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Cardiac 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.
\n \n\n \n \nInteraction between a membrane oscillator generated by voltage-dependent ion channels and an intracellular calcium signal oscillator was present in the earliest models (1984 to 1985) using representations of the sarcoplasmic reticulum. Oscillatory release of calcium is inherent in the calcium-induced calcium release process. Those historical results fully support the synthesis proposed in the articles in this review series. The oscillator mechanisms do not primarily compete with each; they entrain each other. However, there is some asymmetry: the membrane oscillator can continue indefinitely in the absence of the calcium oscillator. The reverse seems to be true only in pathological conditions. Studies from tissue-level work and on the development of the heart also provide valuable insights into the integrative action of the cardiac pacemaker.
\n \n\n \n \nThe majority of Na+ channels in the heart are composed of the tetrodotoxin (TTX)-resistant (KD, 2-6 microm) Nav1.5 isoform; however, recently it has been shown that TTX-sensitive (KD, 1-10 nm) neuronal Na+ channel isoforms (Nav1.1, Nav1.3 and Nav1.6) are also present and functionally important in the myocytes of the ventricles and the sinoatrial (SA) node. In the present study, in mouse SA node pacemaker cells, we investigated Na+ currents under physiological conditions and the expression of cardiac and neuronal Na+ channel isoforms. We identified two distinct Na+ current components, TTX resistant and TTX sensitive. At 37 degrees C, TTX-resistant iNa and TTX-sensitive iNa started to activate at approximately -70 and approximately -60 mV, and peaked at -30 and -10 mV, with a current density of 22 +/- 3 and 18 +/- 1 pA pF(-1), respectively. TTX-sensitive iNa inactivated at more positive potentials as compared to TTX-resistant iNa. Using action potential clamp, TTX-sensitive iNa was observed to activate late during the pacemaker potential. Using immunocytochemistry and confocal microscopy, different distributions of the TTX-resistant cardiac isoform, Nav1.5, and the TTX-sensitive neuronal isoform, Nav1.1, were observed: Nav1.5 was absent from the centre of the SA node, but present in the periphery of the SA node, whereas Nav1.1 was present throughout the SA node. Nanomolar concentrations (10 or 100 nm) of TTX, which block TTX-sensitive iNa, slowed pacemaking in both intact SA node preparations and isolated SA node cells without a significant effect on SA node conduction. In contrast, micromolar concentrations (1-30 microm) of TTX, which block TTX-resistant iNa as well as TTX-sensitive iNa, slowed both pacemaking and SA node conduction. It is concluded that two Na+ channel isoforms are important for the functioning of the SA node: neuronal (putative Nav1.1) and cardiac Nav1.5 isoforms are involved in pacemaking, although the cardiac Nav1.5 isoform alone is involved in the propagation of the action potential from the SA node to the surrounding atrial muscle.
\n \n\n \n \nRelating genotypes to phenotypes is problematic not only owing to the extreme complexity of the interactions between genes, proteins and high-level physiological functions but also because the paradigms for genetic causality in biological systems are seriously confused. This paper examines some of the misconceptions, starting with the changing definitions of a gene, from the cause of phenotype characters to the stretches of DNA. I then assess whether the 'digital' nature of DNA sequences guarantees primacy in causation compared to non-DNA inheritance, whether it is meaningful or useful to refer to genetic programs, and the role of high-level (downward) causation. The metaphors that served us well during the molecular biological phase of recent decades have limited or even misleading impacts in the multilevel world of systems biology. New paradigms are needed if we are to succeed in unravelling multifactorial genetic causation at higher levels of physiological function and so to explain the phenomena that genetics was originally about. Because it can solve the 'genetic differential effect problem', modelling of biological function has an essential role to play in unravelling genetic causation.
\n \n\n \n \nMarkov models (MMs) represent a generalization of Hodgkin-Huxley models. They provide a versatile structure for modelling single channel data, gating currents, state-dependent drug interaction data, exchanger and pump dynamics, etc. This paper uses examples from cardiac electrophysiology to discuss aspects related to parameter estimation. (i) Parameter unidentifiability (found in 9 out of 13 of the considered models) results in an inability to determine the correct layout of a model, contradicting the idea that model structure and parameters provide insights into underlying molecular processes. (ii) The information content of experimental voltage step clamp data is discussed, and a short but sufficient protocol for parameter estimation is presented. (iii) MMs have been associated with high computational cost (owing to their large number of state variables), presenting an obstacle for multicellular whole organ simulations as well as parameter estimation. It is shown that the stiffness of models increases computation time more than the number of states. (iv) Algorithms and software programs are provided for steady-state analysis, analytical solutions for voltage steps and numerical derivation of parameter identifiability. The results provide a new standard for ion channel modelling to further the automation of model development, the validation process and the predictive power of these models.
\n \n\n \n \nBiophysics at the systems level, as distinct from molecular biophysics, acquired its most famous paradigm in the work of Hodgkin and Huxley, who integrated their equations for the nerve impulse in 1952. Their approach has since been extended to other organs of the body, notably including the heart. The modern field of computational biology has expanded rapidly during the first decade of the twenty-first century and, through its contribution to what is now called systems biology, it is set to revise many of the fundamental principles of biology, including the relations between genotypes and phenotypes. Evolutionary theory, in particular, will require re-assessment. To succeed in this, computational and systems biology will need to develop the theoretical framework required to deal with multilevel interactions. While computational power is necessary, and is forthcoming, it is not sufficient. We will also require mathematical insight, perhaps of a nature we have not yet identified. This article is therefore also a challenge to mathematicians to develop such insights.
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