The Interplay between Molten Globules and Heme Disassociation Defines Human Hemoglobin Disassembly

Hemoglobin functions as a tetrameric oxygen transport protein, with each subunit containing a heme cofactor. Its denaturation, either in vivo or in vitro, involves autoxidation to methemoglobin, followed by cofactor loss and globin unfolding. We have proposed a global disassembly scheme for human methemoglobin, linking hemin (ferric protoporphyrin IX) disassociation and apoprotein unfolding pathways. The model is based on the evaluation of circular dichroism and visible absorbance measurements of guanidine-hydrochloride-induced disassembly of methemoglobin and previous measurements of apohemoglobin unfolding. The populations of holointermediates and equilibrium disassembly parameters were estimated quantitatively for adult and fetal hemoglobins. The key stages are characterized by hexacoordinated hemichrome intermediates, which are important for preventing hemin disassociation from partially unfolded, molten globular species during early disassembly and late-stage assembly events. Both unfolding experiments and independent small angle x-ray scattering measurements demonstrate that heme disassociation leads to the loss of tetrameric structural integrity. Our model predicts that after autoxidation, dimeric and monomeric hemichrome intermediates occur along the disassembly pathway inside red cells, where the hemoglobin concentration is very high. This prediction suggests why misassembled hemoglobins often get trapped as hemichromes that accumulate into insoluble Heinz bodies in the red cells of patients with unstable hemoglobinopathies. These Heinz bodies become deposited on the cell membranes and can lead to hemolysis. Alternatively, when acellular hemoglobin is diluted into blood plasma after red cell lysis, the disassembly pathway appears to be dominated by early hemin disassociation events, which leads to the generation of higher fractions of unfolded apo subunits and free hemin, which are known to damage the integrity of blood vessel walls. Thus, our model provides explanations of the pathophysiology of hemoglobinopathies and other disease states associated with unstable globins and red cell lysis and also insights into the factors governing hemoglobin assembly during erythropoiesis.     

Parameter estimation in a stochastic model of the tubuloglomerular feedback mechanism in a rat nephron

A key parameter in the understanding of renal hemodynamics is the gain of the feedback function in the tubuloglomerular feedback mechanism. A dynamic model of autoregulation of renal blood flow and glomerular filtration rate has been extended to include a stochastic differential equations model of one of the main parameters that determines feedback gain. The model reproduces fluctuations and irregularities in the tubular pressure oscillations that the former deterministic models failed to describe. This approach assumes that the gain exhibits spontaneous erratic variations that can be explained by a variety of influences, which change over time (blood pressure, hormone levels, etc.). To estimate the key parameters of the model we have developed a new estimation method based on the oscillatory behavior of the data. The dynamics is characterized by the spectral density, which has been estimated for the observed time series, and numerically approximated for the model. The parameters have then been estimated by the least squares distance between data and model spectral densities. To evaluate the estimation procedure measurements of the proximal tubular pressure from 35 nephrons in 16 rat kidneys have been analyzed, and the parameters characterizing the gain and the delay have been estimated. There was good agreement between the estimated values, and the values obtained for the same parameters in independent, previously published experiments.     

Theoretical evaluation of the parameters of glucose metabolism on the basis of continuous glycemia monitoring data using mathematical modeling

The aim of this paper is to construct a mathematical model that takes the main physiological parameters of blood-glucose regulation into account, in order to identify these parameters for an individual patient according to continuous glucose-monitoring data. The constructed mathematical model consists of six ordinary differential equations that describe the dynamics of changes in glucose concentrations, as well as insulin and anti-insulin factors in the blood. Estimation of the parameters of the equations was performed using an evolutionary programming method. The model predictions were fitted to the continuous glucosemonitoring data. As a result of the identification of the model parameters for two patients with type 1 diabetes mellitus, the estimated insulin secretion was close to zero and the estimated glucose utilization and insulin clearance were increased in comparison with the data for healthy donors. Here, we present a personalized model of the regulation of blood glucose, which can be used to predict the results of continuous glucose monitoring depending on modification of the prescribed glucose-lowering therapy. This approach can significantly reduce the number of iterations of the selection of medical hypoglycemic therapy and therefore increase the effectiveness of treatment according to glucose-monitoring data.

     

Strain measurement in coronary arteries using intravascular ultrasound and deformable images

Atherosclerotic plaque rupture is responsible for the majority of myocardial infarctions and acute coronary syndromes. Rupture is initiated by mechanical failure of the plaque cap, and thus study of the deformation of the plaque in the artery can elucidate the events that lead to myocardial infarction. Intravascular ultrasound (IVUS) provides high resolution in vitro and in vivo cross-sectional images of blood vessels. To extract the deformation field from sequences of IVUS images, a registration process must be performed to correlate material points between image pairs. The objective of this study was to determine the efficacy of an image registration technique termed Warping to determine strains in plaques and coronary arteries from paired IVUS images representing two different states of deformation. The Warping technique uses pointwise differences in pixel intensities between image pairs to generate a distributed body force that acts to deform a finite element model. The strain distribution estimated by image-based Warping showed excellent agreement with a known forward finite element solution, representing the gold standard, from which the displaced image was created. The Warping technique had a low sensitivity to changes in material parameters or material model and had a low dependency on the noise present in the images. The Warping analysis was also able to produce accurate strain distributions when the constitutive model used for the Warping analysis and the forward analysis was different. The results of this study demonstrate that Warping in conjunction with in vivo IVUS imaging will determine the change in the strain distribution resulting from physiological loading and may be useful as a diagnostic tool for predicting the likelihood of plaque rupture through the determination of the relative stiffness of the plaque constituents.     

Inner filter effects and their interferences in the interpretation of culture fluorescence

Inner filter effects and their interferences in the measurement and interpretation of culture fluorescence are discussed. An approximate light intensity model for a typical open-ended culture fluorescence measuring device is developed for calculating the fluorescence response of a component of interest in a general three component solution. The model is tested using well de fined synthetic fluorescent systems. The model is then extended for correlating culture fluorescence with cell density and metabolic state of microbial cultures based on a lumping approximation. The extended model has been utilized to derive culture fluorescence parameters of yeast culture at three distinct metabolic states.     

Hemin interactions and alterations of the subcellular localization of prion protein

Hemin (iron protoporphyrin IX) is a crucial component of many physiological processes acting either as a prosthetic group or as an intracellular messenger. Some unnatural, synthetic porphyrins have potent anti-scrapie activity and can interact with normal prion protein (PrPC). These observations raised the possibility that hemin, as a natural porphyrin, is a physiological ligand for PrPC. Accordingly, we evaluated PrPC interactions with hemin. When hemin (3-10 microM) was added to the medium of cultured cells, clusters of PrPC formed on the cell surface, and the detergent solubility of PrPC decreased. The addition of hemin also induced PrPC internalization and turnover. The ability of hemin to bind directly to PrPC was demonstrated by hemin-agarose affinity chromatography and UV-visible spectroscopy. Multiple hemin molecules bound primarily to the N-terminal third of PrPC, with reduced binding to PrPC lacking residues 34-94. These hemin-PrPC interactions suggest that PrPC may participate in hemin homeostasis, sensing, and/or uptake and that hemin might affect PrPC functions.     

Accumulation and drainage of hemin in the red cell membrane

The subject of hemin intercalation in red cell membranes and the correlation of the accumulated hemin level with the membrane pathology was studied. Methods which made use of dioxan and octan-2-ol mixtures to quantitate small amounts of hemin in membranes were developed. Applying these methods, hemin levels were measured in the cytoskeleton and the remaining lipid core of various red cell membranes. The amount of hemin, in both membrane fractions, was higher in pathological cells of sickle cell anemia and beta-thalassemia as compared to normal circulating cells. Correlation exists between the amount of the membrane-accumulated hemin and the severity of the disease. The level of hemin in the membrane was found to be age dependent, old cells in circulation accumulating more hemin than young cells. The level of hemin in all cells tested was much lower than the amount found previously to cause immediate hemolysis when applied externally (Kirschner-Zilber, I., Rabizadeh, E. and Shaklai, N. (1982) Biochim. Biophys. Acta 690, 20-30). This was explained by the differences between the process leading to immediate lysis and membrane changes recognized as pathological by the in-vivo sequestration mechanism. In search of a physiological mechanism which may drain the cell membrane from the hazardeous hemin, albumin, the main serum protein, was found capable of serving as an efficient agent for extracting hemin trapped in red cell membranes. It is suggested that under normal conditions albumin extracts enough hemin to leave the erythrocyte with unharmful hemin amounts, however, under pathological conditions greater amounts accumulate leading to a shorter cell life span.     

A Computational Model of the Fetal Circulation to Quantify Blood Redistribution in Intrauterine Growth Restriction

Intrauterine growth restriction (IUGR) due to placental insufficiency is associated with blood flow redistribution in order to maintain delivery of oxygenated blood to the brain. Given that, in the fetus the aortic isthmus (AoI) is a key arterial connection between the cerebral and placental circulations, quantifying AoI blood flow has been proposed to assess this brain sparing effect in clinical practice. While numerous clinical studies have studied this parameter, fundamental understanding of its determinant factors and its quantitative relation with other aspects of haemodynamic remodeling has been limited. Computational models of the cardiovascular circulation have been proposed for exactly this purpose since they allow both for studying the contributions from isolated parameters as well as estimating properties that cannot be directly assessed from clinical measurements. Therefore, a computational model of the fetal circulation was developed, including the key elements related to fetal blood redistribution and using measured cardiac outflow profiles to allow personalization. The model was first calibrated using patient-specific Doppler data from a healthy fetus. Next, in order to understand the contributions of the main parameters determining blood redistribution, AoI and middle cerebral artery (MCA) flow changes were studied by variation of cerebral and peripheral-placental resistances. Finally, to study how this affects an individual fetus, the model was fitted to three IUGR cases with different degrees of severity. In conclusion, the proposed computational model provides a good approximation to assess blood flow changes in the fetal circulation. The results support that while MCA flow is mainly determined by a fall in brain resistance, the AoI is influenced by a balance between increased peripheral-placental and decreased cerebral resistances. Personalizing the model allows for quantifying the balance between cerebral and peripheral-placental remodeling, thus providing potentially novel information to aid clinical follow up.     

Long-term intercalation of residual hemin in erythrocyte membranes distorts the cell

The effect of long-term incubation of residual globin-free hemin on whole red blood cell and isolated cytoskeletal proteins was studied. Hemin at concentrations found in pathological red cells was inserted to fresh erythrocytes. Increased hemolysis developed in the hemin-containing cells after a few days at 37 degrees C and after about four weeks at 4 degrees C. Since lipid and hemoglobin peroxidation did not depend on the presence of hemin, time-dependent effects on the cytoskeleton proteins were studied. Observations were: (1) spectrin and protein 4.1 exhibited a time-dependent increasing tendency to undergo hemin-induced peroxidative crosslinking. (2) The ability of the serum proteins, albumin and hemopexin, to draw hemin from spectrin, actin and protein 4.1 decreased with time of incubation with hemin. These results were attributed to time-dependent hemin-induced denaturation of the cytoskeletal proteins. Albumin taken as a control for physiological hemin trap was unaffected by hemin. Small amounts of hemo-spectrin (2-5%) were analyzed in circulating normal cells, and this in vivo hemo-spectrin also failed to release hemin. It was concluded that slow accumulation of hemin, a phenomenon increased in pathological cells, is a toxic event causing erythrocyte destruction.     

Non-Newtonian Blood Flow in Left Coronary Arteries with Varying Stenosis: A Comparative Study

This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that the highest wall shear stress (WSS), velocity and pressure are found in artery having stenosis in all the three branches of LCA. The use of Newtonian blood model is a good approximation for steady as well as transient blood flow boundary conditions if shear rate is above 100 s-1. However, the assumption of steady blood flow results in underestimating the values of flow parameters such as wall shear stress, pressure and velocity.     

Analysis of blood flow in the entire coronary arterial tree

A hemodynamic analysis of coronary blood flow must be based on the measured branching pattern and vascular geometry of the coronary vasculature. We recently developed a computer reconstruction of the entire coronary arterial tree of the porcine heart based on previously measured morphometric data. In the present study, we carried out an analysis of blood flow distribution through a network of millions of vessels that includes the entire coronary arterial tree down to the first capillary branch. The pressure and flow are computed throughout the coronary arterial tree based on conservation of mass and momentum and appropriate pressure boundary conditions. We found a power law relationship between the diameter and flow of each vessel branch. The exponent is approximately 2.2, which deviates from Murray's prediction of 3.0. Furthermore, we found the total arterial equivalent resistance to be 0.93, 0.77, and 1.28 mmHg.ml(-1).s(-1).g(-1) for the right coronary artery, left anterior descending coronary artery, and left circumflex artery, respectively. The significance of the present study is that it yields a predictive model that incorporates some of the factors controlling coronary blood flow. The model of normal hearts will serve as a physiological reference state. Pathological states can then be studied in relation to changes in model parameters that alter coronary perfusion.     

Relativistic DFT calculation of the reaction cycle intermediates of [NiFe] hydrogenase: a contribution to understanding the enzymatic mechanism

Structures and spectroscopic observables of the paramagnetic intermediates of the enzymatic reaction cycle of the metalloenzyme [NiFe] hydrogenase were calculated using relativistic density functional theory (DFT) within the zero-order regular approximation (ZORA). By comparing experimental and calculated magnetic resonance parameters (g- and hyperfine tensors) for the states Ni-A, Ni-B, Ni-C, Ni-L, and Ni-CO the details of the atomic composition of these paramagnetic intermediates could be elucidated that are mostly not available from X-ray structure analysis. In general, good agreement between calculated and experimental observables could be obtained. A detailed picture of the changes of the active center during the catalytic cycle was deduced from the obtained structures. Based on these results, a consistent model for the sequence of redox states including protonation steps is proposed which is important for understanding the mechanism of the [NiFe] hydrogenase.     

Role of spin state on the geometry and nuclear quadrupole resonance parameters in hemin complex

Theoretical calculations of structural parameters, 57Fe, 14N and 17 O electric field gradient (EFG) tensors for full size-hemin group have been carried out using density functional theory. These calculations are intended to shed light on the difference between the geometry parameters, nuclear quadrupole coupling constants (QCC), and asymmetry parameters (eta Q) found in three spin states of hemin; doublet, quartet and sextet. The optimization results reveal a significant change for propionic groups and porphyrin plane in different spin states. It is found that all principal components of EFG tensor at the iron site are sensitive to electronic and geometry structures. A relationship between the EFG tensor at the 14N and 17 O sites and the spin state of hemin complex is also detected.     

The interaction of hemin with skeletal muscle actin

The ability of actin to interact with hemin was studied. It was found that the Soret absorption band of hemin changes in the presence of actin and that hemin is capable of quenching the fluorescence intensity of actin. These findings were indicative of hemin binding to actin. The binding constant for the high affinity site was calculated to be 5.3 X 10(6) M-1. The amounts of native G- and F-actin were estimated by their DNAase I inhibition activity. It was observed that the binding of hemin to G-actin is followed by a slow decrease in the ability of actin to inhibit DNAase I activity and to polymerize upon addition of salts. Binding of hemin to F-actin resulted in a gradual depolymerization of the filaments, to an inactivated form, as expressed by a reduction in the ability of hemin-bound F-actin to inhibit DNAase I activity in the absence as well as in the presence of guanidine-HCl. Electron microscopy studies further corroborated these findings by demonstrating that: (1) hemin-bound G-actin failed to show formation of polymers when salts were added; (2) a marked reduction in the amount of actin polymers was observed in the specimens examined 24 h after mixing with hemin. It is suggested that the elevated amounts of free hemin formed under pathological conditions, might be toxic to cells by interfering with actin polymerization cycles.     

Generalized Linear Dynamics of a Plant-Parasitic Nematode Population and the Economic Evaluation of Crop Rotations

In 1-year experiments, the final population density of nematodes is usually modeled as a function of initial density. Often, estimation of the parameters is precarious because nematode measurements, although laborious and expensive, are imprecise and the range in initial densities may be small. The estimation procedure can be improved by using orthogonal regression with a parameter for initial density on each experimental unit. In multi-year experiments parameters of a dynamic model can be estimated with optimization techniques like simulated annealing or Bayesian methods such as Markov chain Monte Carlo (MCMC). With these algorithms information from different experiments can be combined. In multi-year dynamic models, the stability of the steady states is an important issue. With chaotic dynamics, prediction of densities and associated economic loss will be possible only on a short timescale. In this study, a generic model was developed that describes population dynamics in crop rotations. Mathematical analysis showed stable steady states do exist for this dynamic model. Using the Metropolis algorithm, the model was fitted to data from a multi-year experiment on Pratylenchus penetrans dynamics with treatments that varied between years. For three crops, parameters for a yield loss assessment model were available and gross margin of the six possible rotations comprising these three crops and a fallow year were compared at the steady state of nematode density. Sensitivity of mean gross margin to changes in the parameter estimates was investigated. We discuss the general applicability of the dynamic rotation model and the opportunities arising from combination of the model with Bayesian calibration techniques for more efficient utilization and collection of data relevant for economic evaluation of crop rotations.     

Estimation of kinetic parameters in a structured yeast model using regularisation.

In this work, a procedure for estimating kinetic parameters in biochemically structured models was developed. The approach is applicable when the structure of a kinetic model has been set up and the kinetic parameters should be estimated. The procedure consists of five steps. First, initial values were found in or calculated from literature. Hereafter using sensitivity analysis the most sensitive parameters were identified. In the third step physiological knowledge was combined with the parameter sensitivities to manually tune the most sensitive parameters. In step four, a global optimisation routine was applied for simultaneous estimation of the most sensitive parameters identified during the sensitivity analysis. Regularisation was included in the simultaneous estimation to reduce the effect of insensitive parameters. Finally, confidence intervals for the estimated parameters were calculated. This parameter estimation approach was demonstrated on a biochemically structured yeast model containing 11 reactions and 37 kinetic constants as a case study.     

Analysis of the plant architecture via tree-structured statistical models: the hidden Markov tree models

Plant architecture is the result of repetitions that occur through growth and branching processes. During plant ontogeny, changes in the morphological characteristics of plant entities are interpreted as the indirect translation of different physiological states of the meristems. Thus connected entities can exhibit either similar or very contrasted characteristics. We propose a statistical model to reveal and characterize homogeneous zones and transitions between zones within tree-structured data: the hidden Markov tree (HMT) model. This model leads to a clustering of the entities into classes sharing the same 'hidden state'. The application of the HMT model to two plant sets (apple trees and bush willows), measured at annual shoot scale, highlights ordered states defined by different morphological characteristics. The model provides a synthetic overview of state locations, pointing out homogeneous zones or ruptures. It also illustrates where within branching structures, and when during plant ontogeny, morphological changes occur. However, the labelling exhibits some patterns that cannot be described by the model parameters. Some of these limitations are addressed by two alternative HMT families.     

Binding reaction of hemin to globin

Binding of hemin to globin was studied in the presence of 25 mM caffeine by measuring CD and optical absorption changes in the Soret region. CD and optical absorption spectra after mixing equimolar amounts of hemin and globin were the same as those of ferric hemoglobin. In contrast, addition of excess globin to hemin formed a complex that was distinguishable from ferric hemoglobin in terms of the CD and optical absorption spectra. By comparing the spectra of the complex with those of various hemoglobin derivatives, it was concluded that the complex was globin which carried a hemin exclusively on the alpha chain. This means that the alpha chain of the globin molecule has a greater affinity for hemin than the beta chain, as observed by other investigators using hemin-cyanide. The rate of binding of hemin to globin was estimated by the use of CD and optical absorption stopped-flow apparatus. The rate of hemin binding to the alpha chain of globin was obtained by mixing hemin and excess globin, and that to the beta chain was obtained by mixing equimolar concentrations of hemin and globin. The results showed that hemin was bound to the alpha chain in the globin molecule to form a transient intermediate, followed by its transformation into another intermediate, the transformation was the rate-limiting step, and the beta chain in the globin molecule had a greater affinity for hemin after hemin binding to the alpha chain than before.     

Effects of Long-Term Variations in Cosmic Rhythms upon Human Biochemical Parameters

No studies of human biochemical parameters that were long enough to be comparable with the 11-year solar cycle could be found in the scientific literature. Therefore, we performed an analysis of correlations between fluctuations of blood biochemical parameters detected during a 12-year period and the time courses of some heliogeophysical factors. It was shown that the biochemical system of the blood responds to the influence of these factors. The study was based on 443 results of biochemical tests and 4883 daily records of heliogeophysical parameters. It was shown that the system of biochemical parameters changes synchronously with the impacts studied. This follows from similar spectral harmonics and periods of these physiological and physical processes, including the total correlative estimate (criterion function) of the biochemical parameters, which adequately describes functional changes in the biochemical system of the blood.     

Mathematical model for the estimation of hemodynamic and oxygenation variables by tissue spectroscopy

This article presents a quasistatic, compartmental model of tissue-level hemodynamics and oxygenation that leads to a set of formulas, which is suitable to calculate important physiological variables from the mean tissue concentration and saturation of hemoglobin, measured by tissue spectroscopy. Dimensioned quantities are represented relative to their baseline value in the equations (relative value = perturbed/baseline). All model parameters are non-dimensional. The model is based and extends on a number of previous works: previous models of similar aim and scope are consolidated, and every critical assumptions and approximations are treated explicitly; extensions include for example the incorporation of the Fahraeus-effect and the separate estimation of the volume changes of the arterial and the venous compartments. The information content of spectroscopic data alone is shown to be valuable, but limited: the relative venous volume, the oxygen extraction fraction and the relative cellulovascular coupling (defined as the ratio of blood flow and oxygen consumption) can be calculated from these data, if the alterations in arterial blood volume are negligible. The number of variables estimated by the derived formulas can be increased if local blood flow is measured simultaneously: in this case, the relative arterial and venous volume and resistance, the oxygen extraction fraction, and the relative oxygen consumption can be determined. Given that this model considers arterial blood pressure, saturation and hematocrit as its inputs, when measured, the model becomes applicable in such conditions as hyper- or hypotension, hypoxic hypoxia, hemodilution and hemorrhage, where these variables do change. The estimation of the changes in arterial resistance can be applied to estimate the extent of an autoregulatory response.