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INTRODUCTION: The ionic basis underlying the negative chronotropic effect of acetylcholine (ACh) on sinoatrial (SA) node cells is unresolved and controversial. In the present study, mathematical modeling was used to address this issue. METHODS AND RESULTS: The known concentration-dependent effects of ACh on iK,ACh, iCa,L, and i(f) were introduced into models of rabbit central and peripheral SA node cells. In the central and peripheral models, 9 x 10(-8) and 14 x 10(-8) M ACh, respectively, caused a 50% decrease in pacemaking rate, whereas in rabbit SA node to approximately 7.4 x 10(-8) M ACh caused such a decrease. In the models, iK,ACh was primarily responsible for the decrease and actions of ACh on iCa,L or i(f) alone caused a negligible effect. Although the inhibition of i(f) did not directly contribute to the chronotropic effect, it was indirectly important, because it minimized the opposition by i(f ) to the decrease of rate caused by activation of iK,ACh. The central model was more sensitive to ACh than the peripheral model. CONCLUSION: The chronotropic effect of ACh is principally the result of activation of iK,ACh, and inhibition of iCa,L plays little or no role. Inhibition of i(f) and possible inhibition of ib,Na play an important facilitative role by reducing the ability of i(f) and ib,Na to curtail the chronotropic effect caused by activation of iK,ACh.
\n \n\n \n \nCardiovascular disease, and the cardiovascular side effects of drugs, are essentially multifactorial problems involving interactions between many proteins, dependent on highly organized cell, tissue and organ structures. This is one reason why the side effects of drugs are often unanticipated. It is impossible to unravel such problems without using a systems approach, i.e. focussing on processes, not just molecular components. This inevitably involves modelling as the interactions require quantitative analysis. Modelling is a tool of analysis aimed at understanding, first, and predicting, eventually. We illustrate these principles using modelling of the heart. Models of the cardiac myocyte have benefited from several decades of interaction between experimentation and simulation. They are now sufficiently detailed to have been of use in the development of new drug compounds like ranolazine and ivabradine. With the help of cardiac modelling, we have also been able to unravel the mechanisms underlying the beneficial effect of sodium calcium exchange block for long QT syndrome (LQTS) 2 and LQTS3 patients. Detailed models of the interaction between ion channels and blocking agents provide the basis for modelling drug action from basic principles and predict changes in the inhomogeneous tissue of the heart. We demonstrate that mathematical models are beneficial for unravelling the complex interactions of pharmacodynamics in the heart. Embedding these detailed biophysical cellular scale models into anatomically correct models of the ventricle geometry will enable reconstructions of Torsades de Pointes arrhythmias and of fibrillation, providing a mechanism for linking detailed cellular scale experimental data to clinical applications.
\n \n\n \n \nThe new vogue for systems biology is an important development. It is time to complement reductionist molecular biology by integrative approaches. But this welcome development is in danger of losing its way. Many of the early implementations of the approach are very low level, in some cases hardly more than an extension of genomics and bioinformatics. In this paper, I outline some general principles that could form the basis of systems biology as a truly multilevel approach. We need the insights obtained from a higher level analysis in order to succeed at the lower levels. Higher levels in biological systems impose boundary conditions on the lower levels. Without understanding those conditions and their effects, we will be seriously restricted in understanding the logic of living systems. Sydney Brenner has insisted that \"the cell is the correct level of abstraction.\" I would go further and insist on the value of abstraction at even higher levels than the cell, while recognizing the cell as a landmark level of biological organization. The principles outlined are illustrated with examples from cardiac and other aspects of physiology and biochemistry.
\n \n\n \n \nIn pathological conditions, the exchanger may generate deleterious calcium entry. A drug that inhibited calcium entry, while still allowing transport of calcium out of the cell would then seem attractive. In fact, this is impossible for thermodynamic reasons. Inhibitors may appear to be more effective when the exchanger is operating in net calcium entry mode than in calcium exit mode. This is, however, always attributable to differences in conditions because there is strong internal sodium dependence of drug action on the exchanger. When the exchanger is operating near equilibrium, drug action is found to be equally effective in both directions.
\n \n\n \n \nCo-localization of Na+/Ca2+ exchangers (NCX) with ryanodine receptors (RyRs) is debated. We incorporate local NCX current in a biophysically detailed model of L-type Ca2+ channels (LCCs) and RyRs and study the effect of NCX on the regulation of Ca2+-induced Ca2+ release and the shape of the action potential. In canine ventricular cells, under pathological conditions, e.g., impaired LCCs, local NCXs become an enhancer of sarcoplasmic reticulum release. Under such conditions incorporation of local NCXs is critical to accurately capture mechanisms of excitation-contraction coupling.
\n \n\n \n \nThe effects of NCX knockout were determined in a variety of cardiac cell models. Those of the mouse and rat ventricles, and of atrial cells in other species behave similarly to the experiments on mouse ventricle showing only small effects, and considerable tolerance of NCX knockout. Models of ventricular cells with high action potential plateaus, however, are more sensitive and require compensatory mechanisms to adjust other conductance parameters to enable the cells to resist NCX knockout. The effects can therefore be expected to be species-specific, and it is not possible to extrapolate the mouse results to those that may occur in the Guinea pig or human.
\n \n\n \n \nUnderstanding the logic of living systems requires knowledge of the mechanisms involved at the levels at which functionality is expressed. This information does not reside in the genome, nor even in the individual proteins that genes code for. No functionality is expressed at these levels. It emerges as the result of interactions between many proteins relating to each other in multiple cascades and in interaction with the cellular environment. There is, therefore, no alternative to copying nature and computing these interactions to determine the logic of healthy and diseased states. The rapid growth in biological databases, models of cells, tissues and organs and the development of powerful computing hardware and algorithms have made it possible to explore functionality in a quantitative manner all the way from the level of genes to the physiological function of whole organs and regulatory systems. I use models of the heart to demonstrate that we can now go all the way from individual genetic information (on mutations, for example) to exploring the consequences at a whole organ level.
\n \n\n \n \nCalculations using the Hodgkin-Huxley and one-dimensional cable equations have been performed to determine the expected sensitivity of conduction and refractoriness to changes in the time constant of sodium channel deactivation at negative potentials, as reported experimentally by Rosen (Bioelectromagnetics 24 (2003) 517) when voltage-gated sodium channels are exposed to a 125 mT static magnetic field. The predicted changes in speed of conduction and refractory period are very small.
\n \n\n \n \nSuccessful biological analysis requires that we understand the functional interactions between key components of cells, organs and systems, and how these interactions change in disease. This information resides neither in the genome nor in the individual proteins that genes encode. It lies at the level of protein interactions within the context of sub-cellular, cellular, tissue, organ and system structures. There is therefore no alternative to copying Nature and computing these interactions to determine the logic of healthy and diseased states. The rapid growth in biological databases, models of cells, tissues and organs, and the development of powerful computing hardware and algorithms have made it possible to explore functionality in a quantitative manner all the way from the level of genes to the physiological function of whole organs and regulatory systems. Systems biology of the 21st century is set to become highly quantitative, and therefore one of the most computer-intensive disciplines.
\n \n\n \n \nThe first systems analysis of the functioning of an organism was Claude Bernard's concept of the constancy of the internal environment (le milieu int\u00e9rieur), since it implied the existence of control processes to achieve this. He can be regarded, therefore, as the first systems biologist. The new vogue for systems biology today is an important development, since it is time to complement reductionist molecular biology by integrative approaches. Claude Bernard foresaw that this would require the application of mathematics to biology. This aspect of Claude Bernard's work has been neglected by physiologists, which is why we are not as ready to contribute to the development of systems biology as we should be. In this paper, I outline some general principles that could form the basis of systems biology as a truly multilevel approach from a physiologist's standpoint. We need the insights obtained from higher-level analysis in order to succeed even at the lower levels. The reason is that higher levels in biological systems impose boundary conditions on the lower levels. Without understanding those conditions and their effects, we will be seriously restricted in understanding the logic of living systems. The principles outlined are illustrated with examples from various aspects of physiology and biochemistry. Applying and developing these principles should form a major part of the future of physiology.
\n \n\n \n \nCardiac pacemaking in the sinoatrial (SA) node and atrioventricular (AV) node is generated by an interplay of many ionic currents, one of which is the funny pacemaker current (If). To understand the functional role of If in two different pacemakers, comparative studies of spontaneous activity and expression of the HCN channel in mouse SA node and AV node were performed. The intrinsic cycle length (CL) is 179+/-2.7 ms (n=5) in SA node and 258+/-18.7 ms (n=5) in AV node. Blocking of If current by 1 micromol/L ZD7288 increased the CL to 258+/-18.7 ms (n=5) and 447+/-92.4 ms (n=5) in SA node and AV node, respectively. However, the major HCN channel, HCN4 expressed at low level in the AV node compared to the SA node. To clarify the discrepancy between the functional importance of If and expression level of HCN4 channel, a SA node cell model was used. Increasing the If conductance resulted in decreasing in the CL in the model, which explains the high pacemaking rate and high expression of HCN channel in the SA node. Resistance to the blocking of If in the SA node might result from compensating effects from other currents (especially voltage sensitive currents) involved in pacemaking. The computer simulation shows that the difference in the intrinsic CL could explain the difference in response to If blocking in these two cardiac nodes.
\n \n\n \n \nThe role of the Na+/Ca2+ exchanger (NCX) as the main pathway for Ca2+ extrusion from ventricular myocytes is well established. However, both the role of the Ca2+ entry mode of NCX in regulating local Ca2+ dynamics and the role of the Ca2+ exit mode during the majority of the physiological action potential (AP) are subjects of controversy. The functional significance of NCXs location in T-tubules and potential co-localization with ryanodine receptors was examined using a local Ca2+ control model of low computational cost. Our simulations demonstrate that under physiological conditions local Ca2+ and Na+ gradients are critical in calculating the driving force for NCX and hence in predicting the effect of NCX on AP. Under physiological conditions when 60% of NCXs are located on T-tubules, NCX may be transiently inward within the first 100 ms of an AP and then transiently outward during the AP plateau phase. Thus, during an AP NCX current (INCX) has three reversal points rather than just one. This provides a resolution to experimental observations where Ca2+ entry via NCX during an AP is inconsistent with the time at which INCX is thought to become inward. A more complex than previously believed dynamic regulation of INCX during AP under physiological conditions allows us to interpret apparently contradictory experimental data in a consistent conceptual framework. Our modelling results support the claim that NCX regulates the local control of Ca2+ and provide a powerful tool for future investigations of the control of sarcoplasmic reticulum (SR) Ca2+ release under pathological conditions.
\n \n\n \n \nBioengineering analyses of physiological systems use the computational solution of physical conservation laws on anatomically detailed geometric models to understand the physiological function of intact organs in terms of the properties and behaviour of the cells and tissues within the organ. By linking behaviour in a quantitative, mathematically defined sense across multiple scales of biological organization--from proteins to cells, tissues, organs and organ systems--these methods have the potential to link patient-specific knowledge at the two ends of these spatial scales. A genetic profile linked to cardiac ion channel mutations, for example, can be interpreted in relation to body surface ECG measurements via a mathematical model of the heart and torso, which includes the spatial distribution of cardiac ion channels throughout the myocardium and the individual kinetics for each of the approximately 50 types of ion channel, exchanger or pump known to be present in the heart. Similarly, linking molecular defects such as mutations of chloride ion channels in lung epithelial cells to the integrated function of the intact lung requires models that include the detailed anatomy of the lungs, the physics of air flow, blood flow and gas exchange, together with the large deformation mechanics of breathing. Organizing this large body of knowledge into a coherent framework for modelling requires the development of ontologies, markup languages for encoding models, and web-accessible distributed databases. In this article we review the state of the field at all the relevant levels, and the tools that are being developed to tackle such complexity. Integrative physiology is central to the interpretation of genomic and proteomic data, and is becoming a highly quantitative, computer-intensive discipline.
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