Cardiac endothelial transport and metabolism of adenosine and inosine

Optimization of Versatile Oxindoles as Selective PI3Kδ Inhibitors

The 3,3-disubstituted oxindole moiety is a versatile and rigid three-dimensionally shaped scaffold. When engineered with a purine hinge-binding core, exceptionally selective PI3Kδ kinase inhibitors were discovered by exploiting small differences in isoform selectivity pockets. Crystal structures of early lead 2f bound to PI3Kδ and PI3Kα helped rationalize the high selectivity observed with 2f. By attenuating the lypophilicity and metabolic liabilities of an oxindole moiety, we improved the preclinical species PK and solubility and reduced adenosine uptake activity. The excellent potency and kinome selectivity of 7-azaoxindole 4d and spirooxindole 5d, together with a low plasma clearance and good half-life in rat and dog, supported a low once-daily predicted human dose.

Fractal regional myocardial blood flows pattern according to metabolism, not vascular anatomy

Regional myocardial blood flows are markedly heterogeneous. Fractal analysis shows strong near-neighbor correlation. In experiments to distinguish control by vascular anatomy vs. local vasomotion, coronary flows were increased in open-chest dogs by stimulating myocardial metabolism (catecholamines + atropine) with and without adenosine. During control states mean left ventricular (LV) myocardial blood flows (microspheres) were 0.5-1 ml·g(-1)·min(-1) and increased to 2-3 ml·g(-1)·min(-1) with catecholamine infusion and to ∼4 ml·g(-1)·min(-1) with adenosine (Ado). Flow heterogeneity was similar in all states: relative dispersion (RD = SD/mean) was ∼25%, using LV pieces 0.1-0.2% of total. During catecholamine infusion local flows increased in proportion to the mean flows in 45% of the LV, "tracking" closely (increased proportionately to mean flow), while ∼40% trended toward the mean. Near-neighbor regional flows remained strongly spatially correlated, with fractal dimension D near 1.2 (Hurst coefficient 0.8). The spatial patterns remain similar at varied levels of metabolic stimulation inferring metabolic dominance. In contrast, adenosine vasodilation increased flows eightfold times control while destroying correlation with the control state. The Ado-induced spatial patterns differed from control but were self-consistent, inferring that with full vasodilation the relaxed arterial anatomy dominates the distribution. We conclude that vascular anatomy governs flow distributions during adenosine vasodilation but that metabolic vasoregulation dominates in normal physiological states.

Modeling serotonin uptake in the lung shows endothelial transporters dominate over cleft permeation

A four-region (capillary plasma, endothelium, interstitial fluid, cell) multipath model was configured to describe the kinetics of blood-tissue exchange for small solutes in the lung, accounting for regional flow heterogeneity, permeation of cell membranes and through interendothelial clefts, and intracellular reactions. Serotonin uptake data from the Multiple indicator dilution "bolus sweep" experiments of Rickaby and coworkers (Rickaby DA, Linehan JH, Bronikowski TA, Dawson CA. J Appl Physiol 51: 405-414, 1981; Rickaby DA, Dawson CA, and Linehan JH. J Appl Physiol 56: 1170-1177, 1984) and Malcorps et al. (Malcorps CM, Dawson CA, Linehan JH, Bronikowski TA, Rickaby DA, Herman AG, Will JA. J Appl Physiol 57: 720-730, 1984) were analyzed to distinguish facilitated transport into the endothelial cells (EC) and the inhibition of tracer transport by nontracer serotonin in the bolus of injectate from the free uninhibited permeation through the clefts into the interstitial fluid space. The permeability-surface area products (PS) for serotonin via the inter-EC clefts were ~0.3 ml·g⁻¹·min⁻¹, low compared with the transporter-mediated maximum PS of 13 ml·g⁻¹·min⁻¹ (with Km = ~0.3 μM and Vmax = ~4 nmol·g⁻¹·min⁻¹). The estimates of serotonin PS values for EC transporters from their multiple data sets were similar and were influenced only modestly by accounting for the cleft permeability in parallel. The cleft PS estimates in these Ringer-perfused lungs are less than half of those for anesthetized dogs (Yipintsoi T. Circ Res 39: 523-531, 1976) with normal hematocrits, but are compatible with passive noncarrier-mediated transport observed later in the same laboratory (Dawson CA, Linehan JH, Rickaby DA, Bronikowski TA. Ann Biomed Eng 15: 217-227, 1987; Peeters FAM, Bronikowski TA, Dawson CA, Linehan JH, Bult H, Herman AG. J Appl Physiol 66: 2328-2337, 1989) The identification and quantitation of the cleft pathway conductance from these studies affirms the importance of the cleft permeation.

Reexamining Michaelis-Menten enzyme kinetics for xanthine oxidase

Abbreviated expressions for enzyme kinetic expressions, such as the Michaelis-Menten (M-M) equations, are based on the premise that enzyme concentrations are low compared with those of the substrate and product. When one does progress experiments, where the solute is consumed during conversion to form a series of products, the idealized conditions are violated. Here, we analyzed data of xanthine oxidase in vitro from Escribano et al. (Biochem J 254: 829, 1988) on two conversions in series, hypoxanthine to xanthine to uric acid. Analyses were done using four models: standard irreversible M-M reactions (model 1), Escribano et al.'s M-M forward reaction expressions with product inhibition (model 2), fully reversible M-M equations (model 3), and standard differential equations allowing forward and backward reactions with mass balance accounting for binding (model 4). The results showed that the need for invoking product inhibition vanishes with more complete analyses. The reactions were not quite irreversible, so the backward reaction had a small effect. Even though the enzyme concentration was only 1-2% of the initial substrate concentrations, accounting for the fraction of solutes bound to the enzyme did influence the parameter estimates, but in this case, the M-M model overestimated Michaelis constant values by only about one-third. This article also presents the research and models in a reproducible and publicly available form.

Modeling to link regional myocardial work, metabolism and blood flows

Given the mono-functional, highly coordinated processes of cardiac excitation and contraction, the observations that regional myocardial blood flows, rMBF, are broadly heterogeneous has provoked much attention, but a clear explanation has not emerged. In isolated and in vivo heart studies the total coronary flow is found to be proportional to the rate-pressure product (systolic mean blood pressure times heart rate), a measure of external cardiac work. The same relationship might be expected on a local basis: more work requires more flow. The validity of this expectation has never been demonstrated experimentally. In this article we review the concepts linking cellular excitation and contractile work to cellular energetics and ATP demand, substrate utilization, oxygen demand, vasoregulation, and local blood flow. Mathematical models of these processes are now rather well developed. We propose that the construction of an integrated model encompassing the biophysics, biochemistry and physiology of cardiomyocyte contraction, then combined with a detailed three-dimensional structuring of the fiber bundle and sheet arrangements of the heart as a whole will frame an hypothesis that can be quantitatively evaluated to settle the prime issue: Does local work drive local flow in a predictable fashion that explains the heterogeneity? While in one sense one can feel content that work drives flow is irrefutable, the are no cardiac contractile models that demonstrate the required heterogeneity in local strain-stress-work; quite the contrary, cardiac contraction models have tended toward trying to show that work should be uniform. The object of this review is to argue that uniformity of work does not occur, and is impossible in any case, and that further experimentation and analysis are necessary to test the hypothesis.

Theoretical models for coronary vascular biomechanics: progress & challenges

A key aim of the cardiac Physiome Project is to develop theoretical models to simulate the functional behaviour of the heart under physiological and pathophysiological conditions. Heart function is critically dependent on the delivery of an adequate blood supply to the myocardium via the coronary vasculature. Key to this critical function of the coronary vasculature is system dynamics that emerge via the interactions of the numerous constituent components at a range of spatial and temporal scales. Here, we focus on several components for which theoretical approaches can be applied, including vascular structure and mechanics, blood flow and mass transport, flow regulation, angiogenesis and vascular remodelling, and vascular cellular mechanics. For each component, we summarise the current state of the art in model development, and discuss areas requiring further research. We highlight the major challenges associated with integrating the component models to develop a computational tool that can ultimately be used to simulate the responses of the coronary vascular system to changing demands and to diseases and therapies.

Microcirculation and the physiome projects

The Physiome projects comprise a loosely knit worldwide effort to define the Physiome through databases and theoretical models, with the goal of better understanding the integrative functions of cells, organs, and organisms. The projects involve developing and archiving models, providing centralized databases, and linking experimental information and models from many laboratories into self-consistent frameworks. Increasingly accurate and complete models that embody quantitative biological hypotheses, adhere to high standards, and are publicly available and reproducible, together with refined and curated data, will enable biological scientists to advance integrative, analytical, and predictive approaches to the study of medicine and physiology. This review discusses the rationale and history of the Physiome projects, the role of theoretical models in the development of the Physiome, and the current status of efforts in this area addressing the microcirculation.

Linking cellular energetics to local flow regulation in the heart

A mathematical model has been developed to explain the metabolic and energetic responses induced by abnormal routes of cardiac excitation. For example, in left bundle branch block (LBBB), both glucose uptake and flow are reduced in the septal region, similar to the situation in dogs paced at the right ventricular outflow tract. In these conditions the septum is activated early, the sarcomere lengths shorten rapidly against low left ventricular (LV) pressure, and the blood flow to the interventricular septum diminishes. In contrast, the work load and the blood flow increases in the later-activated LV free wall. To provide a logical, quantitatively appropriate representation, the model links: (1) the processes of excitation-contraction coupling; (2) regional ATP utilization for force development at the cross-bridge, for ion pumping, and for cell maintenance; (3) the regulation of demands on local fatty acid and glucose metabolism for ATP generation by glycolysis and oxidative phosphorylation; and (4) feedback regulation of blood flow to supply substrate and oxygen. The heart is considered as a cylinder composed of two parts: an early-activated region and a late-activated region in tandem, but activated separately with the time delay representing the time for excitation to spread from septum to free wall. The same model equations and parameter sets are used for the two regions. The contraction of the early-activated region stretches the other region, with the result that the early-stimulated region has diminished oxygen requirements compared to those found with simultaneous stimulation. The late-activated region has increased work and increased oxygen consumption, as seen in the intact heart. Integrating the modeling of cardiac energy metabolism with local blood flow regulation and capillary-tissue substrate exchange provides a quantitative description, an hypothesis formulated to stimulate further experimentation to test its validity. The hypothesis "explains" observations of contraction and metabolism in LBBB, but whether this concept can be extended to explain the normal flow heterogeneity in the heart remains unknown.

GENTEX, a general multiscale model for in vivo tissue exchanges and intraorgan metabolism

Endothelial cells lining myocardial capillaries not only impede transport of blood solutes to the contractile cells, but also take up and release substrates, competing with myocytes. Solutes permeating this barrier exhibit concentration gradients along the capillary. This paper introduces a generic model, GENTEX, to characterize blood-tissue exchanges. GENTEX is a whole organ model of the vascular network providing intraorgan flow heterogeneity and accounts for substrate transmembrane transport, binding and metabolism in erythrocytes, plasma, endothelial cells, interstitial space and cardiomyocytes. The model is tested here for the analysis of multiple tracer indicator dilution data on purine nucleoside metabolism in the isolated Krebs-Henseleit-perfused non-working hearts. It has been also used for analysing NMR contrast data for regional myocardial flows and for positron emission tomographic studies of cardiac receptor kinetics. The facilitating transporters, binding sites and enzymatic reactions are nonlinear elements and allow competition between substrates and a reaction sequence of up to five substrate-product reactions in a metabolic network. Strategies for application start with experiment designs incorporating inert reference tracers. For the estimation of endothelial and sarcolemmal permeability-surface area products and metabolism of the substrates and products, model solutions were optimized to fit the data from pairs of tracer injections (of either inosine or adenosine, plus the reference tracers) injected under the same circumstances a few minutes later. The results provide a self-consistent description of nucleoside metabolism in a beating well-perfused rabbit heart, and illustrate the power of the model to fit multiple datasets simultaneously.

Strategies and Tactics in Multiscale Modeling of Cell-to-Organ Systems

Modeling is essential to integrating knowledge of human physiology. Comprehensive self-consistent descriptions expressed in quantitative mathematical form define working hypotheses in testable and reproducible form, and though such models are always "wrong" in the sense of being incomplete or partly incorrect, they provide a means of understanding a system and improving that understanding. Physiological systems, and models of them, encompass different levels of complexity. The lowest levels concern gene signaling and the regulation of transcription and translation, then biophysical and biochemical events at the protein level, and extend through the levels of cells, tissues and organs all the way to descriptions of integrated systems behavior. The highest levels of organization represent the dynamically varying interactions of billions of cells. Models of such systems are necessarily simplified to minimize computation and to emphasize the key factors defining system behavior; different model forms are thus often used to represent a system in different ways. Each simplification of lower level complicated function reduces the range of accurate operability at the higher level model, reducing robustness, the ability to respond correctly to dynamic changes in conditions. When conditions change so that the complexity reduction has resulted in the solution departing from the range of validity, detecting the deviation is critical, and requires special methods to enforce adapting the model formulation to alternative reduced-form modules or decomposing the reduced-form aggregates to the more detailed lower level modules to maintain appropriate behavior. The processes of error recognition, and of mapping between different levels of model complexity and shifting the levels of complexity of models in response to changing conditions, are essential for adaptive modeling and computer simulation of large-scale systems in reasonable time.

Multiscale modeling of cardiac cellular energetics

Multiscale modeling is essential to integrating knowledge of human physiology starting from genomics, molecular biology, and the environment through the levels of cells, tissues, and organs all the way to integrated systems behavior. The lowest levels concern biophysical and biochemical events. The higher levels of organization in tissues, organs, and organism are complex, representing the dynamically varying behavior of billions of cells interacting together. Models integrating cellular events into tissue and organ behavior are forced to resort to simplifications to minimize computational complexity, thus reducing the model's ability to respond correctly to dynamic changes in external conditions. Adjustments at protein and gene regulatory levels shortchange the simplified higher-level representations. Our cell primitive is composed of a set of subcellular modules, each defining an intracellular function (action potential, tricarboxylic acid cycle, oxidative phosphorylation, glycolysis, calcium cycling, contraction, etc.), composing what we call the "eternal cell," which assumes that there is neither proteolysis nor protein synthesis. Within the modules are elements describing each particular component (i.e., enzymatic reactions of assorted types, transporters, ionic channels, binding sites, etc.). Cell subregions are stirred tanks, linked by diffusional or transporter-mediated exchange. The modeling uses ordinary differential equations rather than stochastic or partial differential equations. This basic model is regarded as a primitive upon which to build models encompassing gene regulation, signaling, and long-term adaptations in structure and function. During simulation, simpler forms of the model are used, when possible, to reduce computation. However, when this results in error, the more complex and detailed modules and elements need to be employed to improve model realism. The processes of error recognition and of mapping between different levels of model form complexity are challenging but are essential for successful modeling of large-scale systems in reasonable time. Currently there is to this end no established methodology from computational sciences.

An integrative model of coupled water and solute exchange in the heart

Physiologists have devised many models for interpreting water and solute exchange data in whole organs, but the models have typically neglected key aspects of the underlying physiology to present the simplest possible model for a given experimental situation. We have developed a physiologically realistic model of microcirculatory water and solute exchange and applied it to diverse observations of water and solute exchange in the heart. Model simulations are consistent with the results of osmotic weight transient, tracer indicator dilution, and steady-state lymph sampling experiments. The key model features that permit this unification are the use of an axially distributed blood-tissue exchange region, inclusion of a lymphatic drain in the interstitium, and the independent computation of transcapillary solute and solvent fluxes through three different pathways.

Transient transcapillary exchange of water driven by osmotic forces in the heart

Osmotic transient responses in organ weight after changes in perfusate osmolarity have implied steric hindrance to small-molecule transcapillary exchange, but tracer methods do not. We obtained osmotic weight transient data in isolated, Ringer-perfused rabbit hearts with NaCl, urea, glucose, sucrose, raffinose, inulin, and albumin and analyzed the data with a new anatomically and physicochemically based model accounting for 1) transendothelial water flux, 2) two sizes of porous passages across the capillary wall, 3) axial intracapillary concentration gradients, and 4) water fluxes between myocytes and interstitium. During steady-state conditions approximately 28% of the transcapillary water flux going to form lymph was through the endothelial cell membranes [capillary hydraulic conductivity (Lp) = 1.8 +/- 0.6 x 10-8 cm. s-1. mmHg-1], presumably mainly through aquaporin channels. The interendothelial clefts (with Lp = 4.4 +/- 1.3 x 10-8 cm. s-1. mmHg-1) account for 67% of the water flux; clefts are so wide (equivalent pore radius was 7 +/- 0.2 nm, covering approximately 0.02% of the capillary surface area) that there is no apparent hindrance for molecules as large as raffinose. Infrequent large pores account for the remaining 5% of the flux. During osmotic transients due to 30 mM increases in concentrations of small solutes, the transendothelial water flux was in the opposite direction and almost 800 times as large and was entirely transendothelial because no solute gradient forms across the pores. During albumin transients, gradients persisted for long times because albumin does not permeate small pores; the water fluxes per milliosmolar osmolarity change were 200 times larger than steady-state water flux. The analysis completely reconciles data from osmotic transient, tracer dilution, and lymph sampling techniques.

Endothelial adenosine transporter characterization in perfused guinea pig hearts

Adenosine (Ado), a smooth muscle vasodilator and modulator of cardiac function, is taken up by many cell types via a saturable transporter, blockable by dipyridamole. To quantitate the influences of endothelial cells in governing the blood-tissue exchange of Ado and its concentration in the interstitial fluid, one must define the permeability-surface area products (PS) for Ado via passive transport through interendothelial gaps [PS(g)(Ado)] and across the endothelial cell luminal membrane (PS(ecl)) in their normal in vivo setting. With the use of the multiple-indicator dilution (MID) technique in Krebs-Ringer perfused, isolated guinea pig hearts (preserving endothelial myocyte geometry) and by separating Ado metabolites by HPLC, we found permeability-surface area products for an extracellular solute, sucrose, via passive transport through interendothelial gaps [PS(g)(Suc)] to be 1.9 +/- 0.6 ml. g(-1). min(-1) (n = 16 MID curves in 4 hearts) and took PS(g)(Ado) to be 1. 2 times PS(g)(Suc). MID curves were obtained with background nontracer Ado concentrations up to 800 micrometer, partially saturating the transporter and reducing its effective PS(ecl) for Ado. The estimated maximum value for PS(ecl) in the absence of background adenosine was 1.1 +/- 0.1 ml. g(-1). min(-1) [maximum rate of transporter conformational change to move the substrate from one side of the membrane to the other (maximal velocity; V(max)) times surface area of 125 +/- 11 nmol. g(-1). min(-1)], and the Michaelis-Menten constant (K(m)) was 114 +/- 12 microM, where +/- indicates 95% confidence limits. Physiologically, only high Ado release with hypoxia or ischemia will partially saturate the transporter.