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A Mathematical Model of the Electrophysiological Alterations in Rat Ventricular Myocytes in Type-I Diabetes

Sandeep V. Pandit^*, Wayne R. Giles and Semahat S. Demir^*

^* Joint Graduate Program in Biomedical Engineering, The University of Memphis, and The University of Tennessee Health Science Center, Memphis, Tennessee USA and Department of Physiology and Biophysics, The University of Calgary, Calgary, Canada

Correspondence: Address reprint requests to Semahat S. Demir, PhD, Dept. of Biomedical Engineering, University of Memphis, 330 Engineering Technology Building, Memphis, TN 38152-3210. Tel.: 901-678-3170; Fax: 901-678-5281; E-mail: sdemir{at}memphis.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION SUMMARY ACKNOWLEDGEMENTS REFERENCES

 
Our mathematical model of the rat ventricular myocyte (Pandit et al., 2001) was utilized to explore the ionic mechanism(s) that underlie the altered electrophysiological characteristics associated with the short-term model of streptozotocin-induced, type-I diabetes. The simulations show that the observed reductions in the Ca²⁺-independent transient outward K⁺ current (I_t) and the steady-state outward K⁺ current (I_ss), along with slowed inactivation of the L-type Ca²⁺ current (I_CaL), can result in the prolongation of the action potential duration, a well-known experimental finding. In addition, the model demonstrates that the slowed reactivation kinetics of I_t in diabetic myocytes can account for the more pronounced rate-dependent action potential duration prolongation in diabetes, and that a decrease in the electrogenic Na⁺-K⁺ pump current (I_NaK) results in a small depolarization in the resting membrane potential (V_rest). This depolarization reduces the availability of the Na⁺ channels (I_Na), thereby resulting in a slower upstroke (dV/dt_max) of the diabetic action potential. Additional simulations suggest that a reduction in the magnitude of I_CaL, in combination with impaired sarcoplasmic reticulum uptake can lead to a decreased sarcoplasmic reticulum Ca²⁺ load. These factors contribute to characteristic abnormal [Ca²⁺]_i homeostasis (reduced peak systolic value and rate of decay) in myocytes from diabetic animals. In combination, these simulation results provide novel information and integrative insights concerning plausible ionic mechanisms for the observed changes in cardiac repolarization and excitation-contraction coupling in rat ventricular myocytes in the setting of streptozotocin-induced, type-I diabetes.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION SUMMARY ACKNOWLEDGEMENTS REFERENCES

 
Cardiovascular complications arising from diabetes mellitus are a leading cause of morbidity and mortality (Dillmann, 1989; Standl and Schnell, 2000). In addition to an increased incidence of coronary artery disease, the electrophysiological and the mechanical properties of the myocardium are significantly impaired (Dillmann, 1989; Mahgoub and Abd-elfattah, 1998). The rat constitutes a widely utilized experimental model used to study the effects of diabetes on the heart. In an acute model of type-I (insulin deficient) diabetes, rats are injected with streptozotocin (STZ) (100 mg/kg of body wt.), and then sacrificed 4–6 days after treatment (Shimoni et al., 1994; 1995). Rat ventricular myocytes from this short-term diabetic model exhibit a prolongation of the action potential duration (APD) (Shimoni et al., 1994; 1995), along with altered intracellular Ca²⁺ homeostasis, depicted by a small reduction in the peak systolic value, and a slower decay of the intracellular Ca²⁺ transient ([Ca²⁺]_i) (Ren and Davidoff, 1997). The marked delay in the final repolarization of the action potential may be responsible for the observed lengthening of the QT interval in diabetic patients (Robillon et al., 1999), and this can contribute to the enhanced incidence of cardiac arrhythmias (Ewing et al., 1991). It is therefore important to understand the ionic mechanism(s) that underlie the altered repolarization and the excitation-contraction (E-C) coupling associated with the short-term, type-I, model of diabetes, and to gain quantitative insights into the relationship between these variables.

Experimental studies have shown that injecting STZ results in a reduction in the densities of both the Ca²⁺-independent transient outward K⁺ current (I_t), and the steady-state outward K⁺ current (I_ss) (Shimoni et al., 1994; 1995). The subsequent decrease in the net repolarizing current is responsible for the prolongation of the APD (Shimoni et al., 1994; 1995). In contrast, the subcellular mechanisms responsible for the abnormal [Ca²⁺]_i behavior in the short-term diabetic model are not understood, although it is believed that dysfunction associated with the uptake of Ca²⁺ into the sarcoplasmic reticulum (SR) is responsible (Ren and Davidoff, 1997). Recently it was reported that freshly isolated normal adult rat ventricular myocytes maintained under cell culture conditions with hypoinsulinemia and hyperglycemia developed a phenotype (prolonged APD, slower [Ca²⁺]_i decay), somewhat similar to the one that has been described for myocytes isolated from the in vivo, short-term diabetic model (Davidoff and Ren, 1997; Ren et al., 1997). Hyperglycemic culture conditions are known to activate protein kinase C (PKC). More specifically, the isoform of PKC (PKC) is activated and translocated to the sarcolemma (Malhotra et al., 2001). PKC is the major PKC isoform in the adult rat ventricle (Bogoyevitch et al., 1993; Rybin and Steinberg, 1994). Activation of PKC not only modulates I_t and I_ss (Shimoni, 1999), as is observed in the in vivo diabetic model (Shimoni et al., 1994; 1995), but has also been shown to downregulate the densities of the L-type Ca²⁺ current (I_CaL) (Hu et al., 2000), and the Na⁺-K⁺ pump current (I_NaK) (Buhagiar et al., 2001). Results from the available experimental studies therefore suggest that multiple interdependent ionic mechanisms (I_t, I_ss, I_CaL, I_NaK, and SR uptake) can mediate the electrophysiological alterations associated with this acute, type-I model of diabetes.

One approach for obtaining novel, semiquantitative insights into the complex, nonlinear interactions between different ionic mechanisms in cardiac electrophysiology is to utilize mathematical models that are based closely on experimental findings. In this way the cardiac action potential can be reconstructed, based on detailed biophysical formulations of the underlying ionic currents, pumps, and exchangers (Rudy, 2000; Winslow et al., 2000; Noble, 2002). Recently, we have developed a comprehensive mathematical model for the cardiac action potential of adult rat ventricular myocytes (Pandit et al., 2001). The equations in this model were based on biophysically derived descriptors of experimentally recorded ionic currents, pumps, and the Na⁺-Ca²⁺ exchanger (I_NaCa) in myocytes isolated from the adult rat ventricle. The descriptions for the Ca²⁺ homeostasis mechanisms (dynamics and buffering) in the rat model were adapted (with minimal modifications) from a recent publication of Ca²⁺ handling in the canine midmyocardial cell (Winslow et al., 1999).

The main goal of the present study was to develop a mathematical representation of the diabetic phenotype by incorporating changes in the ionic mechanisms that are suggested by experimental data to underlie the altered electrophysiological characteristics in the short-term, type-I model of STZ-induced diabetes. The model is able to qualitatively simulate the prolongation of the APD in accordance with experimental results (Fig. 1). Moreover, it provides novel insights into the ionic basis for this change in the action potential profile during diabetic conditions, and illustrates the complex, nonlinear relationship between the APD and both intracellular Ca²⁺ homeostasis, and E-C coupling.

View larger version (18K): [in this window] [in a new window]   FIGURE 1  (A) Action potential waveforms for model generated control (solid line) and diabetic (dashed line) action potentials. (B) Experimentally recorded control (solid line) and diabetic (dashed line) action potentials at 1 Hz and 22°C (Shimoni et al., 1994).

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION SUMMARY ACKNOWLEDGEMENTS REFERENCES

I_Na
The density of I_Na was increased by 33%. This was based on recent experimental findings, which reported a variation in the density of I_Na in the rat ventricle, with higher expression in RV myocytes, compared with those from the LV epicardial ones (Ashamalla et al., 2001).

I_t
The density of I_t was increased by 25%, based on reported larger values of I_t in rat RV myocytes than LV epicardium (Casis et al., 1998).

I_CaL, I_ss
The densities of both I_CaL and I_ss were increased by 10%, so that the influx of Ca²⁺ ions via I_CaL (Q_CaL), and the APD₉₀ value during a simulated RV action potential were comparable to corresponding experimental measurements in rat RV myocytes (Kaprielian et al., 1999; MacDonell et al., 1998) (See the Results section for a comparison of simulated and experimental values in normal RV myocytes).

A model of the rat right ventricular cell in the setting of type-I diabetes
The following modifications were made in the computational model of the normal rat RV myocyte to represent the short-term, type-I diabetic myocyte.

I_t
The density of I_t was decreased by 32%. The formulation of I_t also consists of fast and slow inactivation variables, with the relative contribution of the slow variable to overall inactivation being 11% in the normal myocyte. This was increased to 31% in the diabetic myocyte. Both of these changes are based on experimental observations that the density of I_t is reduced, and its reactivation kinetics is slower in diabetic ventricular myocytes (Shimoni et al., 1994; 1995). The simulated current-voltage (I-V) relationship of I_t is shown in Fig. 2 A, along with corresponding experimental data, which was recorded in control and diabetic RV myocytes respectively (Shimoni et al., 1994).

View larger version (9K): [in this window] [in a new window]   FIGURE 2  (A) Simulated current-voltage (I-V) relationship for the Ca2+-independent transient outward K+ current It in control (, solid line) and diabetic (, dashed line) myocytes, which were isolated from the adult rat right ventricle (, represent experimental data from Shimoni et al., 1994). (B) Simulated current-voltage (I-V) relationship for the steady-state outward K+ current Iss in control (, solid line) and diabetic (, dashed line) myocytes, which were isolated from the adult rat right ventricle (, represent experimental data from Shimoni et al., 1994).

I_CaL
The density of I_CaL was reduced by 24%. This was based on recent experimental findings that the activation of PKC in adult rat ventricular myocytes reduces I_CaL density by 27.9 ± 2.2% (Hu et al., 2000). It has also been shown recently that the fast inactivation time constant of I_CaL is slowed (by 40%) in the chronic model of diabetes (Chattou et al., 1999). The fast inactivation time constant of I_Cal in our model was therefore reduced by 10%, to represent the acute diabetic conditions.

I_NaK
It is well-known that the Na⁺-K⁺-ATPase activity is decreased in STZ-induced diabetic rats (Kato et al., 1999). This was incorporated in the diabetic model by reducing the maximum density of I_NaK by 37%. This was based on the reported effects of PKC on I_NaK density measured in rabbit ventricular myocytes (Buhagiar et al., 2001).

The changes in I_CaL and I_NaK were incorporated based on the observation that PKC is activated and then translocated to the sarcolemmal membrane in cultured rat ventricular myocytes maintained under high extracellular glucose concentrations of 25.0 mM (Malhotra et al., 2001). This glucose level is similar to the plasma glucose concentrations recorded in the short-term, type-I, in vivo model of diabetes in rat, viz. 26.3 ± 2.15 mM (Shimoni et al., 1994).

I_BCa, I_BNa
The steady or background Ca²⁺ current (I_BCa) was reduced by 50% in the diabetic myocyte. This was done to maintain almost identical values of diastolic [Ca²⁺]_i during both control and diabetic simulations, in accordance with experimental findings (Ren and Davidoff, 1997). The peak magnitude of I_BCa during resting conditions in the control myocyte is very small (5 pA). Therefore the 50% reduction in I_BCa will not affect the action potential duration significantly in diabetes. Nevertheless, to compensate for a reduction of I_BCa, the Na⁺ background current (I_BNa) conductance was increased by 25% in the diabetic myocyte, so that the total background current (I_B) in the range of membrane potentials near rest in both control and diabetic simulations was almost identical.

SR Ca²⁺-ATPase
Although defects in the SR mechanisms have been well-studied in the chronic model of diabetes (Netticadan et al., 2001), very little quantitative information is available regarding these alterations in the acute model of diabetes (Ren and Davidoff, 1997). A recent study has shown that the SERCA2a protein density is decreased by 60% in a chronic model of diabetes (Netticadan et al., 2001). Similarly, it is known that the affinity of Ca²⁺ ions to the SR pump is also reduced in chronic diabetes (Zhong et al., 2001). Based on these observations in the chronic model of diabetes, it has been postulated that defects in the uptake of Ca²⁺ ions into the SR also underlie the abnormal [Ca²⁺]_i behavior in short-term diabetes (Ren and Davidoff, 1997). The SR Ca²⁺-ATPase scaling factor (K_SR) in the RV computational model was reduced by 45%, and the Ca²⁺-ATPase forward rate parameter (v_maxf) was reduced by 20%, to represent the overall impairment in the refilling of the SR, and simulate an altered [Ca²⁺]_i similar to the one observed experimentally in short-term diabetes.

Other assumptions
The membrane capacitance (C_m) was assigned the same value (100 pF) in the control and the diabetic cell models, consistent with experimental findings (Shimoni et al., 1994). It has been recently reported that the function of the Na⁺-Ca²⁺ exchanger (I_NaCa) is not altered in rat ventricular myocytes cultured under high glucose conditions (Dutta and Davidoff, 2000). Therefore the parameters for I_NaCa were similar in the control and diabetic model formulations. All other ionic mechanisms, as well as the parameters describing the SR Ca²⁺ handling were assumed to be identical in the control and the diabetic models. The extracellular ionic concentrations in both the models were assumed to be constant, and all simulations were carried out at an assumed temperature of 22°C, conditions under which most of the experimental data were recorded.

Computational aspects
The mathematical model was implemented in C, on a SUN Microsystem Sparc Ultra 60 workstation. A Runge-Kutta-Merson numerical integration algorithm, which includes an automatic step-size adjustment that is based on an error estimate, was used for the whole-cell simulations, as in our previous model studies (Demir et al., 1994, 1997, 1999; Pandit et al., 2001). The software package Matlab was also utilized in formulating model equations for the ionic channels. All the results are presented in their steady state, which was defined as the action potential obtained after allowing the model to run for 20 s after a change in the initial conditions. This approach is in accordance with earlier modeling studies examining changes in action potential and [Ca²⁺]_i profiles in pathophysiological conditions such as heart failure (Winslow et al., 1999) and atrial fibrillation (Courtemanche et al., 1999). This ensures rapid rate adaptation of the action potential, but does not take into account the long-term effects in the changes in the intracellular ionic concentrations (Courtemanche et al., 1999). The rat model requires a run time of 10 min on the present computing platform to simulate a steady-state action potential.

	RESULTS

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Action potential waveforms and underlying ionic currents in control and diabetic ventricular myocytes
A stimulus of 0.6 nA was applied for 5 ms, in accordance with experimental protocols (Ward et al., 1997), to generate the simulated control and diabetic action potentials at a frequency of 1.0 Hz and an assumed temperature of 22°C. (Fig. 1 A). The effects of the intracellular Ca²⁺ buffer EGTA in the recording pipette were included in the model in accordance with an earlier formulation (Winslow et al., 1999), because EGTA is used in majority of the electrophysiological experiments of this kind (Shimoni et al., 1994). A set of experimentally recorded action potentials under control and diabetic conditions (Shimoni et al., 1994) are shown in Fig. 1 B. The simulated control RV action potential closely resembles its experimental counterpart (Fig. 1). The simulated diabetic APD is larger than the corresponding control counterpart (Fig. 1 A) in accordance with experimental results (Fig. 1 B). However, the experimentally recorded diabetic action potential exhibits a larger prolongation (Fig. 1 B) than seen in simulations (Fig. 1 A). A quantitative comparison between the simulated and experimental diabetic action potentials was not attempted mainly because of the reportedly large variations in the duration and the shape of experimentally recorded diabetic action potentials, despite similar isolation procedures and recording conditions (e.g., see Fig. 1, B and C, in Shimoni et al., 1994). In particular, the APD₉₀ value varies considerably in individual diabetic cells over time, and from cell to cell (Shimoni et al., 1998). This could be the result of variations in the magnitudes of the K⁺ or background currents in diabetes (Shimoni et al., 1998), or due to the enhancement of the intrinsic action potential heterogeneity, in the rat ventricular myocardium (Watanabe et al., 1983; Ward and Giles, 1997). For these reasons, the emphasis in this modeling study was on determining whether the simulated diabetic action potential could qualitatively reproduce the experimentally observed action potential changes resulting from STZ-induced diabetes. A similar approach was successfully employed in our previous simulations, which compared and contrasted epicardial and endocardial action potentials in adult rat left ventricular myocytes (Pandit et al., 2001).

The simulated control and diabetic action potential characteristics are compared in detail in Table 1. Parameters for the simulated control RV action potential (Table 1) are very close to the corresponding experimental measurements from control myocytes, which were -80.15 ± 0.79 mV (V_rest), 205.6 ± 11.8 V/s (dV/dt_max), 40.94 ± 1.26 mV (peak overshoot), 33.27 ± 5.31 ms (APD₉₀) (All measurements from MacDonell et al., 1998); and 62.8 ± 28.3 M (R_in) (Shimoni et al., 1994). V_rest, R_in, and peak overshoot have similar values in the simulated control and diabetic action potentials, whereas the APD₅₀ and APD₉₀ are larger in the diabetic action potential; this is in qualitative agreement with experimental observations (Shimoni et al., 1994). In fact, even the small depolarization in V_rest (by 0.55 mV), and a small increase in R_in (by 0.31 M) in the simulated diabetic action potential agree with the experimental observation that "the passive properties of diabetic cells were not significantly different from those of the normal cells, although there was a tendency toward a slight depolarization of the resting potential and an increase in input resistance" (Shimoni et al., 1994). Our model also exhibits a small reduction in dV/dt_max during the diabetic action potential (decreased by 5.05%), with respect to the control value.

View larger version (19K): [in this window] [in a new window]   FIGURE 3  Rate dependence of simulated action potentials. (A) Steady-state effects of applying stimuli on the control action potential at 0.5 Hz (solid line) and 2.0 Hz (dashed line). (B) Steady-state effects of applying stimuli on the diabetic action potentials at 0.5 Hz (solid line) and 2.0 Hz (dashed line).

View larger version (11K): [in this window] [in a new window]   FIGURE 4  (A) Simulated action potentials, (B) underlying Ca2+-independent transient outward K+ current (It), and the L-type Ca2+ current (ICaL), and (C) the steady-state outward K+ current (Iss) during the control (solid line) and diabetic (dashed line) conditions.

View larger version (13K): [in this window] [in a new window]   FIGURE 5  (A) Simulated action potentials, (B) underlying Na+-K+ pump current (INaK), the Na+-Ca2+ exchanger current (INaCa), and (C) the background current (IB), and the inward rectifier K+ current (IK1) during control (solid line) and diabetic (dashed line) conditions.

View larger version (11K): [in this window] [in a new window]   FIGURE 6  (A) Simulated action potentials, (B) underlying junctional sarcoplasmic reticulum Ca2+ load ([Ca2+]JSR), and (C) the underlying intracellular Ca2+ transient ([Ca2+]i) during control (solid line) and diabetic (dashed line) conditions.

	DISCUSSION

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Action potential duration and inotropy in diabetes
Initial investigations into the ionic basis of the delayed repolarization in myocytes isolated from the short-term, type-I diabetic model in rats showed that the densities of I_t and I_ss were reduced (Shimoni et al., 1994; 1995). Recent investigations employing molecular biology techniques have shown that the mRNA levels as well as the protein densities of the K⁺ channel -subunits Kv4.2, Kv4.3, and Kv2.1 are downregulated in this acute model of STZ-induced diabetes in rats (Qin et al., 2001). Kv4.2/Kv4.3 -subunits are thought to encode for I_t (Fiset et al., 1997, Oudit et al., 2001); whereas the Kv2.1 -subunit along with other -subunits such as Kv1.5 and Kv3.1/Kv3.2 is thought to underlie the TEA-sensitive K⁺ current I_ss in rat ventricular myocytes (Nerbonne, 2001; Schultz et al., 2001).

In contrast, the role of changes in I_CaL in the diabetic phenotype remains poorly defined. Earlier experiments in chronic diabetes reported no significant changes in I_CaL density (Jourdon and Feuvray, 1993); however, more recent studies have suggested that the density of I_CaL is downregulated (Wang et al., 1995; Chattou et al., 1999), and its fast inactivation time constant is slowed (Chattou et al., 1999). When the diabetic action potential in our model was simulated assuming no changes in I_CaL properties (not shown), the APD was increased, but the model failed to simulate the reported abnormal changes in [Ca²⁺]_i, despite an impaired SR uptake. In fact, under these conditions/assumptions, the peak systolic value of [Ca²⁺]_i was enhanced. Further computational analyses showed that this change in [Ca²⁺]_i was caused by the increase in APD, which was so large (due to no reduction in the inward current I_CaL), that it led to a substantial enhancement of the influx of Ca²⁺ ions via I_CaL (increase by 100%), when compared to the control case. This behavior is consistent with earlier experimental results (Bouchard et al., 1995; Clark et al., 1996), as well as recent model simulations (Pandit et al., 2001), which demonstrated the mechanistic linkage between an increased APD and increased influx of Ca²⁺ ions. The increased influx was the basis of a larger trigger for calcium induced calcium release (CICR), and subsequently increased the efficiency of SR release (Pandit et al., 2001; Sah et al., 2001), thereby compensating for the impaired SR uptake. The end result was a higher peak systolic value for [Ca²⁺]_i.

However, when the diabetic action potential was simulated by incorporating a reduced density and slower inactivation kinetics of I_CaL as well as an impaired SR uptake, the model was able to simultaneously simulate an increased APD and a small decrease in [Ca²⁺]_i amplitude. For example, a reduction in I_CaL density by 24% resulted in a relatively smaller increase in the influx of Ca²⁺ ions during the diabetic action potential (increase by 28%). This smaller trigger for CICR, along with an impaired SR uptake, resulted in the peak systolic value for [Ca²⁺]_i being somewhat smaller during the diabetic action potential (Table 2), which is in accordance with experimental results (Ren and Davidoff, 1997). A reduction in I_CaL (an inward current) will also tend to reduce the APD. However, because this reduction was also accompanied by simultaneous reductions in I_t and I_ss, along with the slower inactivation of I_CaL, the net result was an overall reduction in the outward repolarizing current, thereby prolonging the APD.

Our simulations thus support the hypothesis that changes in the properties of I_CaL are essential in explaining the diabetic phenotype (increased APD, reduced [Ca²⁺]_i), and draw attention to the intricate nonlinear interaction between I_t, I_ss, I_CaL, and SR uptake, which brings about this change.

Rate dependence, excitation, and quiescent properties of ventricular myocytes in type-I diabetes
The recovery from inactivation of I_t in rat model formulations is biphasic in nature, consisting of fast and slow components (Pandit et al., 2001). This is in accordance with experimental observations (Shimoni et al., 1995). The contribution of the slow component to overall inactivation is 11% in the control case, and is enhanced to 31% in the diabetic case. By incorporating the experimentally described slowed recovery in I_t (Shimoni et al., 1994), the model is able to simulate the enhanced prolongation of APD when stimulus frequency was increased from 0.5 Hz to 2.0 Hz under diabetic conditions, compared with the control one (Fig. 3). Interestingly, the fast and slow inactivation variables in the model formulation for I_t have been deemed to represent the contributions of Kv4.2/Kv4.3 and Kv1.4 to I_t respectively (Pandit et al., 2001). The greater contribution of the slower inactivation variable in the diabetic model is in accordance with very recent experimental observations demonstrating that the density of Kv1.4 is substantially enhanced in diabetic conditions (Nishiyama et al., 2001).

Our model also predicts a small decrease (5%) in the upstroke of the diabetic action potential, which has been experimentally observed (Pacher et al., 1999). Our simulations show that the underlying cause for this decrease is the reduction in the availability of the Na⁺ channels, due to the small depolarization of V_rest. Specifically, the steady-state, half-inactivation voltage of I_Na is -76.1 mV; therefore even a small depolarization (0.5–1.0 mV) in V_rest can change the Na⁺ channel availability. Indeed, experimental evidence shows that there is a decrease in the maximum rate of depolarization in STZ-induced diabetic rats, which increases progressively with development of the disease (Pacher et al., 1999). The lack of any significant change in the peak overshoot of the diabetic action potential, when compared to the control one can be explained by a reduction in I_Na, in combination with a simultaneous reduction in I_t. Again, this finding is in accordance with experimental findings, where no significant differences were found in peak overshoot values during chronic diabetes (Casis et al., 2000).

From our quantitative analysis, we note that a small depolarization in V_rest (and the subsequent change in R_in) can be attributed primarily to a downregulation of the electrogenic pump current, I_NaK. Thus, the model is able to replicate the tendency toward depolarization in diabetic myocytes (Shimoni et al., 1994). Interestingly, V_rest is also reported to differ significantly in myocytes maintained under hyperglycemic conditions (Ren et al., 1997). V_rest was -77.0±1.0 mV under high glucose conditions, compared to -81.0±1.0 mV in normal conditions (Ren et al., 1997).

Reported effects of PKC can be integrated into this model
Several investigators have provided strong evidence that the subcellular changes in the diabetic heart may be partially due to alterations in the protein kinase C (PKC) activity, and/or PKC-mediated signal transduction mechanisms. In particular, the translocation of PKC from cystolic to particulate fractions has been described in diabetic myocytes (Koya and King, 1998; Liu et al., 1999). The functional activation of PKC has been observed in the in vivo, STZ-induced model of diabetes (Malhotra et al., 1997), as well as in myocytes maintained under hyperglycemic conditions (Malhotra et al., 2001). Accordingly, our simulations have incorporated the experimentally observed effects of PKC on I_CaL (Hu et al., 2000) and I_NaK (Buhagiar et al., 2001), because the alterations in these currents have not been measured in myocytes isolated from the short-term, in vivo, diabetic model. These changes were necessary in our overall explanation for the abnormal Ca²⁺ homeostasis and changes in V_rest observed in the diabetic myocyte experimentally (Shimoni et al., 1994).

The activation of PKC in hyperglycemic conditions also increases the phosphorylation of troponin I (Malhotra et al., 2001), and cardiac specific over-expression of PKC is known to increase the myofilament sensitivity to Ca²⁺ ions (Takeishi et al., 2000). Additionally, it has been shown that PKC activation slows inactivation of I_Na, which affects the APD₉₀ value in rat ventricular myocytes (Ward and Giles, 1997). However it is unclear at the present time whether this mechanism contributes to an APD prolongation in diabetes. Accordingly, these and other reported effects of PKC isoform-specific activation have not been included in the present model formulations. However, they suggest that the contribution of additional ionic mechanisms/biophysical processes to the diabetic phenotype cannot be ruled out.

Limitations
These results and insights from rat ventricular myocytes under diabetic conditions should be extrapolated with caution when attempting to relate them to similar human studies, because the ventricular action potential and the underlying ionic currents are very different in humans and rats. A second limitation of the present study is that the SR Ca²⁺ dynamics have been adapted from a canine common pool model (Winslow et al., 1999). The Ca²⁺ dynamics in rat are now known to be different from their canine counterparts (Bers, 2001). Future modifications that incorporate and validate the model for the specific properties in rat, as well as formulations for a more sophisticated local control model of the Ca²⁺ dynamics will be essential to simulate [Ca²⁺]_i homeostasis and mechanisms such as graded SR release (Greenstein and Winslow, 2001). A third limitation is that the present model does not account for the changes in the intracellular Na⁺ concentration ([Na⁺]_i), which might occur during prolonged periods of pacing (the present simulation results are illustrated after a train of 20 pulses). Experimental studies have reported both an increase in [Na⁺]_i (Warley, 1991), and a decrease in [Na⁺]_i (Katoh et al., 1995) during diabetes; thus this important issue remains controversial. Our model also does not incorporate a formulation for the Na⁺-H⁺ exchanger, which is an important mediator of Na⁺ ion influx in rat ventricular myocytes (Despa et al., 2002), and is depressed during diabetes (Pierce et al., 1990). In summary, both experimental ambiguities and modeling limitations prevent the present study from accounting for the changes in [Na⁺]_i during long-term pacing. Finally, we note that the changes in I_CaL and SR activity in the diabetic model are based on observations in cultured myocytes and chronic diabetic conditions respectively, because corresponding data from the short-term, STZ-induced model of diabetes in rat are not available. Further experiments are therefore necessary to obtain quantitative data regarding the changes in the intracellular Ca²⁺ dynamics under well-defined type-I diabetic conditions. Thereafter, this aspect of the present modeling effort can and should be improved and updated.

	SUMMARY

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION SUMMARY ACKNOWLEDGEMENTS REFERENCES

 
The results of this model development provide novel insights into the plausible ionic mechanisms that can account for the changes in the action potential profile and the abnormal excitation-contraction coupling in rat ventricular myocytes induced with type-I diabetes. APD prolongation is due to a reduction of the K⁺ currents I_t and I_ss, along with slowed inactivation of I_CaL. The abnormal Ca²⁺ homeostasis (smaller peak, reduced rate of decay) can be attributed to a decreased SR load, which results from a combination of a downregulation in I_CaL and an impaired SR uptake. The small depolarization of the resting membrane potential (V_rest) is due to a decrease in the Na⁺-K⁺ pump current. The change in V_rest reduces the availability of the Na⁺ channels, causing a slower upstroke of the action potential (dV/dt_max). These interacting factors are summarized in Fig. 7, which in diagram form present the interdependent biophysical mechanisms for the observed electrophysiological changes, and in that way, highlight potential targets for reversing the diabetic cellular phenotype by means of gene therapy approaches (Trost et al., 2002). A future interesting extension of this study could involve exploring the action potential variations in the rat left ventricle during diabetes and predicting the subsequent changes in T-wave shape, and could be based on a recent modeling study (Gima and Rudy, 2002).

View larger version (15K): [in this window] [in a new window]   FIGURE 7  Diagram summarizing the electrophysiological alterations and their underlying causes as revealed by this mathematical model in the setting of short-term, type-I (insulin dependent), STZ-induced diabetes in rat ventricular myocytes.

	ACKNOWLEDGEMENTS

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The authors acknowledge the support provided by the Whitaker Foundation (to S.S. Demir), the Herff Foundation (to S.V. Pandit), Alberta Heritage Foundation for Medical Research, Canadian Institutes of Health Research, Heart and Stroke Foundation of Canada, and National Institutes of Health (to W.R. Giles).

Submitted on May 7, 2002; accepted for publication October 10, 2002.

	REFERENCES

TOP ABSTRACT INTRODUCTION METHODS RESULTS DISCUSSION SUMMARY ACKNOWLEDGEMENTS REFERENCES

 
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