scholarly journals Integro-differential equations for the self-organisation of liver zones by competitive exclusion of cell-types

1987 ◽  
Vol 29 (2) ◽  
pp. 156-194 ◽  
Author(s):  
L. Bass ◽  
A. J. Bracken ◽  
K. Holmåker ◽  
B. R. F. Jefferies
Keyword(s):  
Differential Equations ◽  
Enzymatic Activity ◽  
Cell Types ◽  
Stationary Solutions ◽  
Stable Set ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Hepatic Sinusoid ◽  
Jump Discontinuities ◽  
Cell Densities

AbstractA model is developed for the seif-organisation of zones of enzymatic activity along a liver capillary (hepatic sinusoid) lined with cells of two types, which contain different enzymes and compete for sites on the wall of the sinusoid. An effectively non-local interaction between the cells arises from local consumption of oxygen from blood flowing throug1 the sinusoid, which gives rise to gradients of oxygen concentration in turn influencing rates of division and of death of the two cell-types. The process is modelled by a pair of coupled non-linear integro-differential equations for the cell-densities as functions of time and position along the sinusoid. Existence of a unique, bounded, non-negative solution of the equations is proved, for prescribed initial values. The equations admit infinitely many stationary solutions, but it is shown that all except one are unstable, for any given set of the model parameters. The remaining solution is shown to be asymptotically stable against a large class of perturbations. For certain ranges of the model parameters, the asymptotically stable stationaxy solution has a zonal structure, with cells of one type located entirely upstream of cells of the other type, and with jump discontinuities in the cell densities at a certain distance along the sinusoid. Such sinusoidal zones can account for zones of enzymatic activity observed in the intact liver. Exceptional cases are found for singular choices of model parameters, such that stationary cell-densities cannot be asymptotically stable individually, but together form an asymptotically stable set. Certain mathematical questions are left open, notably the behaviour of large deviations from stationary solutions, and the global stability of such solutions. Possible generalisations of the model are described.

scholarly journals Characterizing the Tumor Immune Microenvironment with Tyramide-Based Multiplex Immunofluorescence

2020 ◽  
Vol 25 (4) ◽  
pp. 417-432
Author(s):  
Hidetoshi Mori ◽  
Jennifer Bolen ◽  
Louis Schuetter ◽  
Pierre Massion ◽  
Clifford C. Hoyt ◽  
...  
Keyword(s):  
Tumor Microenvironment ◽  
Multispectral Imaging ◽  
Imaging System ◽  
Predictive Biomarkers ◽  
Cell Types ◽  
Immune Microenvironment ◽  
Tumor Immune Microenvironment ◽  
Manual Processing ◽  
Cell Densities ◽  
Immune Profiling

AbstractMultiplex immunofluorescence (mIF) allows simultaneous antibody-based detection of multiple markers with a nuclear counterstain on a single tissue section. Recent studies have demonstrated that mIF is becoming an important tool for immune profiling the tumor microenvironment, further advancing our understanding of the interplay between cancer and the immune system, and identifying predictive biomarkers of response to immunotherapy. Expediting mIF discoveries is leading to improved diagnostic panels, whereas it is important that mIF protocols be standardized to facilitate their transition into clinical use. Manual processing of sections for mIF is time consuming and a potential source of variability across numerous samples. To increase reproducibility and throughput we demonstrate the use of an automated slide stainer for mIF incorporating tyramide signal amplification (TSA). We describe two panels aimed at characterizing the tumor immune microenvironment. Panel 1 included CD3, CD20, CD117, FOXP3, Ki67, pancytokeratins (CK), and DAPI, and Panel 2 included CD3, CD8, CD68, PD-1, PD-L1, CK, and DAPI. Primary antibodies were first tested by standard immunohistochemistry and single-plex IF, then multiplex panels were developed and images were obtained using a Vectra 3.0 multispectral imaging system. Various methods for image analysis (identifying cell types, determining cell densities, characterizing cell-cell associations) are outlined. These mIF protocols will be invaluable tools for immune profiling the tumor microenvironment.

scholarly journals Universal intracellular biomolecule delivery with precise dosage control

2018 ◽  
Vol 4 (10) ◽  
pp. eaat8131 ◽  
Author(s):  
Y. Cao ◽  
H. Chen ◽  
R. Qiu ◽  
M. Hanna ◽  
E. Ma ◽  
...  
Keyword(s):  
Cell Membrane ◽  
Electric Fields ◽  
Low Voltage ◽  
Intracellular Delivery ◽  
Cell Types ◽  
Controlled Delivery ◽  
Biological Research ◽  
Biological Applications ◽  
Primary Cells ◽  
Cell Densities

Intracellular delivery of mRNA, DNA, and other large macromolecules into cells plays an essential role in an array of biological research and clinical therapies. However, current methods yield a wide variation in the amount of material delivered, as well as limitations on the cell types and cargoes possible. Here, we demonstrate quantitatively controlled delivery into a range of primary cells and cell lines with a tight dosage distribution using a nanostraw-electroporation system (NES). In NES, cells are cultured onto track-etched membranes with protruding nanostraws that connect to the fluidic environment beneath the membrane. The tight cell-nanostraw interface focuses applied electric fields to the cell membrane, enabling low-voltage and nondamaging local poration of the cell membrane. Concurrently, the field electrophoretically injects biomolecular cargoes through the nanostraws and into the cell at the same location. We show that the amount of material delivered is precisely controlled by the applied voltage, delivery duration, and reagent concentration. NES is highly effective even for primary cell types or different cell densities, is largely cargo agnostic, and can simultaneously deliver specific ratios of different molecules. Using a simple cell culture well format, the NES delivers into >100,000 cells within 20 s with >95% cell viability, enabling facile, dosage-controlled intracellular delivery for a wide variety of biological applications.

scholarly journals TOPOLOGICAL EQUIVALENCE FOR DISCONTINUOUS RANDOM DYNAMICAL SYSTEMS AND APPLICATIONS

2013 ◽  
Vol 14 (01) ◽  
pp. 1350007 ◽  
Author(s):  
HUIJIE QIAO ◽  
JINQIAO DUAN
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Stochastic Differential Equations ◽  
Lévy Processes ◽  
Levy Processes ◽  
Topological Equivalence ◽  
Random Differential Equation ◽  
Jump Discontinuities ◽  
Non Gaussian

After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differential equations have countable jump discontinuities in time. Topological equivalence (or conjugacy) for such an Itô stochastic differential equation and its transformed random differential equation is established. Consequently, a stochastic Hartman–Grobman theorem is proved for the linearization of the Itô stochastic differential equation. Furthermore, for Marcus stochastic differential equations, this topological equivalence is used to prove the existence of global random attractors.

Robustness Analysis of a Simple and Augmented Proportional Plus Derivative Controller in Trajectory Following Robots Using the Floquet Theory

2018 ◽  
Vol 13 (7) ◽  
Author(s):  
B. Sandeep Reddy ◽  
Ashitava Ghosal
Keyword(s):  
Numerical Simulation ◽  
Degrees Of Freedom ◽  
Floquet Theory ◽  
Robustness Analysis ◽  
Periodic Trajectory ◽  
Model Parameters ◽  
Asymptotically Stable ◽  
Pd Controller ◽  
Simulation Results ◽  
Trajectory Following

This paper deals with the issue of robustness in control of robots using the proportional plus derivative (PD) controller and the augmented PD controller. In the literature, a variety of PD and model-based controllers for multilink serial manipulator have been claimed to be asymptotically stable for trajectory tracking, in the sense of Lyapunov, as long as the controller gains are positive. In this paper, we first establish that for simple PD controllers, the criteria of positive controller gains are insufficient to establish asymptotic stability, and second that for the augmented PD controller the criteria of positive controller gains are valid only when there is no uncertainty in the model parameters. We show both these results for a simple planar two-degrees-of-freedom (2DOFs) robot with two rotary (R) joints, following a desired periodic trajectory, using the Floquet theory. We provide numerical simulation results which conclusively demonstrate the same.

A simple microcomputer-based system for real-time analysis of cell behaviour

1987 ◽  
Vol 87 (1) ◽  
pp. 171-182
Author(s):  
J.A. Dow ◽  
J.M. Lackie ◽  
K.V. Crocket
Keyword(s):  
Real Time ◽  
Search Algorithm ◽  
Cell Types ◽  
Real Time Analysis ◽  
Lighting Conditions ◽  
Previous Frame ◽  
Real Time Tracking ◽  
Cell Densities ◽  
Different Cell Types

An image analysis package based on a BBC microcomputer has been developed, which can simultaneously track many moving cells in vitro. Cells (rabbit neutrophil leucocytes, BHK C13 fibroblasts, or PC12 phaeochromocytoma cells) are viewed under phase optics with a monochrome TV camera, and the signal digitized. Successive frames are acquired by the computer as a 640 X 256 pixel array. Under controlled lighting conditions, cells can readily be isolated from the background by binary filtering. In real-time tracking, the positions of a given cell in successive frames are obtained by searching the area around the cell's centroid in the previous frame. A simple box-search algorithm is described, which proves highly successful at low cell densities. The resilience of different search algorithms to various exceptional conditions (such as collisions) is discussed. The success of this system in real-time tracking is largely dependent upon the leisurely speed of movement of cells, and on obtaining a clean, high quality optical image to analyse. The limitations of this technique for different cell types, and the possible configurations of more sophisticated hardware, are outlined. This system provides a versatile and automated solution to the problem of studying the movement of tissue cells.

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