase angle impedance characteristics and a phase transition.

We report measurements of the electrical impedance of human erythrocytes in the frequency range from 1 Hz to 10 MHz, and for temperatures from 4 to 40 degrees C. In order to achieve high sensitivity in this frequency range, we embedded the cells in the pores of a filter, which constrains the current to pass through the cells in the pores. Based on the geometry of the cells embedded in the filter a circuit model is proposed for the cell-filter saline system. A constant phase angle (CPA) element, i.e., an impedance of the form Z = A/(j omega)alpha, where A is a constant, j = square root of -1, omega is angular frequency, and 0 less than alpha less than 1 has been used to describe the ac response of the interface between the cell surface and the electrolyte solution, i.e., the electrical double layer. The CPA and other elements of the circuit model are determined by a complex nonlinear least squares (CNLS) fit, which simultaneously fits the real and imaginary parts of the experimental data to the circuit model. The specific membrane capacitance is determined to be 0.901 +/- 0.036 microF/cm2, and the specific cytoplasm conductivity to be 0.413 +/- 0.031 S/m at 26 degrees C. The temperature dependence of the cytoplasm conductivity, membrane capacitance, and CPA element has been obtained. The membrane capacitance increases markedly at approximately 37 degrees C, which suggests a phase transition in the cell membrane.