Vladimir E. Bondarenko

C-Type Inactivation Involves a Significant Decrease in the Intracellular Aqueous Pore Volume of Kv1.4 K+ Channels Expressed in Xenopus Oocytes

Channels are water‐filled membrane‐spanning proteins, which undergo conformational changes as they gate, i.e. open or close. These conformational changes affect both the shape of the channel and the volume of the water‐filled pore. We measured the changes in pore volume associated with activation, deactivation, C‐type inactivation and recovery in an N‐terminal‐deleted mutant of the Kv1.4 K+ channel (Kv1.4ΔN) expressed in Xenopus oocytes. We used giant‐patch and cut‐open oocyte voltage clamp techniques and applied solutes which are too large to enter the pore mouth to exert osmotic pressure and thus favour smaller pore volume conformations. Applied intracellular osmotic pressure (300 mm sucrose) sped inactivation (time constants (τinactivation): control, 0.66 ± 0.09 s; hyperosmotic solution, 0.29 ± 0.04 s; n= 5, P < 0.01), sped deactivation (τdeactivation: control, 18.8 ± 0.94 ms; hyperosmotic solution, 8.01 ± 1.92 ms; n= 5, P < 0.01), and slowed activation (τactivation: control, 1.04 ± 0.05 ms; hyperosmotic solution, 1.96 ± 0.31 ms; n= 5, P < 0.01). These effects were reversible and solute independent. We estimated the pore volume change on inactivation to be about 4500 Å3. Osmotic pressure had no effect when applied extracellularly. These data suggest that the intracellular side of the pore closes during C‐type inactivation and the volume change is similar to that associated with activation or deactivation. This is also similar to the pore volume estimated from the crystal structure of KcsA and MthK K+ channels. Intracellular osmotic pressure also strongly inhibited re‐opening currents associated with recovery from inactivation, which is consistent with a physical similarity between the C‐type inactivated and resting closed state.

Activation properties of Kv4.3 channels: time, voltage and [K+]o dependence

Rapidly inactivating, voltage‐dependent K+ currents play important roles in both neurones and cardiac myocytes. Kv4 channels form the basis of these currents in many neurones and cardiac myocytes and their mechanism of inactivation appears to differ significantly from that reported for Shaker and Kv1.4 channels. In most channel gating models, inactivation is coupled to the kinetics of activation. Hence, there is a need for a rigorous model based on comprehensive experimental data on Kv4.3 channel activation. To develop a gating model of Kv4.3 channel activation, we studied the properties of Kv4.3 channels in Xenopus oocytes, without endogenous KChIP2 ancillary subunits, using the perforated cut‐open oocyte voltage clamp and two‐electrode voltage clamp techniques. We obtained high‐frequency resolution measurements of the activation and deactivation properties of Kv4.3 channels. Activation was sigmoid and well described by a fourth power exponential function. The voltage dependence of the activation time constants was best described by a biexponential function corresponding to at least two different equivalent charges for activation. Deactivation kinetics are voltage dependent and monoexponential. In contrast to other voltage‐sensitive K+ channels such as HERG and Shaker, we found that elevated extracellular [K+] modulated the activation process by slowing deactivation and stabilizing the open state. Using these data we developed a model with five closed states and voltage‐dependent transitions between the first four closed states coupled to a voltage‐insensitive transition between the final closed (partially activated) state and the open state. Our model closely simulates steady‐state and kinetic activation and deactivation data.

Transmural heterogeneity of repolarization and Ca2+ handling in a model of mouse ventricular tissue

Mouse hearts have a diversity of action potentials (APs) generated by the cardiac myocytes from different regions. Recent evidence shows that cells from the epicardial and endocardial regions of the mouse ventricle have a diversity in Ca(2+) handling properties as well as K(+) current expression. To examine the mechanisms of AP generation, propagation, and stability in transmurally heterogeneous tissue, we developed a comprehensive model of the mouse cardiac cells from the epicardial and endocardial regions of the heart. Our computer model simulates the following differences between epicardial and endocardial myocytes: 1) AP duration is longer in endocardial and shorter in epicardial myocytes, 2) diastolic and systolic intracellular Ca(2+) concentration and intracellular Ca(2+) concentration transients are higher in paced endocardial and lower in epicardial myocytes, 3) Ca(2+) release rate is about two times larger in endocardial than in epicardial myocytes, and 4) Na(+)/Ca(2+) exchanger rate is greater in epicardial than in endocardial myocytes. Isolated epicardial cells showed a higher threshold for stability of AP generation but more complex patterns of AP duration at fast pacing rates. AP propagation velocities in the model of two-dimensional tissue are close to those measured experimentally. Simulations show that heterogeneity of repolarization and Ca(2+) handling are sustained across the mouse ventricular wall. Stability analysis of AP propagation in the two-dimensional model showed the generation of Ca(2+) alternans and more complex transmurally heterogeneous irregular structures of repolarization and intracellular Ca(2+) transients at fast pacing rates.

Control and `anticontrol' of chaos in an analog neural network with time delay

Abstract The results of study of an analog neural network model with time delay which produces chaos similar to the human and animal EEGs are presented. It is found that the time delay plays an important role in the control of chaos and production of different chaotic and non-chaotic outputs. An increase in neural network asymmetry (increase of the neuron excitability) leads to the phenomenon similar to the epilepsy. Two cases of the chaos control by the action of the external low-dimensional chaotic force are considered: (1) on the neural network with developed non-chaotic activity (anticontrol); (2) on the neural network with developed low-dimensional chaos. In the first case, we obtained suppression of pathological non-chaotic activity at the optimal amplitude of external low-dimensional chaotic force. In both cases, the chaotic neural network demonstrates the phenomenon similar to a stochastic resonance for internal spontaneous oscillations under the action of external low-dimensional chaotic force instead of random noise, as studied previously.

A Compartmentalized Mathematical Model of the β1-Adrenergic Signaling System in Mouse Ventricular Myocytes

The β1-adrenergic signaling system plays an important role in the functioning of cardiac cells. Experimental data shows that the activation of this system produces inotropy, lusitropy, and chronotropy in the heart, such as increased magnitude and relaxation rates of [Ca2+]i transients and contraction force, and increased heart rhythm. However, excessive stimulation of β1-adrenergic receptors leads to heart dysfunction and heart failure. In this paper, a comprehensive, experimentally based mathematical model of the β1-adrenergic signaling system for mouse ventricular myocytes is developed, which includes major subcellular functional compartments (caveolae, extracaveolae, and cytosol). The model describes biochemical reactions that occur during stimulation of β1-adrenoceptors, changes in ionic currents, and modifications of Ca2+ handling system. Simulations describe the dynamics of major signaling molecules, such as cyclic AMP and protein kinase A, in different subcellular compartments; the effects of inhibition of phosphodiesterases on cAMP production; kinetics and magnitudes of phosphorylation of ion channels, transporters, and Ca2+ handling proteins; modifications of action potential shape and duration; magnitudes and relaxation rates of [Ca2+]i transients; changes in intracellular and transmembrane Ca2+ fluxes; and [Na+]i fluxes and dynamics. The model elucidates complex interactions of ionic currents upon activation of β1-adrenoceptors at different stimulation frequencies, which ultimately lead to a relatively modest increase in action potential duration and significant increase in [Ca2+]i transients. In particular, the model includes two subpopulations of the L-type Ca2+ channels, in caveolae and extracaveolae compartments, and their effects on the action potential and [Ca2+]i transients are investigated. The presented model can be used by researchers for the interpretation of experimental data and for the developments of mathematical models for other species or for pathological conditions.

S3b Amino Acid Substitutions and Ancillary Subunits Alter the Affinity of Heteropoda venatoria Toxin 2 for Kv4.3

Heteropoda venatoria toxin 2 (HpTx2) is an inhibitor cystine knot (ICK)-gating modifier toxin that selectively inhibits Kv4 channels. To characterize the molecular determinants of interaction, we performed alanine scanning of the Kv4.3 S3b region. HpTx2-Kv4.3 interaction had an apparent Kd value of 2.3 μM. Two alanine mutants in Kv4.3 increased Kd values to 6.4 μM for V276A and 25 μM for L275A. Simultaneous mutation of both amino acids to alanine nearly eliminated toxin interaction. Unlike Hanatoxin and other well characterized ICK toxins, HpTx2 binding does not require a charged amino acid for interaction. To determine whether the identity of the S3b binding site amino acids altered HpTx2 specificity, we constructed Kv4.3 [LV275IF]. This mutation decreased the Kd value to 0.54 μM, suggesting that the hydrophobic character of the putative binding site is the most important property for interaction with HpTx2. One mutant, N280A, caused stronger interaction of HpTx2 with Kv4.3; the Kd value for Kv4.3 [N280A] was 0.26 μM. To understand Kv4.3-based transient outward currents in native tissues, we tested the affinity of HpTx2 for Kv4.3 coexpressed with KChIP2b. The toxins Kd value for Kv4.3 + KChIP2b was 0.95 μM. KChIP2b stabilizes the closed state of Kv4.3, suggesting that the increased toxin affinity is due to increased stabilization of the closed state. These data show that HpTx2 binding to Kv4.3 has aspects in common with other ICK gating modifier toxins but that the interventions that increase toxin affinity suggest flexibility toward channel binding that belies its unusual specificity for Kv4 channels.

A Mathematical Model of the Mouse Ventricular Myocyte Contraction

Mathematical models of cardiac function at the cellular level include three major components, such as electrical activity, Ca2+ dynamics, and cellular shortening. We developed a model for mouse ventricular myocyte contraction which is based on our previously published comprehensive models of action potential and Ca2+ handling mechanisms. The model was verified with extensive experimental data on mouse myocyte contraction at room temperature. In the model, we implemented variable sarcomere length and indirect modulation of the tropomyosin transition rates by Ca2+ and troponin. The resulting model described well steady-state force-calcium relationships, dependence of the contraction force on the sarcomere length, time course of the contraction force and myocyte shortening, frequency dependence of the contraction force and cellular contraction, and experimentally measured derivatives of the myocyte length variation. We emphasized the importance of the inclusion of variable sarcomere length into a model for ventricular myocyte contraction. Differences in contraction force and cell shortening for epicardial and endocardial ventricular myocytes were investigated. Model applicability for the experimental studies and model limitations were discussed.

Mathematical modeling mechanisms of arrhythmias in transgenic mouse heart overexpressing TNF-α.

Transgenic mice overexpressing tumor necrosis factor-α (TNF-α mice) possess many of the features of human heart failure, such as dilated cardiomyopathy, impaired Ca(2+) handling, arrhythmias, and decreased survival. Although TNF-α mice have been studied extensively with a number of experimental methods, the mechanisms of heart failure are not completely understood. We created a mathematical model that reproduced experimentally observed changes in the action potential (AP) and Ca(2+) handling of isolated TNF-α mice ventricular myocytes. To study the contribution of the differences in ion currents, AP, Ca(2+) handling, and intercellular coupling to the development of arrhythmias in TNF-α mice, we further created several multicellular model tissues with combinations of wild-type (WT)/reduced gap junction conductance, WT/prolonged AP, and WT/decreased Na(+) current (I(Na)) amplitude. All model tissues were examined for susceptibility to Ca(2+) alternans, AP propagation block, and reentry. Our modeling results demonstrated that, similar to experimental data in TNF-α mice, Ca(2+) alternans in TNF-α tissues developed at longer basic cycle lengths. The greater susceptibility to Ca(2+) alternans was attributed to the prolonged AP, resulting in larger inactivation of I(Na), and to the decreased SR Ca(2+) uptake and corresponding smaller SR Ca(2+) load. Simulations demonstrated that AP prolongation induces an increased susceptibility to AP propagation block. Programmed stimulation of the model tissues with a premature impulse showed that reduced gap junction conduction increased the vulnerable window for initiation reentry, supporting the idea that reduced intercellular coupling is the major factor for reentrant arrhythmias in TNF-α mice.

Closed-state inactivation in Kv4.3 isoforms is differentially modulated by protein kinase C

Kv4.3, with its complex open- and closed-state inactivation (CSI) characteristics, is a primary contributor to early cardiac repolarization. The two alternatively spliced forms, Kv4.3-short (Kv4.3-S) and Kv4.3-long (Kv4.3-L), differ by the presence of a 19-amino acid insert downstream from the sixth transmembrane segment. The isoforms are similar kinetically; however, the longer form has a unique PKC phosphorylation site. To test the possibility that inactivation is differentially regulated by phosphorylation, we expressed the Kv4.3 isoforms in Xenopus oocytes and examined changes in their inactivation properties after stimulation of PKC activity. Whereas there was no difference in open-state inactivation, there were profound differences in CSI. In Kv4.3-S, PMA reduced the magnitude of CSI by 24% after 14.4 s at -50 mV. In contrast, the magnitude of CSI in Kv4.3-L increased by 25% under the same conditions. Mutation of a putatively phosphorylated threonine (T504) to aspartic acid within a PKC consensus recognition sequence unique to Kv4.3-L eliminated the PMA response. The change in CSI was independent of the intervention used to increase PKC activity; identical results were obtained with either PMA or injected purified PKC. Our previously published 11-state model closely simulated our experimental data. Our data demonstrate isoform-specific regulation of CSI by PKC in Kv4.3 and show that the carboxy terminus of Kv4.3 plays an important role in regulation of CSI.

A Model of the Interaction between N-type and C-type Inactivation in Kv1.4 Channels

Kv1.4 channels are Shaker-related voltage-gated potassium channels with two distinct inactivation mechanisms. Fast N-type inactivation operates by a ball-and-chain mechanism. Slower C-type inactivation is not so well defined, but involves intracellular and extracellular conformational changes of the channel. We studied the interaction between inactivation mechanisms using two-electrode voltage-clamp of Kv1.4 and Kv1.4ΔN (amino acids 2-146 deleted to remove N-type inactivation) heterologously expressed in Xenopus oocytes. We manipulated C-type inactivation by introducing a lysine-tyrosine point mutation (K532Y, equivalent to Shaker T449Y) that diminishes C-type inactivation. We used experimental data to develop a comprehensive computer model of Kv1.4 channels to determine the interaction between activation and N- and C-type inactivation mechanisms needed to replicate the experimental data. C-type inactivation began at lower voltage preactivated states, whereas N-type inactivation was coupled directly to the open state. A model with distinct N- and C-type inactivated states was not able to reproduce experimental data, and direct transitions between N- and C-type inactivated states were required, i.e., there is coupling between N- and C-type inactivated states. C-type inactivation is the rate-limiting step determining recovery from inactivation, so understanding C-type inactivation, and how it is coupled to N-type inactivation, is critical in understanding how channels act to repetitive stimulation.