Mathematical models are invaluable tools for understanding the relationships between components of a complex system. In the biological context, mathematical models help us understand the complex web ...of interrelations between various components (DNA, proteins, enzymes, signaling molecules etc.) in a biological system, gain better understanding of the system as a whole, and in turn predict its behavior in an altered state (e.g. disease). Mathematical modeling has enhanced our understanding of multiple complex biological processes like enzyme kinetics, metabolic networks, signal transduction pathways, gene regulatory networks, and electrophysiology. With recent advances in high throughput data generation methods, computational techniques and mathematical modeling have become even more central to the study of biological systems. In this review, we provide a brief history and highlight some of the important applications of modeling in biological systems with an emphasis on the study of excitable cells. We conclude with a discussion about opportunities and challenges for mathematical modeling going forward. In a larger sense, the review is designed to help answer a simple but important question that theoreticians frequently face from interested but skeptical colleagues on the experimental side: “What is the value of a model?”
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Arrhythmogenic cardiomyopathy (AC) is closely associated with desmosomal mutations in a majority of patients. Arrhythmogenesis in patients with AC is likely related to remodeling of cardiac gap ...junctions and increased levels of fibrosis. Recently, using experimental models, we also identified sodium channel dysfunction secondary to desmosomal dysfunction.
To assess the immunoreactive signal levels of the sodium channel protein NaV1.5, as well as connexin43 (Cx43) and plakoglobin (PKG), in myocardial specimens obtained from patients with AC.
Left and right ventricular free wall postmortem material was obtained from 5 patients with AC and 5 controls matched for age and sex. Right ventricular septal biopsies were taken from another 15 patients with AC. All patients fulfilled the 2010 revised Task Force Criteria for the diagnosis of AC. Immunohistochemical analyses were performed using antibodies against Cx43, PKG, NaV1.5, plakophilin-2, and N-cadherin.
N-cadherin and desmoplakin immunoreactive signals and distribution were normal in patients with AC compared to controls. Plakophilin-2 signals were unaffected unless a plakophilin-2 mutation predicting haploinsufficiency was present. Distribution was unchanged compared to that in controls. Immunoreactive signal levels of PKG, Cx43, and NaV1.5 were disturbed in 74%, 70%, and 65% of the patients, respectively.
A reduced immunoreactive signal of PKG, Cx43, and NaV1.5 at the intercalated disks can be observed in a large majority of the patients. Decreased levels of Nav1.5 might contribute to arrhythmia vulnerability and, in the future, potentially could serve as a new clinically relevant tool for risk assessment strategies.
Voltage-gated Nav channels are required for normal electrical activity in neurons, skeletal muscle, and cardiomyocytes. In the heart, Nav1.5 is the predominant Nav channel, and Nav1.5-dependent ...activity regulates rapid upstroke of the cardiac action potential. Nav1.5 activity requires precise localization at specialized cardiomyocyte membrane domains. However, the molecular mechanisms underlying Nav channel trafficking in the heart are unknown. In this paper, we demonstrate that ankyrin-G is required for Nav1.5 targeting in the heart. Cardiomyocytes with reduced ankyrin-G display reduced Nav1.5 expression, abnormal Nav1.5 membrane targeting, and reduced Na⁺ channel current density. We define the structural requirements on ankyrin-G for Nav1.5 interactions and demonstrate that loss of Nav1.5 targeting is caused by the loss of direct Nav1.5-ankyrin-G interaction. These data are the first report of a cellular pathway required for Nav channel trafficking in the heart and suggest that ankyrin-G is critical for cardiac depolarization and Nav channel organization in multiple excitable tissues.
Cardiac arrhythmias are a major cause of morbidity and mortality worldwide. Although recent advances in cell-based models, including human-induced pluripotent stem cell-derived cardiomyocytes ...(iPSC-CM), are contributing to our understanding of electrophysiology and arrhythmia mechanisms, preclinical animal studies of cardiovascular disease remain a mainstay. Over the past several decades, animal models of cardiovascular disease have advanced our understanding of pathological remodeling, arrhythmia mechanisms, and drug effects and have led to major improvements in pacing and defibrillation therapies. There exist a variety of methodological approaches for the assessment of cardiac electrophysiology and a plethora of parameters may be assessed with each approach. This guidelines article will provide an overview of the strengths and limitations of several common techniques used to assess electrophysiology and arrhythmia mechanisms at the whole animal, whole heart, and tissue level with a focus on small animal models. We also define key electrophysiological parameters that should be assessed, along with their physiological underpinnings, and the best methods with which to assess these parameters.
Nordihydroguaiaretic acid (NDGA), a dicatechol and phytochemical polyphenolic antioxidant and an established inhibitor of human arachidonic acid (AA) 5-lipoxygenase (LOX) and 15-LOX, is widely used ...to ascertain the role of LOXs in vascular endothelial cell (EC) function. As the modulatory effect of NDGA on phospholipase D (PLD), an important lipid signaling enzyme in ECs, thus far has not been reported, here we have investigated the modulation of PLD activity and its regulation by NDGA in the bovine pulmonary artery ECs (BPAECs). NDGA induced the activation of PLD (phosphatidic acid formation) in cells in a dose- and time-dependent fashion that was significantly attenuated by iron chelator and antioxidants. NDGA induced the formation of reactive oxygen species (ROS) in cells in a dose- and time-dependent manner as evidenced from fluorescence microscopy and fluorimetry of ROS and electron paramagnetic resonance spectroscopy of oxygen radicals. Also, NDGA caused a dose-dependent loss of intracellular glutathione (GSH) in BPAECs. Protein tyrosine kinase (PTyK)-specific inhibitors significantly attenuated NDGA-induced PLD activation in BPAECs. NDGA also induced a dose- and time-dependent phosphorylation of tyrosine in proteins in cells. NDGA caused in situ translocation and relocalization of both PLD
1
and PLD
2
isoforms, in a time-dependent fashion. Cyclooxygenase (COX) inhibitors were ineffective in attenuating NDGA-induced PLD activation in BPAECs, thus ruling out the activation of COXs by NDGA. NDGA inhibited the AA-LOX activity and leukotriene C
4
(LTC
4
) formation in cells. On the other hand, the 5-LOX-specific inhibitors, 5, 8, 11, 14-eicosatetraynoic acid and kaempferol, were ineffective in activating PLD in BPAECs. Antioxidants and PTyK-specific inhibitors effectively attenuated NDGA cytotoxicity in BPAECs. The PLD-specific inhibitor, 5-fluoro-2-indolyl deschlorohalopemide (FIPI), significantly attenuated and protected against the NDGA-induced PLD activation and cytotoxicity in BPAECs. For the first time, these results demonstrated that NDGA, the classic phytochemical polyphenolic antioxidant and LOX inhibitor, activated PLD causing cytotoxicity in ECs through upstream oxidant signaling and protein tyrosine phosphorylation.
Cardiac fibroblasts (CFs) maintain the fibrous extracellular matrix (ECM) that supports proper cardiac function. Cardiac injury induces a transition in the activity of CFs to promote cardiac ...fibrosis. CFs play a critical role in sensing local injury signals and coordinating the organ level response through paracrine communication to distal cells. However, the mechanisms by which CFs engage cell-cell communication networks in response to stress remain unknown. We tested a role for the action-associated cytoskeletal protein β
-spectrin in regulating CF paracrine signaling. Conditioned culture media (CCM) was collected from WT and β
-spectrin deficient (
) CFs. WT CFs treated with
CCM showed increased proliferation and collagen gel compaction compared to control. Consistent with the functional measurements,
CCM contained higher levels of pro-inflammatory and pro-fibrotic cytokines and increased concentration of small extracellular vesicles (30-150 nm diameter, exosomes). Treatment of WT CFs with exosomes isolated from
CCM induced a similar phenotypic change as that observed with complete CCM. Treatment of
CFs with an inhibitor of the β
-spectrin-associated transcription factor, STAT3, decreased the levels of both cytokines and exosomes in conditioned media. This study expands the role of the β
-spectrin/STAT3 complex in stress-induced regulation of CF paracrine signaling.
Diastolic dysfunction and delayed ventricular repolarization are typically observed in the elderly, but whether these defects are intimately associated with the progressive manifestation of the aging ...myopathy remains to be determined. In this regard, aging in experimental animals is coupled with increased late Na
current (
) in cardiomyocytes, raising the possibility that
conditions the modality of electrical recovery and myocardial relaxation of the aged heart. For this purpose, aging male and female wild-type (WT) C57Bl/6 mice were studied together with genetically engineered mice with phosphomimetic (gain of function, GoF) or ablated (loss of function, LoF) mutations of the sodium channel Nav1.5 at Ser571 associated with, respectively, increased and stabilized
. At ∼18 mo of age, WT mice developed prolonged duration of the QT interval of the electrocardiogram and impaired diastolic left ventricular (LV) filling, defects that were reversed by
inhibition. Prolonged repolarization and impaired LV filling occurred prematurely in adult (∼5 mo) GoF mutant mice, whereas these alterations were largely attenuated in aging LoF mutant animals. Ca
transient decay and kinetics of myocyte shortening/relengthening were delayed in aged (∼24 mo) WT myocytes, with respect to adult cells. In contrast, delayed Ca
transients and contractile dynamics occurred at adult stage in GoF myocytes and further deteriorated in old age. Conversely, myocyte mechanics were minimally affected in aging LoF cells. Collectively, these results document that Nav1.5 phosphorylation at Ser571 and the late Na
current modulate the modality of myocyte relaxation, constituting the mechanism linking delayed ventricular repolarization and diastolic dysfunction.
We have investigated the impact of the late Na current (
) on cardiac and myocyte function with aging by using genetically engineered animals with enhanced or stabilized
, due to phosphomimetic or phosphoablated mutations of Nav1.5. Our findings support the notion that phosphorylation of Nav1.5 at Ser571 prolongs myocardial repolarization and impairs diastolic function, contributing to the manifestations of the aging myopathy.
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