Metabolic dynamics in the human red cell. Part II--Interactions with the environment

The maintenance of human red cell volume under multitude of trying physiological conditions is a self regulated dynamic process. Theoretical and experimental studies on red cell osmotic states have been primarily focussed on three different interdependent areas: the permeative properties of the red cell membrane, the kinetic studies of transmembrane fluxes of various ionic and nonionic chemical constituents of the red cell and plasma, and the ideal and non-ideal thermodynamic formulation of the osmotic states. The primary objective of this work is to provide a general model that converges the above mentioned components of the red cell and its environment under one umbrella. Such a model facilitates the simultaneous interpretation and prediction of quantitative changes in the red cell volume, pH, Donnan ratios, osmotic effects, plasma volume, transmembrane fluxes, and permeable and impermeable solute concentration.     

Kinetic Studies of a Doubly Bound Red Cell Antigen-Antibody System

The Polybrene method for detection of red cell antibodies which utilizes continuous flow equipment was modified so that kinetic studies could be performed on red cell antibodies doubly bound between adjacent red cells. In the anti-Rh_o-Rh_o erythrocyte system, deaggregation by temperature was studied over an antibody concentration range of from approximately 1 to 500 antibody molecules per erythrocyte, a residence time range of approximately eightfold, and a temperature range of from 10 to 55°C. The rate of dissociation of antigen-antibody complex, as determined from deaggregation of antibody-dependent red cell aggregates, was found to be of apparent zero order. The apparent activation energy for the antigen-antibody reaction under the experimental conditions was determined and found to be higher than would be expected for singly bound antigen-antibody systems. Possible explanations are considered for these findings in terms of an antigen-antibody bond-breaking model.     

Multi-level Modeling of Light-Induced Stomatal Opening Offers New Insights into Its Regulation by Drought

Plant guard cells gate CO₂ uptake and transpirational water loss through stomatal pores. As a result of decades of experimental investigation, there is an abundance of information on the involvement of specific proteins and secondary messengers in the regulation of stomatal movements and on the pairwise relationships between guard cell components. We constructed a multi-level dynamic model of guard cell signal transduction during light-induced stomatal opening and of the effect of the plant hormone abscisic acid (ABA) on this process. The model integrates into a coherent network the direct and indirect biological evidence regarding the regulation of seventy components implicated in stomatal opening. Analysis of this signal transduction network identified robust cross-talk between blue light and ABA, in which [Ca²⁺]_c plays a key role, and indicated an absence of cross-talk between red light and ABA. The dynamic model captured more than 10³¹ distinct states for the system and yielded outcomes that were in qualitative agreement with a wide variety of previous experimental results. We obtained novel model predictions by simulating single component knockout phenotypes. We found that under white light or blue light, over 60%, and under red light, over 90% of all simulated knockouts had similar opening responses as wild type, showing that the system is robust against single node loss. The model revealed an open question concerning the effect of ABA on red light-induced stomatal opening. We experimentally showed that ABA is able to inhibit red light-induced stomatal opening, and our model offers possible hypotheses for the underlying mechanism, which point to potential future experiments. Our modelling methodology combines simplicity and flexibility with dynamic richness, making it well suited for a wide class of biological regulatory systems.     

Determination of Urea Permeability in Red Cells by Minimum Method : A test of the phenomenological equations

A new method has been developed for measuring the permeability coefficient, ω, of small nonelectrolytes. The method depends upon a mathematical analysis of the time course of cell volume changes in the neighborhood of the minimum volume following addition of a permeating solute to an isosmolal buffer. Coefficients determined by the minimum volume method agree with those obtained using radioactive tracers. ω for urea in human red cells was found to decrease as the volume flow, J_v, into the cell increased. Such behavior is entirely unexpected for a single uniform rate-limiting barrier on the basis of the linear phenomenological equations derived from irreversible thermodynamics. However, the present findings are consonant with a complex membrane system consisting of a tight barrier on the outer face of the human red cell membrane and a somewhat less restrictive barrier behind it closer to the inner membrane face. A theoretical analysis of such a series model has been made which makes predictions consistent with the experimental findings.     

Action of antimicrobial peptides: two-state model

The argument and experimental evidence are presented for a two-state model that explains the action of both helical and beta-sheet antimicrobial peptides after they bind to the plasma membranes of cells. Each peptide has two distinct physical states of binding to lipid bilayers. At low peptide-to-lipid ratios (P/L), the peptide tends to adsorb in the lipid headgroup region in a functionally inactive state. At a P/L above a threshold value P/L, the peptide forms a multiple-pore state that is lethal to a cell. The susceptibility of a cell to an antimicrobial peptide depends on the value of P/L that is determined by the lipid composition of the cell membrane. This model provides plausible explanations for the experimental findings that the susceptibility of different bacteria to a peptide is not directly correlated to its binding affinity, different peptides preferentially kill different pathogens, and peptides exhibit varying levels of lytic activity against different eukaryotic cells.     

Minimum energy analysis of membrane deformation applied to pipet aspiration and surface adhesion of red blood cells.

An experimental procedure is demonstrated which can be used to determine the interfacial free energy density for red cell membrane adhesion and membrane elastic properties. The experiment involves micropipet aspiration of a flaccid red blood cell and manipulation of the cell proximal to a surface where adhesion occurs. A minimum free energy method is developed to model the equilibrium contour of unsupported membrane regions and to evaluate the partial derivatives of the total free energy, which correspond to the micropipet suction force and the interfacial free energy density of adhesion. It is shown that the bending elasticity of the red cell membrane does not contribute significantly to the pressure required to aspirate a flaccid red cell. Based on experimental evidence, the upper bound for the bending or curvature elastic modulus of the red cell membranes is 10-12 ergs (dyn-cm). Analysis of the adhesion experiment shows that interfacial free energy densities for red cell adhesion can be measured from a lower limit of 10-4 ergs/cm2 to an upper limit established by the membrane tension for lysis of 5-10 ergs/cm2.     

Species-related variations in tissue antioxidant status--II. Differences in susceptibility to oxidative challenge.

1. In order to investigate possible species-related variations in antioxidant capacity, the susceptibility of red cells from various species (e.g. rat, rabbit, pig and quail) to depletion of glutathione (GSH) and formation of malondialdehyde (MDA), an indirect measure of lipid peroxidation, following in vitro oxidative challenge with t-butylhydroperoxide (tBHP) has been examined. 2. Marked differences in sensitivity were found, although the relative order of susceptibilities varied depending on the index of oxidation used. 3. For example, pig erythrocytes showed the highest sensitivity to depletion of GSH but the greatest resistance to tBHP-induced MDA formation. 4. Red cell susceptibility to oxidative stress under the experimental conditions used was not predictable from basal levels of GSH or from the activities of antioxidant enzymes, suggesting a prominent role of non-enzymatic antioxidants. 5. Species-dependent differences in antioxidant capacity were also found to extend to myocardial tissue homogenates and some degree of parallelism was noted with tBHP-induced MDA formation in red cells of the same species. 6. Thus, the relative resistance of both tissues from pig contrasted with the high susceptibility of red cells and myocardium from rat and quail. 7. This parallelism allows the suggestion that the functional consequences of antioxidant interventions might be discernible from measurements involving red cells. 8. Our findings may have potentially important implications in the interpretation and comparison of data obtained with experimental models of disease states in which oxidative processes are implicated when differences in species are involved.     

Wall shear stress in backward-facing step flow of a red blood cell suspension.

An experimental investigation of the wall shear stress distribution downstream of a backward-facing step is carried out. The wall shear stress distribution was determined by measuring the deformation of a gel layer, attached to the wall downstream of the step. Speckle pattern interferometry was applied to measure the deformation of the gel layer. The measured deformation, combined with the properties of the gel layer, served as an input for a finite element solid mechanics computation to determine the stress distribution in the gel layer. The wall shear stress, required to generate the measured deformation of the gel layer, was determined from these computations. A Newtonian buffer solution and a non-Newtonian red blood cell suspension were used as measuring fluids. The deformation of the gel layer was determined for a Newtonian buffer solution to evaluate the method and to obtain the properties of the gel layer. Subsequently, the wall shear stress distribution for the non-Newtonian red blood cell suspension was determined for three different flow rates. The inelastic non-Newtonian Carreau-Yasuda model served as constitutive model for the red blood cell suspension. Using this model, the velocity and wall shear stress distribution were computed by means of a finite element fluid mechanics computation. From the comparison between the numerical and the experimental results, it can be concluded that wall shear stresses, induced by the red blood cell suspension, can be modeled accurately by employing a Carreau-Yasuda model.     

The Dynamics of Stress p53-Mdm2 Network Regulated by p300 and HDAC1

We construct a stress p53-Mdm2-p300-HDAC1 regulatory network that is activated and stabilised by two regulatory proteins, p300 and HDAC1. Different activation levels of observed due to these regulators during stress condition have been investigated using a deterministic as well as a stochastic approach to understand how the cell responds during stress conditions. We found that these regulators help in adjusting p53 to different conditions as identified by various oscillatory states, namely fixed point oscillations, damped oscillations and sustain oscillations. On assessing the impact of p300 on p53-Mdm2 network we identified three states: first stabilised or normal condition where the impact of p300 is negligible, second an interim region where p53 is activated due to interaction between p53 and p300, and finally the third regime where excess of p300 leads to cell stress condition. Similarly evaluation of HDAC1 on our model led to identification of the above three distinct states. Also we observe that noise in stochastic cellular system helps to reach each oscillatory state quicker than those in deterministic case. The constructed model validated different experimental findings qualitatively.     

An expanded two-state allosteric model for interactions of human hemoglobin A with nonsaturating concentrations of 2,3-diphosphoglycerate

Oxygen binding curves (OEC) for red cell suspensions have a biphasic shape and reduced n50 values when the concentration of 2,3-diphosphoglycerate (DPG) is lowered by aging or experimental procedures. The mechanism for the abnormal shape of the OEC has been related to variations in the activity of free DPG. DPG binds to tetrameric Hb at a single site, and in red cells its normal concentration is equivalent to that of tetrameric Hb. This equivalence renders the oxygen affinity of Hb and the shape of the OEC very sensitive to small changes in the activity of DPG. The OEC for stripped Hb solutions in the presence of nonsaturating concentrations of DPG also exhibit a biphasic shape but with much larger changes in the n values than observed for red cells. Upon addition of chloride, a known competitor of DPG binding to Hb, the shape of the OEC becomes similar to that of red cell suspensions with the same DPG/Hb ratio. Studies on Hb solutions in the presence of varying concentrations of DPG, but without chloride, have revealed that the cofactor shifts the entire OEC to the right, including both its upper and lower asymptotes. This finding indicates that DPG lowers the intrinsic oxygen affinity for both the T and R states. Theoretical considerations leading to a successful modeling of OEC obtained under varying conditions of DPG and chloride require an expanded two-state allosteric model in which allowance is made for DPG-dependent variations in the dissociation constants of oxygen for both the T and R conformations.     

Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study

This study presents a method for the reduction of biophysically-based kinetic models for the active transport of ions. A lumping scheme is presented which exploits the differences in timescales associated with fast and slow transitions between model states, while maintaining the thermodynamic properties of the model. The goal of this approach is to contribute to modelling of the effects of disturbances to metabolism, associated with ischaemic heart disease, on cardiac cell function.

The approach is illustrated for the sodium-potassium pump in the myocyte. The lumping scheme is applied to produce a 4-state representation from the detailed 15-state model of Läuger and Apell, Eur. Biophys. J. 13 (1986) 309, for which the principles of free energy transduction are used to link the free energy released from ATP hydrolysis (ΔG_ATP) to the transition rates between states of the model. An iterative minimisation algorithm is implemented to determine the transition rate parameters based on the model fit to experimental data. Finally, the relationship between ΔG_ATP and pump cycling direction is investigated and compared with recent experimental findings.     

Measurement of biophysical properties of red blood cells by resistive pulse spectroscopy: volume, shape, surface area, and deformability

This paper presents a simple, new approach to the determination of size, shape, surface area, and deformability information for cells, notably red blood cells. The results are obtained by combining experimental measurements from resistive pulse spectroscopy (an extension of electronic cell-sizing methodology) with theoretical calculations for model cell systems. Assuming constancy of surface area and approximating red cell shapes by both prolate and oblate ellipsoids of revolution, values are determined for cell shape factor and volume under a variety of conditions. For red blood cells under low-stress conditions, shape factor, volume, and surface area results are found to be consistent with those available from the literature, when the oblate model is used. The applicability of this approach for determination of red cell properties under altered conditions is demonstrated by results for cell volume, at varying osmotic pressure and mechanical shear (tensile) stress. By quantitating the change in cell shape with stress, a new numerical scale for measuring cell deformability is also obtained, and data are presented on its variation for red cells at different osmolalities, over the range of 140 to 500 mOsm.     

Computation of the average shear-induced deformation of red blood cells as a function of osmolality

A model was developed for computing the average deformation of red cells as a function of suspending medium osmolality. It assumes a population of red cells characterized by a single value for surface area and for isotonic volume, but having a Gaussian distribution in mean intracellular hemoglobin concentration (MCHC). The ability of cells of a given hemoglobin concentration to deform is assumed to be limited by either the amount of redundant surface area available or the intracellular viscosity, determined by the intracellular hemoglobin concentration. The surface area limitation is calculated by finding the dimensions of a prolate ellipsoid having the volume and surface area of the red cell. The viscosity limitation is incorporated in two ways. First, the ratio of intracellular to extracellular viscosity must lie below a certain threshold to permit deformation, and second, its magnitude determines the extent of cell elongation. This model gave a reasonable fit to experimental data for a threshold viscosity ratio close to 1. Extension to cell populations for which either mean cell hemoglobin concentration or surface area had been modified also provided a close reproduction of the experimental curves.     

Spectral dynamics of individual bacterial light-harvesting complexes: alternative disorder model

The bacterial (Rhodopseudomonas acidophila) photosynthetic peripheral light-harvesting complex of type 2 (LH2) exhibits rich fluorescence spectral dynamics at room temperature. The fluorescence spectrum of individual LH2 shifts either to the blue or to the red during the experimental observation time of a few minutes. These spectral changes are often reversible and occur between levels of a distinctly different peak wavelength. Furthermore, they are accompanied by a change of the spectral line shape. To interpret the dynamics of spectral changes, an energetic disorder model associated with easily explainable structural changes of the protein is proposed. This model assumes that each pigment in the tightly coupled ring of bacteriochlorophylls can be in two states of electronic transition energy due to the protein-pigment interaction. The transition between these structural, and hence spectroscopic, states occurs through the thermally induced conformational potential energy barrier crossing. Although simplified, the model allows us to reproduce the bulk fluorescence spectrum, the distribution of the single-molecule spectral peak wavelength and its changes, and the statistics of the duration of the spectral states. It also provides an intuitively clear picture of possible protein dynamics in LH2. At the same time, it requires additional sophistication since it essentially does not reproduce the red occurrences of single LH2 spectra.     

Factors defining the rate of oxygen uptake by the red blood cell

Using numerical methods, the initial rates of oxygen uptake by the red blood cell have been computed. The methods accommodate both a water layer and membrane which may act as diffusive impedance to gas influx. The differential solubilities of the gas in these two layers have also been incorporated in the methods. The presence of a 0.50–0.65 μm deoxygenated water layer has been calculated to simulate the experimental results by Roughton (1959). Experimental studies of CO and NO uptake by the red cell could also be simulated. Although a membrane-only model with given parameters can also account for the observed rates of oxygenation of the red cell (Weingardenet al., submitted for publication), the additional incorporation of differential solubilities of oxygen in the different layers of the RBC yields results that indicate a three layer model to be more plausible. Using a thin layer-red cell oxygenation system, the rates of oxygenation were determined for red cells surrounded by a 4.2 μm deoxygenated water layer. The rates were found to compare favorably to the results of the theoretical model.     

The binding of hemoglobin to membranes of normal and sickle erythrocytes.

The binding of hemoglobins A, S, and A2 to red cell membranes prepared by hypotonic lysis from normal blood and blood from persons with sickle cell anemia was quantified under a variety of conditions using hemoglobin labelled by alkylation with 14C-labelled Nitrogen Mustard. Membrane morphology was examined by electron microscopy. Normal membranes were found capable of binding native hemoglobin A and hemoglobin S in similar amounts when incubated at low hemoglobin: membrane ratios, but at high ratios hemoglobin saturation levels of the membranes increased progressively for hemoglobin A, hemoglobin S and hemoglobin A2, respectively, in order of increasing electropositivity. Binding was unaffected by variations in temperature (4-22 degrees C) and altered little by the presence of sulfhydryl reagents, but was inhibited at pH levels above 7.35; disrupted at high ionic strength; and dependent on the ionic composition of the media. These findings suggest that electrostatic, but not hydrophobic or sulfhydryl bonds are important in membrane binding of the hemoglobin under the conditions studied. An increased retention of hemoglobin in preparations of membranes from red cells of patients with sickle cell anemia (homozygote S) was attributable to the dense fraction of homozygote S red cells rich in irreversibly sickled cells, and the latter membranes had a smaller residual binding capacity for new hemoglobin. This suggests that in homozygote S cells which have become irreversibly sickled cells in vivo, there are membrane changes which involve alteration and/or blockade of hemoglobin binding sites. These findings support the notion that hemoglobin participates in the dynamic structure of the red cell membrane in a manner which differs in normal and pathological states.     

Modeling hematopoietic system response caused by chronic exposure to ionizing radiation

A new model of the hematopoietic system response in humans chronically exposed to ionizing radiation describes the dynamics of the hematopoietic stem cell compartment as well as the dynamics of each of the four blood cell types (lymphocytes, neutrophiles, erythrocytes, and platelets). The required model parameters were estimated based on available results of human and experimental animal studies. They include the steady-state number of hematopoietic stem cells and peripheral blood cell lines in an unexposed organism, amplification parameters for each blood line, parameters describing proliferation and apoptosis, parameters of feedback functions regulating the steady-state numbers, and characteristics of radiosensitivity related to cell death and non-lethal cell damage. The model predictions were tested using data on hematological measurements (e.g., blood counts) performed in 1950–1956 in the Techa River residents chronically exposed to ionizing radiation since 1949. The suggested model of hematopoiesis is capable of describing experimental findings in the Techa River Cohort, including: (1) slopes of the dose–effect curves reflecting the inhibition of hematopoiesis due to chronic ionizing radiation, (2) delay in effect of chronic exposure and accumulated character of the effect, and (3) dose-rate patterns for different cytopenic states (e.g., leukopenia, thrombocytopenia).     

Transient relative motion of two cells in a channel flow

The hydrodynamic interaction of a red blood cell and a white blood cell in microvessels is studied, by use of a two-dimensional numerical model. The red blood cell, modeled as a small rigid circular cylinder, and the white blood cell, modeled as a larger rigid circular cylinder, are immersed in an incompressible Newtonian fluid in a two-dimensional channel. It is assumed that no external force or moment acts on the model cells, and the effect of inertia forces on the motion of the fluid and the cells is neglected. The velocity field of the suspending fluid and the instantaneous velocities of the two model cells are computed by the finite element method. Using the translational velocities of the model cells obtained, the trajectories of their relative motion are determined, for various initial positions. It is shown that the cells may or may not pass each other or separate, depending on the initial positions. The present results compare well to the experimental results.     

An on-lattice agent-based Monte Carlo model simulating the growth kinetics of multicellular tumor spheroids

PurposeTo develop an on-lattice agent-based model describing the growth of multicellular tumor spheroids using simple Monte Carlo tools.MethodsCells are situated on the vertices of a cubic grid. Different cell states (proliferative, hypoxic or dead) and cell evolution rules, driven by 10 parameters, and the effects of the culture medium are included. About twenty spheroids of MCF-7 human breast cancer were cultivated and the experimental data were used for tuning the model parameters.ResultsSimulated spheroids showed adequate sizes of the necrotic nuclei and of the hypoxic and proliferative cell phases as a function of the growth time, mimicking the overall characteristics of the experimental spheroids. The relation between the radii of the necrotic nucleus and the whole spheroid obtained in the simulations was similar to the experimental one and the number of cells, as a function of the spheroid volume, was well reproduced. The statistical variability of the Monte Carlo model described the whole volume range observed for the experimental spheroids. Assuming that the model parameters vary within Gaussian distributions it was obtained a sample of spheroids that reproduced much better the experimental findings.ConclusionsThe model developed allows describing the growth of in vitro multicellular spheroids and the experimental variability can be well reproduced. Its flexibility permits to vary both the agents involved and the rules that govern the spheroid growth. More general situations, such as, e. g., tumor vascularization, radiotherapy effects on solid tumors, or the validity of the tumor growth mathematical models can be studied.     

K-Na transport: the Brewer model replaces the active transport model

In the 1940's several experimental observations were made regarding the K+ and Na+ content of chilled and restored red blood cells. As a consequence, the concept of active transport was developed. Brewer, a physicist, developed a model for membrane transport based on the electrical properties of double bonds in the ground and excited states. Of particular importance is the membrane double bond P = O. This model was largely formulated from isotope concentration studies using mass spectroscopy, photospectrometry and the nature of malignant cells. In this study, it is shown that the Brewer model completely explains the experimental results which led to the concept of active transport. In addition, it also explains the results of some adjunct experiments.