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We demonstrate that the maximum entropy production principle (MEPP) serves as a physical selection principle for the description of the most probable non-equilibrium steady states in simple enzymatic reactions. A theoretical approach is developed, which enables maximization of the density of entropy production with respect to the enzyme rate constants for the enzyme reaction in a steady state. Mass and Gibbs free energy conservations are considered as optimization constraints. In such a way computed optimal enzyme rate constants in a steady state yield also the most uniform probability distribution of the enzyme states. This accounts for the maximal Shannon information entropy. By means of the stability analysis it is also demonstrated that maximal density of entropy production in that enzyme reaction requires flexible enzyme structure, which enables rapid transitions between different enzyme states. These results are supported by an example, in which density of entropy production and Shannon information entropy are numerically maximized for the enzyme Glucose Isomerase.

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 (PGE(2) and PGD(2)) and one LT (LTC(4)), 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 LTC(4)‐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.

It is shown that Onsager's principle of the least dissipation of energy is equivalent to the maximum entropy production principle. It is known that solutions of the linearized Boltzmann equation make extrema of entropy production. It is argued, in the case of stationary processes, that this extremum is a maximum rather than a minimum., 12 pages, revtex4

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.

Ovaj rad obrađuje problem predviđanja mehaničkog odziva dijela zajedničke arterije glave (ZAG). Zaostala naprezanja u arteriji uzeta su u obzir uporabom termo-mehaničke analogije (TMA), koja se primjenjuje u ovom radu za potrebe modeliranja mehaničkog odziva dvoslojne strukture stijenke arterije. Obično se modeliranju zaostalih naprezanja u arteriji pristupi s uzdužno otvorenim modelom arterije, tzv. cut-open section, koji u slučaju bolesnikove arterije nije poznat. S TMA pristupom, umjesto uporabe uzdužno prerezane stijenke arterije, koja doduše osigurava početno stanje bez zaostalih naprezanja, u termo-mehaničkom modelu zajedničke arterije glave također je postignuto početno stanje bez zaostalih naprezanja ali na modelu stvarne, in vivo arterije. Tim pristupom, zaostalo naprezanje u ZAG aproksimirano je podvrgavanjem ZAG modela obujamskom deformacijom, t.j. primjenom odgovarajućih termičkih dilatacija. Takav pristup potvrđen je na modelu arterije kružnog presjeka i postizanjem stanja bez naprezanja u slučaju uzdužnog rezanja stijenke., This work deals with the prediction of the mechanical response of a section of a human common carotid artery (CCA). The arterial residual stress state is accounted for using the thermomechanical analogy (TMA) approach, which is applied in this work to model the mechanical response of a two-layered arterial structure. The starting point to model the arterial residual stress state is normally the cut-open section, which is in the case of patient-specific artery not known. With TMA approach, however, instead of using the arterial zero-stress cut-open configuration to predict the arterial residual stress state, a thermomechanical model of the CCA is considered with its zero-stress geometry defined based on the actual CCA in vivo configuration. The approximation to the CCA residual stress state is then obtained by exposing the auxiliary CCA model to a volumetric deformation, enforced via adequate thermal dilatations. The approach is validated on a circular arterial model and by predicting the CCA cut-open zero-stress state.

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.

Aspirin-induced asthma (AIA) is a severe inflammatory disease, which affects aspirin-intolerant patients after ingestion of aspirin or other non-steroidal anti-inflammatory drugs (NSAIDs). In this article, a mathematical model describing arachidonic acid metabolism and its interaction with NSAIDs, is used to study the strategy for safe managing of NSAIDs to AIA patients. Three different AIA patient populations are taken into consideration. First, the values of aspirin and ibuprofen limiting doses that might induce symptoms of AIA are calculated and compared to experimentally observed threshold doses to enlighten which AIA patient population is susceptible to aspirin and ibuprofen. Second, the methodology of NSAID administration is studied on AIA populations susceptible to aspirin and ibuprofen by using 1,000 mg dose of aspirin and 200 or 400 mg dose of ibuprofen followed by PGE(2) analogue dosing. Our model results show that successive doses of PGE(2) analogue applied at appropriate time after aspirin or ibuprofen ingestion would enable administration of both NSAIDs to AIA patients. PGE(2) analogue doses and the corresponding times of their applications are calculated. The model is also used to estimate the duration of symptoms of AIA for different aspirin and ibuprofen doses.

Polyelectrolyte multilayer film capsules with different micrometer sizes were assembled for pH and salt sensing devices. Encapsulation of labelled poly(acrylic acid) (PAA AF ) in CaCO 3 particles increases their potential usage in the biological environment. Microcapsules were analyzed with flowcytometry to obtain individual response of a spherical-like microsensor that behaves as Donnan system. The linear pH response of microparticles and microcapsules is quite broad and is useful in physiological range. The salt response is up to 0.1 M and was also predicted with simple mathematical model.

The deswelling behavior of cross-linked DNA gels reports on DNA-cosolute interactions and gives a basis for the development of responsive DNA formulations. An investigation of the deswelling kinetics shows that an increase in the surfactant tail length gives a pronouncedly slower deswelling kinetics. In the same conditions, single stranded gels exhibited faster deswelling kinetics when compared with double stranded networks. It was also found that DNA gels display a nonmonotonic volume change with time, deswelling followed by reswelling, when immersed in surfactant solutions. Kinetic modeling of surfactant uptake by the DNA gel was done using a stochastic approach of mass transfer between the bulk solution, the surface, and the inner volume of the gels. Diffusion coefficients and kinetic constants can be derived from the separated model uptake curves for the gel surface and the gel interior volume.

The transmembrane distribution of membrane constituents in the two leaflets of a cylindrical bilayer, which is in contact on both sides with an electrolyte solution, was studied by mathematical modeling. The model considers electrostatic interactions between the charged membrane molecules and the monovalent ions of the electrolyte solution, the bending elasticity of the membrane, as well as the anisotropy of the molecular intrinsic shape in the membrane. We showed that the strongly anisotropic uncharged membrane constituents are distributed asymmetrically between the two leaflets of the membrane. The asymmetric transmembrane distribution of charged weakly anisotropic membrane constituents is caused by the difference between the ionic strengths in the outer solutions and those in the inner solutions. For strongly anisotropic charged constituents in the membrane, we found that the asymmetric transmembrane distribution is driven by an interplay between the shape and the charge of the membrane constituents, as well as the difference between the ionic strengths in the outer solutions and those in the inner solutions. We also showed that the composition of the bilayer and the intrinsic curvatures of membrane components influence the stability of the tube.

Evidence is presented that all three theoretically predicted modes of phase separation take place in the ternary system polysulfone(PSf)/ N , N -dimethyl acetamide(DMA)/water during the process of wet phase separation (WPS). The elementary process of solidification is reconsidered with regard to the (non-) equilibrium phase separation. Cast solutions with more than 15 wt% of PSf undergo nucleation and growth of the polymer lean phase with formation of separation membranes characterised by a cellular structure. When cast solutions with about 5–7 wt% of PSf undergo WPS, somewhere inside the ternary system conditions are established so that alongside other solidified PSf structures the bicontinuous spinodal structures superimposed by bead-like structures are also formed. Variety of lacy PSf structures with less/more polymer beads is the manifestation of the primary phase separation by the spinodal mode superimposed by the secondary phase separation taking place by heterogeneous nucleation and growth of the polymer rich phase mode. Latex formation during the WPS will also be explained. Skin formation on the cast solution – coagulation bath interface by direct accumulation of polymer is established regardless of the PSf content in the cast solution.

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.

The prediction of the arterial zero-stress state is as of yet an unresolved problem in the field of modelling the mechanical response of patientspecific arteries. This is because the configuration associated with arterial zero-stress state is impossible to obtain experimentally. However, the zero-stress configuration (or, equivalently, the residual stresses related to this configuration) represents the crucial data of any numerical analysis. In this study, the mechanical response of a pre-stressed, pressurised, hyperelastic tube (representing the artery) is determined without knowing the initial zero-stress configuration of the artery. Instead, to predict the arterial residual (bending and stretching) stresses, a corresponding thermomechanical analogy is used. As shown in the paper, the arterial residual stress state can equally be obtained by thermally loading a properly defined closed tube. Thus, based on the loaded state of the corresponding thermomechanical model, the arterial residual stress sate is constructed, from where the arterial loaded state can be obtained. The initial configuration of the thermomechanical model is defined on the basis of the arterial loaded configuration. The methodology is validated by predicting the zero-stress state of the artery. The predicted equilibrium state of the artery, when cut longitudinally and transversally, has the form of an opened-up tube with a relatively low stress state in comparison to the arterial residual stresses. The results thus demonstrate that arterial residual stresses that are predicted with the corresponding thermomechanical model exhibited the bending distribution, which proves the methodology to be adequate. Določitev breznapetostnega stanja arterij predstavlja še vedno nerazrešen problem na področju numeričnega modeliranja mehanskega odziva realnih arterij. Breznapetostno stanje arterije, ki ima v splošnem obliko krožnega sektorja, je namreč eksperimentalno nemogoče določiti. Oblika breznapetostnega stanja (oziroma temu pripadajoče zaostalo napetostno stanje) pa je pomembno zato, ker predstavlja začetno stanje in tako ključen podatek sleherne numerične analize. Arterije se za karakterizacijo njihovega mehanskega odziva običajno obravnava kot idealno krožne cevi, to pomeni idealno krožne in ravne. Takšna poenostavitev omogoča določitev zaostalih napetosti arterije brez poznavanja njihovega breznapetostnega stanja. Prisotnost zaostalih napetosti je posledica homogenizacije odziva arterij in vivo. Napetostno stanje arterije in vivo bi bilo namreč izrazito nehomogeno z velikim transmuralnim gradientom brez upoštevanja zaostalih napetosti. Zaradi njihove porazdelitve skozi debelino žilne stene se jih običajno asociira z upogibnimi napetostmi. Na notranji površini kolobarja so zaostale napetosti tlačne, medtem ko so na zunanji površini natezne.

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.

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.

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.

Zeta potential (ZP) of poly-tetrafluoroethylen (PTFE) and polyamide 6 (PA 6) foils was measured using the streaming potential method. All measurements were carried out in a flat cell where PTFE foils are usually used in electrokinetic measurements as a part of the measuring device, to form the channel and to achieve a proper distance between the foils surface of measured samples. The primary interest of the present work was to investigate the influence of pretreatment of PTFE foils on their electrokinetic properties in order to find out to what extent such pretreatment may affect measuring results of other samples and to develop a procedure of PTFE foils preparation with purpose to achieve the same initial conditions for all measurements.

Asymmetric and porous polysulfone (PSf) membranes were prepared by wet phase separation. Binary (PSf)/N,N-dimethylacetamide (DMA) solutions with polymer concentrations of 12.5–30 wt % were cast in thicknesses of 80–700 μm and immersed in a coagulation bath of pure water. The morphology of the formed membranes' cross sections consisted of a cellular structure and macrovoids; the cellular structure density was highest when the cast solution contained about 21 wt % PSf, regardless of the cast thickness. The membranes' pure water permeability decreased as the cast thickness increased. The instantaneous onset of the turbidity, regardless of the PSf content and cast thickness, its steep growth, and relatively high end value were the main characteristics of the turbidity phenomena taking place during the formation of the protomembranes. Again, the membrane-forming system with a PSf/DMA solution with about 21 wt % polymer, regardless of the cast thickness, had the highest turbidity end value. The shrinkage of the cast solutions into the corresponding protomembrane was also examined quantitatively. Inverse experiments showed that the direction of the gravitation field had no influence on the shrinkage of the membrane-forming ternary system or the membranes' morphology and its water permeability. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 1667–1674, 2005

The direct accumulation of polymer, the nucleation and growth of the polymer lean as well as the polymer rich phase and the spinodal phase separation are postulated as four elementary processes of the mechanisms of the polymeric membrane formation by wet-phase separation. With the study of five different polymer/solvent:water systems they are discriminated by the investigation of the turbidity and the shrinkage phenomena taking place during (proto)membrane formation, as well as by the measurement of the pure water permeability and by the inspection of the membranes’ cross-section morphology. The general scheme of membrane formation mechanisms is arranged by gathering the groups of different modes of mass transport and the group of nonsolvent/solvent/polymer forms of solidification as elementary processes; by forming combinations of the so postulated elementary processes in time and space particular mechanisms are established.

Intracellular calcium oscillations, which are oscillatory changes of cytosolic calcium concentration in response to agonist stimulation, are experimentally well observed in various living cells. Simple calcium oscillations represent the most common pattern and many mathematical models have been published to describe this type of oscillation. On the other hand, relatively few theoretical studies have been proposed to give an explanation of complex intracellular calcium oscillations, such as bursting and chaos. In this paper, we develop a new possible mechanism for complex calcium oscillations based on the interplay between three calcium stores in the cell: the endoplasmic reticulum (ER), mitochondria and cytosolic proteins. The majority ( approximately 80%) of calcium released from the ER is first very quickly sequestered by mitochondria. Afterwards, a much slower release of calcium from the mitochondria serves as the calcium supply for the intermediate calcium exchanges between the ER and the cytosolic proteins causing bursting calcium oscillations. Depending on the permeability of the ER channels and on the kinetic properties of calcium binding to the cytosolic proteins, different patterns of complex calcium oscillations appear. With our model, we are able to explain simple calcium oscillations, bursting and chaos. Chaos is also observed for calcium oscillations in the bursting mode.

Hollow polyelectrolyte capsules were fabricated by means of stepwise adsorption of polyelectrolytes followed by dissolution of the templating core. The capsule wall thickness was approximately 20 nm. The diameter of the capsules is given by the size of the templates (3.3 μm). These capsules exclude poly(styrenesulfonate) (PSS) from a molecular weight of 4200 upward but are permeable for small ions and 6-carboxyfluorescein (6-CF). By means of adding PSS in acidic form to the bulk solution, a Donnan equilibrium between the bulk and internal solution encapsulated within the capsules was created. The pH in the capsule interior is more basic. This difference in pH is larger than a unit for capsules of 3.3 μm in diameter. Addition of NaCl decreases this pH difference. A theoretical model is developed that describes the observed pH difference. The essential assumptions of the model are the selective permeability of the capsule wall, charging of the capsule together with its interior according to its capacitance,...

Intracellular calcium oscillations provide a natural clock that may be of crucial importance for the timing of many cellular processes. Elucidating of the mechanisms underlying these oscillations is of particular interest. The theoretical description presented here extends existing models of calcium oscillations by allowing for two types of proteins differing in their calcium-binding properties. This model reflects experimental findings by considering both a fast calcium-binding process to low-affinity protein binding sites such as found in the N-domains of calmodulin or troponin C and a class of high-affinity calcium binding proteins with slow binding kinetics (e.g., parvalbumin or the C-domains of calmodulin and troponin C). Furthermore, recalling that calcium is mainly stored in small subcompartments of the ER, it is argued that only a small fraction of its overall volume participates in the rapid release and uptake of calcium. The effect of the size of this fraction is studied. The hypothesis saying that any electric potential difference across the ER membrane would be dissipated by the highly permeant ions is critically examined by an analytical estimation based on the electroneutrality condition and by numerical integration of the complete model equations. It is predicted theoretically that the transmembrane potential of the ER calcium stores, which is up to now virtually impossible to determine in experiment, builds up in the millivolt range at physiological concentrations of monovalent ions. The phenomenology of oscillations is studied by numerical integration. The model reproduces experimentally observed values of frequency and amplitude as well as the typical spike-like shape of oscillations. The model reveals also the time course of a shift of the bound Ca2+ population from the low-affinity binding sites to the high-affinity binding sites.

The time dependent uptake of 1-anilino-8-naphthalene sulphonate (ANS) by bovine erythrocytes was studied. Experimental results were compared with theoretical predictions in order to determine the inner erythrocyte membrane surface potential. The value of the inner membrane surface potential under physiological conditions was estimated as −35 mV. In addition, the number of ANS binding sites on the outer surface of the single bovine erythrocyte membrane was determined as 2.2 × 106.

There have been many attempts to use optimization approaches to study the biological evolution of enzyme kinetics. Our basic assumption here is that the biological evolution of catalytic cycle fluxes between enzyme internal functional states is accompanied by increased entropy production of the fluxes and increased Shannon information entropy of the states. We use simplified models of enzyme catalytic cycles and bioenergetically important free-energy transduction cycles to examine the extent to which this assumption agrees with experimental data. We also discuss the relevance of Prigogine’s minimal entropy production theorem to biological evolution.

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.

A mathematical model is presented to simulate transverse lipid movement in the human erythrocyte membrane from one membrane monolayer to the other. The model is based on a system of differential equations describing the time-dependence of phospholipid redistribution and the steady-state distribution. Different translocation mechanisms are considered in a combined way. These are the ATP-dependent carrier mediated translocation, the carrier mediated facilitated diffusion and carrier independent transbilayer diffusion. Using realistic values of model parameters the model allows calculation of the transbilayer motion and distribution of phospholipids of the human erythrocyte membrane for several biologically relevant conditions and different experimental conditions.

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.

We report on novel observations on the appearance of macrovoids in the ternary cellulose acetate (CA)/acetone (ACE)/water membrane forming system. The membranes are prepared by the wet phase separation whereby the cast solution is composed of ACE and polymer, and the coagulation bath is pure water only. It is found that the macrovoid formation in a 12.5 wt.% cast solution strongly depends on the cast solution thickness: macrovoids appear at the thickness of 500 μm but not at 150 and 300 μm.

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 β-Lactamase enzymes and their optimal values predicted by the maximum entropy production principle, which agrees with earlier observations that β-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.

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.

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.

A theoretical approach to determine nearly spherical shapes of phospholipid vesicles is developed. The method is general in the sense that it does not depend on any symmetry restrictions. Equilibrium shapes are assumed to correspond to the minimum of the membrane bending elastic energy at constant values of the membrane area, the vesicle volume and the difference of areas of the two leaflets of the phospholipid bilayer. The bending energy and the constraints are expanded up to fourth order terms in the deviation from a sphere, and in the subsequent calculations all terms up to the third order are included. The deviation is expressed as a series of spherical harmonics. It sis shown that the stability of the solutions can be tested by inspecting the eigenvalues of the matrix of second derivatives of the bending energy with respect to independent amplitudes of spherical harmonics expansion. The method is applied to the calculation of axisymmetric and nonaxisymmetric shapes, and the influences of different approximations are discussed. It is shown that at variations of the leaflet area difference stable oblate and stable prolate shapes are transformed into each other in a continuous manner.

Xylem is modelled as the closed system coupled to the root and phloem via semi-permeable membranes. The importance of the fixed volume of the xylem in the osmotic process between xylem and phloem is analysed. It is shown that negative pressure, a concept accepted as a driving force for the upward xylem water transport in many scientific discussions [1, 2], is closely related to this process. It is shown that there is a self-consistency between decrease of the pressure in the xylem and increase of the concentration of the sugar in phloem, respectively, in dependence of the height.

Posuda stalnog obujma podijeljena je u dva dijela polupropusnom opnom. U jednom dijelu je otopina a u drugom otapalo. Razvojem slobodne energije po srednjoj udaljenosti među molekulama otapala pokazano je da je otopina pod povišenim tlakom dok je otapalo pod naprezanjem istezanja. Uobičajeno je stanje istezanja opisati negativnim tlakom [1]. U biljkama kroz ksilem podiže se voda, s nešto minerala, od korijena do listova dok kroz floem prolazi otopina šećera. Ksilem i floem modelirani su kao sustav sa stalnim obujmom u kome su oni povezani polupropusnom opnom. Pokazano je da je osmoza pod stalnim obujmom dobar mehanizam kojim se može tumačiti podizanje vode u visokim stablima [2, 3]. [1] Imre, K.A. 2007, On the existence of negative pressure states. phys. stat. sol. (b) 244, 893–899 [2] Zimmermann, U., Schneider, H., Wegner L. H., and Haase A. 2004. Water ascent in tall trees: does evolution of land plants rely on a highly metastable state? New Phytol. 162:575-615 [3] Lampinen, M. J., and Noponen, T. 2003. Thermodynamic analysis of the interaction of the xylem water and phloem sugar solution and its significance for the cohesion theory. J. Theor. Biol. 224:285-298.

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.

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.