A mathematical model of water flux through aortic tissue

Water flux in porcine aortic segments produced by the sudden application of a hydrostatic pressure gradient has been described in a recent paper by Harrison and Massaro (1976). A mathematical model is developed here to explain the results obtained when pressure is applied to either covered or uncovered samples. The model predicts that the rate of exudation in both instances should be substantially identical for a period of time ∼ 0.2τ, where τ is the consolidation time. The consolidation time is proportional to the hydraulic resistance to liquid flow, and inversely proportional to the compressive stiffness of the artery. The existence of a time-dependent water flux in an arteryin vivo during periodic pressurization is predicted by the mathematical model if the resistance to water flow at the endothelium is not excessive. The pore pressure within the bulk of the media is predicted to pulsate in a highly unexpected fashion. These predictions follow naturally from the fact that the consolidation phenomenon in large arteries, as determined by the compression tests of Harrison and Massaro, is of long duration, much longer than the period of a heartbeat. Pressure gradientsin vivo in interstitial fluid are then confined to a very small fraction of the total arterial wall thickness. A potential for plasma “sloshing” across the endothelial junctions exists. The convective flux of water across an endothelial layer may therefore be of a pulsatile character in normal arteriesin vivo.     

A theoretical model for electron transport through chlorophyll-containing bileaflet membranes

Summary A model of electron transport through bileaflet membranes comprised of chlorophylls and carotenoids is proposed and can account for the photoresponses observed in chloroplast-extract membranes. Some features of the model are as follows: In the absence of any specific additive, such as phycocyanin, the energy barrier for electron transfer between chromophores in the membrane and a redox pair in the aqueous solution is significantly high, so that the only realistic mechanism for electron exchange through the interface is by quantum-mechanical tunneling. In an analogy to theories developed for the explanation of semiconductor electrode behavior, the essential requirement of energy overlap between occupied and unoccupied electronic states on either side of the membrane-water interface is explored. The extent of overlap can be controlled by the potential difference developed across the interface. The presence of the carotenoids can reduce the energy barrier for electron movement within she membrane so that excited electrons can pass from the chlorophyll chromophores on one tide of the membrane interface to those on the other side. It is suggested that electron tunneling is the mechanism by which reducing substances belonging to a redox pair of high oxidation-reduction potential deliver their electrons to vacant orbitals in the photosynthetic membranes.     

A theoretical model for the intercistronic region

Punctuation in polycistronic messages is very probably not restricted to a single nonsense triplet. In the present paper a simple theoretical model is proposed of an intercistronic region (having the length of 15 bases) which would protect the cell against the damage resulting from any suppressor or frameshift mutation. The model is discussed with reference to the experimental data reported in recent literature and to the possible experimental approach to test its validity.     

A simple computer model for albumin and water distribution and flux in man

The physiological and mathematical basis for a simple computer model of albumin and water distribution in man is described. The factors which are important in determining albumin and water flux are discussed and some clinical implications are considered.     

Voltage-regulated water flux through aquaporin channels in silico

Aquaporins (AQPs) facilitate the passive flux of water across biological membranes in response to an osmotic pressure. A number of AQPs, for instance in plants and yeast, have been proposed to be regulated by phosphorylation, cation concentration, pH change, or membrane-mediated mechanical stress. Here we report an extensive set of molecular dynamics simulations of AQP1 and AQP4 subject to large membrane potentials in the range of ±1.5 V, suggesting that AQPs may in addition be regulated by an electrostatic potential. As the regulatory mechanism we identified the relative population of two different states of the conserved arginine in the aromatic/arginine constriction region. A positive membrane potential was found to stabilize the arginine in an up-state, which allows rapid water flux, whereas a negative potential favors a down-state, which reduces the single-channel water permeability.     

A coupled carbon and water flux model to predict vegetation structure

Abstract. A coupled carbon and water flux model (BIOME2) captures the broad-scale environmental controls on the natural distribution of vegetation structural and phenological types in Australia. Model input consists of latitude, soil type, and mean monthly climate (temperature, precipitation, and sunshine hours) data on a 1/10° grid. Model output consists of foliage projective cover (FPC) for the quantitative combination of plant types that maximizes net primary production (NPP). The model realistically simulates changes in FPC along moisture gradients as a consequence of the trade-off between light capture and water stress. A two-layer soil hydrology model also allows simulation of the competitive balance between grass and woody vegetation including the strong effects of soil texture.     

Cycle flux algebra for ion and water flux through the KcsA channel single-file pore links microscopic trajectories and macroscopic observables

In narrow pore ion channels, ions and water molecules diffuse in a single-file manner and cannot pass each other. Under such constraints, ion and water fluxes are coupled, leading to experimentally observable phenomena such as the streaming potential. Analysis of this coupled flux would provide unprecedented insights into the mechanism of permeation. In this study, ion and water permeation through the KcsA potassium channel was the focus, for which an eight-state discrete-state Markov model has been proposed based on the crystal structure, exhibiting four ion-binding sites. Random transitions on the model lead to the generation of the net flux. Here we introduced the concept of cycle flux to derive exact solutions of experimental observables from the permeation model. There are multiple cyclic paths on the model, and random transitions complete the cycles. The rate of cycle completion is called the cycle flux. The net flux is generated by a combination of cyclic paths with their own cycle flux. T.L. Hill developed a graphical method of exact solutions for the cycle flux. This method was extended to calculate one-way cycle fluxes of the KcsA channel. By assigning the stoichiometric numbers for ion and water transfer to each cycle, we established a method to calculate the water-ion coupling ratio (CR(w-i)) through cycle flux algebra. These calculations predicted that CR(w-i) would increase at low potassium concentrations. One envisions an intuitive picture of permeation as random transitions among cyclic paths, and the relative contributions of the cycle fluxes afford experimental observables.     

A theory for water and macromolecular transport in the pulmonary artery wall with a detailed comparison to the aorta

The pulmonary artery (PA) wall, which has much higher hydraulic conductivity and albumin void space and approximately one-sixth the normal transmural pressure of systemic arteries (e.g, aorta, carotid arteries), is rarely atherosclerotic, except under pulmonary hypertension. This study constructs a detailed, two-dimensional, wall-structure-based filtration and macromolecular transport model for the PA to investigate differences in prelesion transport processes between the disease-susceptible aorta and the relatively resistant PA. The PA and aorta models are similar in wall structure, but very different in parameter values, many of which have been measured (and therefore modified) since the original aorta model of Huang et al. (23). Both PA and aortic model simulations fit experimental data on transwall LDL concentration profiles and on the growth of isolated endothelial (horseradish peroxidase) tracer spots with circulation time very well. They reveal that lipid entering the aorta attains a much higher intima than media concentration but distributes better between these regions in the PA than aorta and that tracer in both regions contributes to observed tracer spots. Solutions show why both the overall transmural water flow and spot growth rates are similar in these vessels despite very different material transport parameters. Since early lipid accumulation occurs in the subendothelial intima and since (matrix binding) reaction kinetics depend on reactant concentrations, the lower intima lipid concentrations in the PA vs. aorta likely lead to slower accumulation of bound lipid in the PA. These findings may be relevant to understanding the different atherosusceptibilities of these vessels.     

A theoretical and non-destructive experimental approach for direct inclusion of measured collagen orientation and recruitment into mechanical models of the artery wall

Gradual collagen recruitment has been hypothesized as the underlying mechanism for the mechanical stiffening with increasing stress in arteries. In this work, we investigated this hypothesis in eight rabbit carotid arteries by directly measuring the distribution of collagen recruitment stretch under increasing circumferential loading using a custom uniaxial (UA) extension device combined with a multi-photon microscope (MPM). This approach allowed simultaneous mechanical testing and imaging of collagen fibers without traditional destructive fixation methods. Fiber recruitment was quantified from 3D rendered MPM images, and fiber orientation was measured in projected stacks of images. Collagen recruitment was observed to initiate at a finite strain, corresponding to a sharp increase in the measured mechanical stiffness, confirming the previous hypothesis and motivating the development of a new constitutive model to capture this response. Previous constitutive equations for the arterial wall have modeled the collagen contribution with either abrupt recruitment at zero strain, abrupt recruitment at finite strain or as gradual recruitment beginning at infinitesimal strain. Based on our experimental data, a new combined constitutive model was presented in which fiber recruitment begins at a finite strain with activation stretch represented by a probability distribution function. By directly including this recruitment data, the collagen contribution was modeled using a simple Neo-Hookean equation. As a result, only two phenomenological material constants were required from the fit to the stress stretch data. Three other models for the arterial wall were then compared with these results. The approach taken here was successful in combining stress-strain analysis with simultaneous microstructural imaging of collagen recruitment and orientation, providing a new approach by which underlying fiber architecture may be quantified and included in constitutive equations.     

A theoretical model for estimating the margination constant of leukocytes

Background  

Blood leukocytes constitute two interchangeable sub-populations, the marginated and circulating pools. These two sub-compartments are found in normal conditions and are potentially affected by non-normal situations, either pathological or physiological. The dynamics between the compartments is governed by rate constants of margination (M) and return to circulation (R). Therefore, estimates of M and R may prove of great importance to a deeper understanding of many conditions. However, there has been a lack of formalism in order to approach such estimates. The few attempts to furnish an estimation of M and R neither rely on clearly stated models that precisely say which rate constant is under estimation nor recognize which factors may influence the estimation.     

A theoretical model for the control mechanisms in biochemical reactions

A mathematical representation for the analysis of control mechanisms in biochemical reactions is presented. First, the theoretical concept of concentration in biological systems is developed. Then a system consisting of two functions λ and τ is constructed as a network of single output automata. The range of λ is taken to be formed by a set of twostates qualitatively different from the “repair function” Φ _f of a mappingf: A→B in the stimulated Φ¹ and unstimulated state Φ⁰. Likewise, the range of τ is formed by the set δ={f ^o ,f ¹} wheref ¹ means the mappingf in its stimulated state andf ^o in the unstimulated one. It is demonstrated that the mathematical structure described acts as a control mechanism over thef and Φ _f , so that two biochemical components,A→B, are transformed at a controlled rate. Some of the biological applications of this model are briefly examined. The Jacob-Monod model, the enzymatic adaptation phenomenon, and the “rheon unit” hypothesis are discussed within our framework. Eventually, a concrete model for the RNA-polymerase mechanism, based on the above discussion, is presented.     

A theoretical model for lipid monolayer phase transitions

We present a theoretical model for the liquid-expanded to liquid-condensed phase transition observed in many phospholipid monolayer films. The total two-dimensional pressure in the model is the sum of the hydrocarbon chain pressure and the surface pressure. The hydrocarbon chain pressure is calculated in an extended version of a model published earlier. The surface pressure results from a lowering of the surface tension in the monolayer over that of pure water, thus producing a force on a Langmuir float. When these two contributions are added, $\text{π/A}$ isotherms are obtained which have slope discontinuities very similar to those observed experimentally. These results indicate that a successful model for lipid phase behavior must consider the interactions between head groups and water as well as cooperative hydrocarbon chain melting.     

A theoretical model for immobilized whole cell enzyme

A method of estimating effectiveness factor for immobilized whole cells is developed by considering microbial cells as microspheres containing enzyme activity dispersed in the gel phase of the support matrix. The proper model equations describing the system are solved and the corresponding effectiveness factors calculated for various bead sizes, and numbers and activities of cells. The cell wall resistance (permeability) is found to be one of most important variables in the system. The model is applied in predicting the experimental data of other investigators.     

A theoretical model of localized heat and water vapor transport in the human respiratory tract

A steady-state, one-dimensional theoretical model of human respiratory heat and water vapor transport is developed. Local mass transfer coefficients measured in a cast replica of the upper respiratory tract are incorporated into the model along with heat transfer coefficients determined from the Chilton-Colburn analogy and from data in the literature. The model agrees well with reported experimental measurements and predicts that the two most important parameters of the human air-conditioning process are: the blood temperature distribution along the airway walls, and the total cross-sectional area and perimeter of the nasal cavity. The model also shows that the larynx and pharynx can actually gain water over a respiratory cycle and are the regions of the respiratory tract most subject to drying. With slight modification, the model can be used to investigate respiratory heat and water vapor transport in high stress environments, pollutant gas uptake in the respiratory tract, and the connection between respiratory air-conditioning and the function of the mucociliary escalator.     

A new theoretical model for the origin of amino acid homochirality

Amino acid homochirality, as a unique behavior of life, could have originated synchronously with the genetic code. In this paper, phosphoryl amino-acid -5′-nucleosides with P－N bond are postulated to be a chiral origin model in prebiotic molecular evolution. The enthalpy change in the intramolecular interaction between the nucleotide base and the amino-acid side-chain determines the sta-bility of the particular complex, resulting in a preferred conformation associated with the chirality of amino acids. Based on the theoretical model, our experiments and calculations show that the chiral selection of the earliest amino acids for L-enantiomers seems to be a strict stereochemi-cal/physicochemical determinism. As other amino acids developed biosynthetically from the earliest amino acids, we infer that the chirality of the later amino acids was inherited from the precursor amino acids. This idea probably goes far back in history, but it is hoped that it will be a guide for further ex-periments in this area.