Modeling the Effect of Red Blood Cells Deformability on Blood Flow Conditions in Human Carotid Artery Bifurcation.

The purpose of this work is to predict the effect of impaired red blood cells (RBCs) deformability on blood flow conditions in human carotid artery bifurcation. First, a blood viscosity model is developed that predicts the steady-state blood viscosity as a function of shear rate, plasma viscosity, and mechanical (and geometrical) properties of RBC's. Viscosity model is developed by modifying the well-known Krieger and Dougherty equation for monodisperse suspensions by using the dimensional analysis approach. With the approach, we manage to account for the microscopic properties of RBC's, such as their deformability, in the macroscopic behavior of blood via blood viscosity. In the second part of the paper, the deduced viscosity model is used to numerically predict blood flow conditions in human carotid artery bifurcation. Simulations are performed for different values of RBC's deformability and analyzed by investigating parameters, such as the temporal mean wall shear stress (WSS), oscillatory shear index (OSI), and mean temporal gradient of WSS. The analyses show that the decrease of RBC's deformability decrease the regions of low WSS (i.e., sites known to be prevalent at atherosclerosis-prone regions); increase, in average, the value of WSS along the artery; and decrease the areas of high OSI. These observations provide an insight into the influence of blood's microscopic properties, such as the deformability of RBC's, on hemodynamics in larger arteries and their influence on parameters that are known to play a role in the initiation and progression of atherosclerosis.

Contribution of Rho kinase to the early phase of the calcium-contraction coupling in airway smooth muscle.

We investigated theoretically and experimentally the role of Rho kinase (RhoK) in Ca(2+)-contraction coupling in rat airways. Isometric contraction was measured on tracheal, extrapulmonary and intrapulmonary bronchial rings. Intracellular [Ca(2+)] was recorded in freshly isolated tracheal myocytes. Stimulation by carbachol (0.3 and 10 µm) and 50 mm external KCl induced a short-time, Hill-shaped contraction obtained within 90 s, followed by a sustained or an additional delayed contraction. Responses of [Ca(2+)](i) to acetylcholine consisted in a fast peak followed by a plateau and, in 42% of the cells, superimposed Ca(2+) oscillations. The RhoK inhibitor Y27632 (10 µm) did not alter the [Ca(2+)](i) response. Whatever the agonist, Y27632 did not modify the basal tension but decreased the amplitude of the short-duration response, without altering the additional delayed contraction. The Myosin Light Chain Phosphatase (MLCP) inhibitor calyculin A increased the basal tension and abolished the effect of RhoK. KN93 (Ca(2+)-calmodulin-dependent protein kinase II inhibitor) and DIDS (inhibitor of Ca(2+)-activated Cl(-) channels) had no influence on the RhoK effect. We built a theoretical model of Ca(2+)-dependent active/inactive RhoK ratio and subsequent RhoK-dependent MLCP inactivation, which was further coupled with a four-state model of the contractile apparatus and Ca(2+)-dependent MLCK activation. The model explains the time course of the short-duration contraction and the role of RhoK by Ca(2+)-dependent activation of MLCK and RhoK, which inactivates MLCP. Oscillatory and non-oscillatory [Ca(2+)](i) responses result in a non-oscillatory contraction, the amplitude of which is encoded by the plateau value and oscillation frequency. In conclusion, Ca(2+)-dependent but CaMK II-independent RhoK activation contributes to the early phase of the contractile response via MLCP inhibition.

MLC-kinase/phosphatase control of Ca2+ signal transduction in airway smooth muscles.

In airway smooth muscles, kinase/phosphatase-dependent phosphorylation and dephosphorylation of the myosin light chain (MLC) have been revealed by many authors as important steps in calcium (Ca(2+)) signalling pathway from the variation of Ca(2+) concentration in cytosol to the force development. Here, a theoretical analysis of the control action of MLC-kinase (MLCK) and MLC-phosphatase (MLCP) in Ca(2+) signalling is presented and related to the general control principles of these enzymes, which were previously studied by Reinhart Heinrich and his co-workers. The kinetic scheme of the mathematical model considers interactions among Ca(2+), calmodulin (CaM) and MLCK and the well-known 4-state actomyosin latch bridge model, whereby a link between them is accomplished by the conservation relation of all species of MLCK. The mathematical model predicts the magnitude and velocity of isometric force in smooth muscles upon transient biphasic Ca(2+) signal. The properties of signal transduction in the system such as the signalling time, signal duration and signal amplitude, which are reflected in the properties of force developed, are studied by the principles of the metabolic control theory. The analysis of our model predictions confirms as shown by Reinhart Heinrich and his co-workers that MLCK controls the amplitude of signal more than its duration, whereas MLCP controls both. Finally, the simulations of elevated total content of MLCK, a typical feature of bronchial muscles of asthmatic subjects and spontaneously hypertensive rats as well as potentiation of MLCP catalytic activity, are carried out and are discussed in view of an increase in the force magnitude.

Energy conservation and maximal entropy production in enzyme reactions.

A procedure for maximization of the density of entropy production in a single stationary two-step enzyme reaction is developed. Under the constraints of mass conservation, fixed equilibrium constant of a reaction and fixed products of forward and backward enzyme rate constants the existence of maximum in the density of entropy production is demonstrated. In the state with maximal density of entropy production the optimal enzyme rate constants, the stationary concentrations of the substrate and the product, the stationary product yield as well as the stationary reaction flux are calculated. The test, whether these calculated values of the reaction parameters are consistent with their corresponding measured values, is performed for the enzyme Glucose Isomerase. It is found that calculated and measured rate constants agree within an order of magnitude, whereas the calculated reaction flux and the product yield differ from their corresponding measured values for less than 20 % and 5 %, respectively. This indicates that the enzyme Glucose Isomerase, considered in a non-equilibrium stationary state, as found in experiments using the continuous stirred tank reactors, possibly operates close to the state with the maximum in the density of entropy production.

Theoretical and experimental investigation of calcium-contraction coupling in airway smooth muscle.

We investigated theoretically and experimentally the Ca2+-contraction coupling in rat tracheal smooth muscle. [Ca2+]i, isometric contraction and myosin light chain (MLC) phosphorylation were measured in response to 1 mM carbachol. Theoretical modeling consisted in coupling a model of Ca2+-dependent MLC kinase (MLCK) activation with a four-state model of smooth muscle contractile apparatus. Stimulation resulted in a short-time contraction obtained within 1 min, followed by a long-time contraction up to the maximal force obtained in 30 min. ML-7 and Wortmannin (MLCK inhibitors) abolished the contraction. Chelerythrine (PKC inhibitor) did not change the short-time, but reduced the long-time contraction. [Ca2+]i responses of isolated myocytes recorded during the first 90 s consisted in a fast peak, followed by a plateau phase and, in 28% of the cells, superimposed Ca2+ oscillations. MLC phosphorylation was maximal at 5 s and then decreased, whereas isometric contraction followed a Hill-shaped curve. The model properly predicts the time course of MLC phosphorylation and force of the short-time response. With oscillating Ca2+ signal, the predicted force does not oscillate. According to the model, the amplitude of the plateau and the frequency of oscillations encode for the amplitude of force, whereas the peak encodes for force velocity. The long-time phase of the contraction, associated with a second increase in MLC phosphorylation, may be explained, at least partially, by MLC phosphatase (MLCP) inhibition, possibly via PKC inhibition.

Theoretical model of the interactions between Ca2+, calmodulin and myosin light chain kinase.

Active Ca2+/calmodulin (CaM)-dependent myosin light chain kinase (MLCK) plays an important role in the process of MLC phosphorylation and consecutive smooth muscle contraction. Here, we propose a mathematical model of a detailed kinetic scheme describing interactions among Ca2+, CaM and MLCK and taking into account eight different aggregates. The main model result is the prediction of the Ca2+ dependent active form of MLCK, which is in the model taken as proportional to the concentration of Ca4CaM.MLCK complex. Wegscheider's condition is additionally applied as a constraint enabling the prediction of some parameter values that have not yet been obtained by experiments.

Dynamic model of eicosanoid production with special reference to non-steroidal anti-inflammatory drug-triggered hypersensitivity.

The authors developed a mathematical model of arachidonic acid (AA) degradation to prostaglandins (PGs) and leukotrienes (LTs), which are implicated in the processes of inflammation and hypersensitivity to non-steroidal anti-inflammatory drugs (NSAIDs). The model focuses on two PGs (PGE2 and PGD2) and one LT (LTC4), their % increases and their ratios. Results are compared with experimental studies obtained from non-asthmatics (NAs), and asthmatics tolerant (ATA) or intolerant (AIA) to aspirin. Simulations are carried out for predefined model populations NA, ATA and three AIA, based on the differences of two enzymes, PG E synthase and/or LTC4-synthase in two states, that is, no-inflammation and inflammation. Their model reveals that the model population with concomitant malfunctions in both enzymes is the most sensitive to NSAIDs, since the duration and the capacity for bronchoconstriction risk are highest after simulated oral dosing of indomethacin. Furthermore, inflammation prolongs the duration of the bronchoconstriction risk in all AIA model populations, and the sensitivity analysis reveals multiple possible scenarios leading to hypersensitivity, especially if inflammatory processes affect the expression of multiple enzymes of the AA metabolic pathway. Their model estimates the expected fold-changes in enzyme activities and gives valuable information for further targeted transcriptomic/proteomic and metabolomic studies.

Poisson-Helmholtz-Boltzmann model of the electric double layer: analysis of monovalent ionic mixtures.

In the classical mean-field description of the electric double layer, known as the Poisson-Boltzmann model, ions interact exclusively through their Coulomb potential. Ion specificity can arise through solvent-mediated, nonelectrostatic interactions between ions. We employ the Yukawa pair potential to model the presence of nonelectrostatic interactions. The combination of Yukawa and Coulomb potential on the mean-field level leads to the Poisson-Helmholtz-Boltzmann model, which employs two auxiliary potentials: one electrostatic and the other nonelectrostatic. In the present work we apply the Poisson-Helmholtz-Boltzmann model to ionic mixtures, consisting of monovalent cations and anions that exhibit different Yukawa interaction strengths. As a specific example we consider a single charged surface in contact with a symmetric monovalent electrolyte. From the minimization of the mean-field free energy we derive the Poisson-Boltzmann and Helmholtz-Boltzmann equations. These nonlinear equations can be solved analytically in the weak perturbation limit. This together with numerical solutions in the nonlinear regime suggests an intricate interplay between electrostatic and nonelectrostatic interactions. The structure and free energy of the electric double layer depends sensitively on the Yukawa interaction strengths between the different ion types and on the nonelectrostatic interactions of the mobile ions with the surface.

Enzyme kinetics and the maximum entropy production principle.

A general proof is derived that entropy production can be maximized with respect to rate constants in any enzymatic transition. This result is used to test the assumption that biological evolution of enzyme is accompanied with an increase of entropy production in its internal transitions and that such increase can serve to quantify the progress of enzyme evolution. The state of maximum entropy production would correspond to fully evolved enzyme. As an example the internal transition ES↔EP in a generalized reversible Michaelis-Menten three state scheme is analyzed. A good agreement is found among experimentally determined values of the forward rate constant in internal transitions ES→EP for three types of ß-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that ß-Lactamase enzymes are nearly fully evolved. The optimization of rate constants as the consequence of basic physical principle, which is the subject of this paper, is a completely different concept from a) net metabolic flux maximization or b) entropy production minimization (in the static head state), both also proposed to be tightly connected to biological evolution.

Bacterial chemotaxis and entropy production.

Entropy production is calculated for bacterial chemotaxis in the case of a migrating band of bacteria in a capillary tube. It is found that the speed of the migrating band is a decreasing function of the starting concentration of the metabolizable attractant. The experimentally found dependence of speed on the starting concentration of galactose, glucose and oxygen is fitted with power-law functions. It is found that the corresponding exponents lie within the theoretically predicted interval. The effect of the reproduction of bacteria on band speed is considered, too. The acceleration of the band is predicted due to the reproduction rate of bacteria. The relationship between chemotaxis, the maximum entropy production principle and the formation of self-organizing structure is discussed.

Flow cytometry of HEK 293T cells interacting with polyelectrolyte multilayer capsules containing fluorescein-labeled poly(acrylic acid) as a pH sensor.

Polyelectrolyte multilayer sensor capsules, 5 microm in diameter, which contained fluorescein-labeled poly(acrylic acid) (PAAAF) as pH-sensitive reporter molecules, were fabricated and employed to explore their endocytotic uptake into HEK 293T cells by flow cytometry. The percentage of capsules residing in the endolysosomal compartment was estimated from the fluorescence intensity decrease caused by acidification. Capsules attached to the extracellular surface of the plasma membrane were identified by trypan blue quenching. The number of capsules in the cytoplasm was rather small, being below the detection limit of the method. The advantages of polyelectrolyte multilayer capsules are that the fluorophore is protected from interaction with cellular compartments and that the multilayer can be equipped with additional functions.

Mathematical modeling of the myosin light chain kinase activation.

The mathematical model presented here describes the interactions among Ca2+, calmodulin (CaM), and myosin light chain kinase (MLCK) and consists of a kinetic scheme taking into account 7 reactions instead of 12 as proposed previously. We derive a system of 5 nonlinear ordinary differential equations. Solving it yields the prediction of active MLCK as a function of [Ca2+] whereby the active MLCK is defined to be proportional to the Ca4CaM.MLCK complex concentration. The model predictions are compared with other theoretical and experimental predictions of active MLCK as well as with the results of our previously proposed complex model.

Mathematical modeling of the relation between myosin phosphorylation and stress development in smooth muscles.

In this paper the 4-state latch bridge model proposed by Rembold and Murphy is expanded; first by incorporation of the analytical expression of Ca2+ dependent MLCK activation from the work of Kato et al. and second, by inclusion of the myosin dephosphorylation based on the Michaelis-Menten kinetics. The analysis of the proposed model and the comparison with the original model results as well as with the experimental data is presented. The model is able to predict the steady-state isometric stress and the myosin phosphorylation in dependence on steady cytosolic [Ca2+] as well as the temporal evolution of the system in dependence on the input Ca2+ signal in the form of biphasic transient, whereby our model results are in several aspects in better agreement with experimental observations.

Mathematical modelling of ca(2+) oscillations in airway smooth muscle cells.

The action of different agonists such as acetylcholine on the membrane of airway smooth muscle cells may induce cytosolic Ca(2+) oscillations which can be a part of the Ca(2+) signalling pathway, eventually leading to cell contraction. The aim of the present study is to present a mathematical model of the possible effect of the initial Ca(2+) distribution within the cell on the form and frequency of induced Ca(2+) oscillations. It takes into account intracellular Ca(2+) stores such as sarcoplasmic reticulum and cytosolic proteins as well as Ca(2+) exchange across the plasma membrane. We are able to demonstrate a closer agreement of model predictions with observed Ca(2+) traces for a significantly wider range of parameter values, as was previously reported. We show also that the total cellular Ca(2+) content is an important system parameter especially because of the content in sarcoplasmic reticulum. At a total Ca(2+) increase of about 20%, the oscillation frequency increases by 25%; also, damped oscillations become sustained. Cases are indicated in which such a situation could occur.

Entrapment of a weak polyanion and H+/Na+ exchange in confined polyelectrolyte microcapsules.

An approach for the entrapment of a polyanion by polyelectrolyte microcapsules is reported. It is based on a reversal changing of microcapsule wall permeability from neutral to basic pH. Polyelectrolyte microcapsules were templated on latex (polystyrene) particles by the layer-by-layer adsorption of oppositely charged polymers of sodium poly(styrene sulfonate) and poly(allylamine hydrochloride), followed by core removal using tetrahydrofuran. In alkaline conditions, the microcapsules swell and become permeable for polymers. During encapsulation, the addition of salt ions increases the amount of the polymer encapsulated and contributes to its protonation because of redistribution of H+ ions across a semipermeable microcapsule wall. The redistribution of small ions across the microcapsule wall was tuned by adding salt according to the Donnan equilibrium and was characterized by H+ sensitive dyes.