
Cardiac arrhythmias are serious myocardial electrical disturbances that affect the rate and rhythm of heartbeats. Despite the rapidly accumulating data about the pathophysiology and the treatment, new insights are required to improve the overall clinical outcome of patients with cardiac arrhythmias. Three major arrhythmogenic processes can contribute to the pathogenesis of cardiac arrhythmias; 1) enhanced automaticity, 2) afterdepolarization-triggered activity and 3) reentry circuits. The mathematical model of the quantum tunneling of ions is used to investigate these mechanisms from a quantum mechanical perspective. The mathematical model focuses on applying the principle of quantum tunneling to sodium and potassium ions. This implies that these ions have a non-zero probability of passing through the gate, which has an energy that is higher than the kinetic energy of ions. Our mathematical findings indicate that, under pathological conditions, which affect ion channels, the quantum tunneling of sodium and potassium ions is augmented. This augmentation creates a state of hyperexcitability that can explain the enhanced automaticity, after depolarizations that are associated with triggered activity and a reentry circuit. Our mathematical findings stipulate that the augmented and thermally assisted quantum tunneling of sodium and potassium ions can depolarize the membrane potential and trigger spontaneous action potentials, which may explain the automaticity and afterdepolarization. Furthermore, the quantum tunneling of potassium ions during an action potential can provide a new insight regarding the formation of a reentry circuit. Introducing these quantum mechanical aspects may improve our understanding of the pathophysiological mechanisms of cardiac arrhythmias and, thus, contribute to finding more effective anti-arrhythmic drugs.
Citation: Mohammed I. A. Ismail, Abdallah Barjas Qaswal, Mo'ath Bani Ali, Anas Hamdan, Ahmad Alghrabli, Mohamad Harb, Dina Ibrahim, Mohammad Nayel Al-Jbour, Ibrahim Almobaiden, Khadija Alrowwad, Esra'a Jaibat, Mira Alrousan, Mohammad Banifawaz, Mohammed A. M. Aldrini, Aya Daikh, Nour Aldarawish, Ahmad Alabedallat, Ismail M. I. Ismail, Lou'i Al-Husinat. Quantum mechanical aspects of cardiac arrhythmias: A mathematical model and pathophysiological implications[J]. AIMS Biophysics, 2023, 10(3): 401-439. doi: 10.3934/biophy.2023024
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Cardiac arrhythmias are serious myocardial electrical disturbances that affect the rate and rhythm of heartbeats. Despite the rapidly accumulating data about the pathophysiology and the treatment, new insights are required to improve the overall clinical outcome of patients with cardiac arrhythmias. Three major arrhythmogenic processes can contribute to the pathogenesis of cardiac arrhythmias; 1) enhanced automaticity, 2) afterdepolarization-triggered activity and 3) reentry circuits. The mathematical model of the quantum tunneling of ions is used to investigate these mechanisms from a quantum mechanical perspective. The mathematical model focuses on applying the principle of quantum tunneling to sodium and potassium ions. This implies that these ions have a non-zero probability of passing through the gate, which has an energy that is higher than the kinetic energy of ions. Our mathematical findings indicate that, under pathological conditions, which affect ion channels, the quantum tunneling of sodium and potassium ions is augmented. This augmentation creates a state of hyperexcitability that can explain the enhanced automaticity, after depolarizations that are associated with triggered activity and a reentry circuit. Our mathematical findings stipulate that the augmented and thermally assisted quantum tunneling of sodium and potassium ions can depolarize the membrane potential and trigger spontaneous action potentials, which may explain the automaticity and afterdepolarization. Furthermore, the quantum tunneling of potassium ions during an action potential can provide a new insight regarding the formation of a reentry circuit. Introducing these quantum mechanical aspects may improve our understanding of the pathophysiological mechanisms of cardiac arrhythmias and, thus, contribute to finding more effective anti-arrhythmic drugs.
The constituent members in a system mainly found in nature can be interacting with each other through cooperation and competition. Demonstrations for such systems involve biological species, countries, businesses, and many more. It's very much intriguing to investigate in a comprehensive manner numerous social as well as biological interactions existent in dissimilar species/entities utilizing mathematical modeling. The predation and the competition species are the most famous interactions among all such types of interactions. Importantly, Lotka [1] and Volterra [2] in the 1920s have announced individually the classic equations portraying population dynamics. Such illustrious equations are notably described as predator-prey (PP) equations or Lotka-Volterra (LV) equations. In this structure, PP/LV model represents the most influential model for interacting populations. The interplay between prey and predator together with additional factors has been a prominent topic in mathematical ecology for a long period. Arneodo et al. [3] have established in 1980 that a generalized Lotka-Volterra biological system (GLVBS) would depict chaos phenomena in an ecosystem for some explicitly selected system parameters and initial conditions. Additionally, Samardzija and Greller [4] demonstrated in 1988 that GLVBS would procure chaotic reign from the stabled state via rising fractal torus. LV model was initially developed as a biological concept, yet it is utilized in enormous diversified branches for research [5,6,7,8]. Synchronization essentially is a methodology of having different chaotic systems (non-identical or identical) following exactly a similar trajectory, i.e., the dynamical attributes of the slave system are locked finally into the master system. Specifically, synchronization and control have a wide spectrum for applications in engineering and science, namely, secure communication [9], encryption [10,11], ecological model [12], robotics [13], neural network [14], etc. Recently, numerous types of secure communication approaches have been explored [15,16,17,18] such as chaos modulation [18,19,20,21], chaos shift keying [22,23] and chaos masking [9,17,20,24]. In chaos communication schemes, the typical key idea for transmitting a message through chaotic/hyperchaotic models is that a message signal is nested in the transmitter system/model which originates a chaotic/ disturbed signal. Afterwards, this disturbed signal has been emitted to the receiver through a universal channel. The message signal would finally be recovered by the receiver. A chaotic model has been intrinsically employed both as receiver and transmitter. Consequently, this area of chaotic synchronization & control has sought remarkable considerations among differential research fields.
Most prominently, synchronization theory has been in existence for over 30 years due to the phenomenal research of Pecora and Carroll [25] established in 1990 using drive-response/master-slave/leader-follower configuration. Consequently, many authors and researchers have started introducing and studying numerous control and synchronization methods [9,26,27,28,29,30,31,32,33,34,35,36] etc. to achieve stabilized chaotic systems for possessing stability. In [37], researchers discussed optimal synchronization issues in similar GLVBSs via optimal control methodology. In [38,39], the researchers studied the adaptive control method (ACM) to synchronize chaotic GLVBSs. Also, researchers [40] introduced a combination difference anti-synchronization scheme in similar chaotic GLVBSs via ACM. In addition, authors [41] investigated a combination synchronization scheme to control chaos existing in GLVBSs using active control strategy (ACS). Bai and Lonngren [42] first proposed ACS in 1997 for synchronizing and controlling chaos found in nonlinear dynamical systems. Furthermore, compound synchronization using ACS was first advocated by Sun et al. [43] in 2013. In [44], authors discussed compound difference anti-synchronization scheme in four chaotic systems out of which two chaotic systems are considered as GLVBSs using ACS and ACM along with applications in secure communications of chaos masking type in 2019. Some further research works [45,46] based on ACS have been reported in this direction. The considered chaotic GLVBS offers a generalization that allows higher-order biological terms. As a result, it may be of interest in cases where biological systems experience cataclysmic changes. Unfortunately, some species will be under competitive pressure in the coming years and decades. This work may be comprised as a step toward preserving as many currently living species as possible by using the proposed synchronization approach which is based on master-slave configuration and Lyapunov stability analysis.
In consideration of the aforementioned discussions and observations, our primary focus here is to develop a systematic approach for investigating compound difference anti-synchronization (CDAS) approach in 4 similar chaotic GLVBSs via ACS. The considered ACS is a very efficient yet theoretically rigorous approach for controlling chaos found in GLVBSs. Additionally, in view of widely known Lyapunov stability analysis (LSA) [47], we discuss actively designed biological control law & convergence for synchronization errors to attain CDAS synchronized states.
The major attributes for our proposed research in the present manuscript are:
● The proposed CDAS methodology considers four chaotic GLVBSs.
● It outlines a robust CDAS approach based active controller to achieve compound difference anti-synchronization in discussed GLVBSs & conducts oscillation in synchronization errors along with extremely fast convergence.
● The construction of the active control inputs has been executed in a much simplified fashion utilizing LSA & master-salve/ drive-response configuration.
● The proposed CDAS approach in four identical chaotic GLVBSs of integer order utilizing ACS has not yet been analyzed up to now. This depicts the novelty of our proposed research work.
This manuscript is outlined as follows: Section 2 presents the problem formulation of the CDAS scheme. Section 3 designs comprehensively the CDAS scheme using ACS. Section 4 consists of a few structural characteristics of considered GLVBS on which CDAS is investigated. Furthermore, the proper active controllers having nonlinear terms are designed to achieve the proposed CDAS strategy. Moreover, in view of Lyapunov's stability analysis (LSA), we have examined comprehensively the biological controlling laws for achieving global asymptotical stability of the error dynamics for the discussed model. In Section 5, numerical simulations through MATLAB are performed for the illustration of the efficacy and superiority of the given scheme. Lastly, we also have presented some conclusions and the future prospects of the discussed research work in Section 6.
We here formulate a methodology to examine compound difference anti-synchronization (CDAS) scheme viewing master-slave framework in four chaotic systems which would be utilized in the coming up sections.
Let the scaling master system be
˙wm1= f1(wm1), | (2.1) |
and the base second master systems be
˙wm2= f2(wm2), | (2.2) |
˙wm3= f3(wm3). | (2.3) |
Corresponding to the aforementioned master systems, let the slave system be
˙ws4= f4(ws4)+U(wm1,wm2,wm3,ws4), | (2.4) |
where wm1=(wm11,wm12,...,wm1n)T∈Rn, wm2=(wm21,wm22,...,wm2n)T∈Rn, wm3=(wm31,wm32,...,wm3n)T∈Rn, ws4=(ws41,ws42,...,ws4n)T∈Rn are the state variables of the respective chaotic systems (2.1)–(2.4), f1,f2,f3,f4:Rn→Rn are four continuous vector functions, U=(U1,U2,...,Un)T:Rn×Rn×Rn×Rn→Rn are appropriately constructed active controllers.
Compound difference anti-synchronization error (CDAS) is defined as
E=Sws4+Pwm1(Rwm3−Qwm2), |
where P=diag(p1,p2,.....,pn),Q=diag(q1,q2,.....,qn),R=diag(r1,r2,.....,rn),S=diag(s1,s2,.....,sn) and S≠0.
Definition: The master chaotic systems (2.1)–(2.3) are said to achieve CDAS with slave chaotic system (2.4) if
limt→∞‖E(t)‖=limt→∞‖Sws4(t)+Pwm1(t)(Rwm3(t)−Qwm2(t))‖=0. |
We now present our proposed CDAS approach in three master systems (2.1)–(2.3) and one slave system (2.4). We next construct the controllers based on CDAS approach by
Ui= ηisi−(f4)i−KiEisi, | (3.1) |
where ηi=pi(f1)i(riwm3i−qiwm2i)+piwm1i(ri(f3)i−qi(f2)i), for i=1,2,...,n.
Theorem: The systems (2.1)–(2.4) will attain the investigated CDAS approach globally and asymptotically if the active control functions are constructed in accordance with (3.1).
Proof. Considering the error as
Ei= siws4i+piwm1i(riwm3i−qiwm2i),fori=1,2,3,.....,n. |
Error dynamical system takes the form
˙Ei= si˙ws4i+pi˙wm1i(riwm3i−qiwm2i)+piwm1i(ri˙wm3i−qi˙wm2i)= si((f4)i+Ui)+pi(f1)i(riwm3i−qiwm2i)+piwm1i(ri(f3)i−qi(f2)i)= si((f4)i+Ui)+ηi, |
where ηi=pi(f1)i(riwm3i−qiwm2i)+piwm1i(ri(f3)i−qi(f2)i), i=1,2,3,....,n. This implies that
˙Ei= si((f4)i−ηisi−(f4)i−KiEisi)+ηi= −KiEi | (3.2) |
The classic Lyapunov function V(E(t)) is described by
V(E(t))= 12ETE= 12ΣE2i |
Differentiation of V(E(t)) gives
˙V(E(t))=ΣEi˙Ei |
Using Eq (3.2), one finds that
˙V(E(t))=ΣEi(−KiEi)= −ΣKiE2i). | (3.3) |
An appropriate selection of (K1,K1,.......,Kn) makes ˙V(E(t)) of eq (3.3), a negative definite. Consequently, by LSA [47], we obtain
limt→∞Ei(t)=0,(i=1,2,3). |
Hence, the master systems (2.1)–(2.3) and slave system (2.4) have attained desired CDAS strategy.
We now describe GLVBS as the scaling master system:
{˙wm11=wm11−wm11wm12+b3w2m11−b1w2m11wm13,˙wm12=−wm12+wm11wm12,˙wm13=b2wm13+b1w2m11wm13, | (4.1) |
where (wm11,wm12,wm13)T∈R3 is state vector of (4.1). Also, wm11 represents the prey population and wm12, wm13 denote the predator populations. For parameters b1=2.9851, b2=3, b3=2 and initial conditions (27.5,23.1,11.4), scaling master GLVBS displays chaotic/disturbed behaviour as depicted in Figure 1(a).
The base master systems are the identical chaotic GLVBSs prescribed respectively as:
{˙wm21=wm21−wm21wm22+b3w2m21−b1w2m21wm23,˙wm22=−wm22+wm21wm22,˙wm23=b2wm23+b1w2m21wm23, | (4.2) |
where (wm21,wm22,wm23)T∈R3 is state vector of (4.2). For parameter values b1=2.9851, b2=3, b3=2, this base master GLVBS shows chaotic/disturbed behaviour for initial conditions (1.2,1.2,1.2) as displayed in Figure 1(b).
{˙wm31=wm31−wm31wm32+b3w2m31−b1w2m31wm33,˙wm32=−wm32+wm31wm32,˙wm33=b2wm33+b1w2m31wm33, | (4.3) |
where (wm31,wm32,wm33)T∈R3 is state vector of (4.3). For parameters b1=2.9851, b2=3, b3=2, this second base master GLVBS displays chaotic/disturbed behaviour for initial conditions (2.9,12.8,20.3) as shown in Figure 1(c).
The slave system, represented by similar GLVBS, is presented by
{˙ws41=ws41−ws41ws42+b3w2s41−b1w2s41ws43+U1,˙ws42=−ws42+ws41ws42+U2,˙ws43=b2ws43+b1w2s41ws43+U3, | (4.4) |
where (ws41,ws42,ws43)T∈R3 is state vector of (4.4). For parameter values, b1=2.9851, b2=3, b3=2 and initial conditions (5.1,7.4,20.8), the slave GLVBS exhibits chaotic/disturbed behaviour as mentioned in Figure 1(d).
Moreover, the detailed theoretical study for (4.1)–(4.4) can be found in [4]. Further, U1, U2 and U3 are controllers to be determined.
Next, the CDAS technique has been discussed for synchronizing the states of chaotic GLVBS. Also, LSA-based ACS is explored & the necessary stability criterion is established.
Here, we assume P=diag(p1,p2,p3), Q=diag(q1,q2,q3), R=diag(r1,r2,r3), S=diag(s1,s2,s3). The scaling factors pi,qi,ri,si for i=1,2,3 are selected as required and can assume the same or different values.
The error functions (E1,E2,E3) are defined as:
{E1=s1ws41+p1wm11(r1wm31−q1wm21),E2=s2ws42+p2wm12(r2wm32−q2wm22),E3=s3ws43+p3wm13(r3wm33−q3wm23). | (4.5) |
The major objective of the given work is the designing of active control functions Ui,(i=1,2,3) ensuring that the error functions represented in (4.5) must satisfy
limt→∞Ei(t)=0for(i=1,2,3). |
Therefore, subsequent error dynamics become
{˙E1=s1˙ws41+p1˙wm11(r1wm31−q1wm21)+p1wm11(r1˙wm31−q1˙wm21),˙E2=s2˙ws42+p2˙wm12(r2wm32−q2wm22)+p2wm12(r2˙wm32−q2˙wm22),˙E3=s3˙ws43+p3˙wm13(r3wm33−q3wm23)+p3wm13(r3˙wm33−q3˙wm23). | (4.6) |
Using (4.1), (4.2), (4.3), and (4.5) in (4.6), the error dynamics simplifies to
{˙E1=s1(ws41−ws41ws42+b3w2s41−b1w2s41ws43+U1)+p1(wm11−wm11wm12+b3w2m11−b1w2m11wm13)(r1wm31−q1wm21)+p1wm11(r1(wm31−wm31wm32+b3w2m31−b1w2m31wm33)−q1(wm21−wm21wm22+b3w2m21−b1w2m21wm23),˙E2=s2(−ws42+ws41ws42+U2)+p2(−wm12+wm11wm12)(r2wm32−q2wm22)+p2wm12(r2(−wm32+wm31wm32)−q2(−wm22+wm21wm22)),˙E3=s3(b2ws43+b1w2s41ws43+U3)+p3(b2wm13+b1w2m11wm13)(r3wm33−q3wm23)+p3wm13(r3(b2wm33+b1w2m31wm33)−q3(b2wm23+b1w2m21wm23)). | (4.7) |
Let us now choose the active controllers:
U1= η1s1−(f4)1−K1E1s1, | (4.8) |
where η1=p1(f1)1(r1wm31−q1wm21)+p1wm11(r1(f3)1−q1(f2)1), as described in (3.1).
U2= η2s2−(f4)2−K2E2s2, | (4.9) |
where η2=p2(f1)2(r2wm32−q2wm22)+p2wm12(r2(f3)2−q2(f2)2).
U3= η3s3−(f4)3−K3E3s3, | (4.10) |
where η3=p3(f1)3(r3wm33−q3wm23)+p3wm13(r3(f3)3−q3(f2)3) and K1>0,K2>0,K3>0 are gaining constants.
By substituting the controllers (4.8), (4.9) and (4.10) in (4.7), we obtain
{˙E1=−K1E1,˙E2=−K2E2,˙E3=−K3E3. | (4.11) |
Lyapunov function V(E(t)) is now described by
V(E(t))= 12[E21+E22+E23]. | (4.12) |
Obviously, the Lyapunov function V(E(t)) is +ve definite in R3. Therefore, the derivative of V(E(t)) as given in (4.12) can be formulated as:
˙V(E(t))= E1˙E1+E2˙E2+E3˙E3. | (4.13) |
Using (4.11) in (4.13), one finds that
˙V(E(t))= −K1E21−K2E22−K3E23<0, |
which displays that ˙V(E(t)) is -ve definite.
In view of LSA [47], we, therefore, understand that CDAS error dynamics is globally as well as asymptotically stable, i.e., CDAS error E(t)→0 asymptotically for t→∞ to each initial value E(0)∈R3.
This section conducts a few simulation results for illustrating the efficacy of the investigated CDAS scheme in identical chaotic GLVBSs using ACS. We use 4th order Runge-Kutta algorithm for solving the considered ordinary differential equations. Initial conditions for three master systems (4.1)–(4.3) and slave system (4.4) are (27.5,23.1,11.4), (1.2,1.2,1.2), (2.9,12.8,20.3) and (14.5,3.4,10.1) respectively. We attain the CDAS technique among three masters (4.1)–(4.3) and corresponding one slave system (4.4) by taking pi=qi=ri=si=1, which implies that the slave system would be entirely anti-synchronized with the compound of three master models for i=1,2,3. In addition, the control gains (K1,K2,K3) are taken as 2. Also, Figure 2(a)–(c) indicates the CDAS synchronized trajectories of three master (4.1)–(4.3) & one slave system (4.4) respectively. Moreover, synchronization error functions (E1,E2,E3)=(51.85,275.36,238.54) approach 0 as t tends to infinity which is exhibited via Figure 2(d). Hence, the proposed CDAS strategy in three masters and one slave models/systems has been demonstrated computationally.
In this work, the investigated CDAS approach in similar four chaotic GLVBSs using ACS has been analyzed. Lyapunov's stability analysis has been used to construct proper active nonlinear controllers. The considered error system, on the evolution of time, converges to zero globally & asymptotically via our appropriately designed simple active controllers. Additionally, numerical simulations via MATLAB suggest that the newly described nonlinear control functions are immensely efficient in synchronizing the chaotic regime found in GLVBSs to fitting set points which exhibit the efficacy and supremacy of our proposed CDAS strategy. Exceptionally, both analytic theory and computational results are in complete agreement. Our proposed approach is simple yet analytically precise. The control and synchronization among the complex GLVBSs with the complex dynamical network would be an open research problem. Also, in this direction, we may extend the considered CDAS technique on chaotic systems that interfered with model uncertainties as well as external disturbances.
The authors gratefully acknowledge Qassim University, represented by the Deanship of Scientific Research, on the financial support for this research under the number 10163-qec-2020-1-3-I during the academic year 1441 AH/2020 AD.
The authors declare there is no conflict of interest.
[1] |
Huikuri HV, Castellanos A, Myerburg RJ (2001) Sudden death due to cardiac arrhythmias. New Engl J Med 345: 1473-1482. https://doi.org/10.1056/NEJMra000650 ![]() |
[2] |
Srinivasan NT, Schilling RJ (2018) Sudden cardiac death and arrhythmias. Arrhyth Electrophysi Rev 7: 111. https://doi.org/10.15420/aer.2018:15:2 ![]() |
[3] |
John RM, Tedrow UB, Koplan BA, et al. (2012) Ventricular arrhythmias and sudden cardiac death. Lancet 380: 1520-1529. https://doi.org/10.1016/S0140-6736(12)61413-5 ![]() |
[4] |
Janse MJ, Wit AL (1989) Electrophysiological mechanisms of ventricular arrhythmias resulting from myocardial ischemia and infarction. Physiol Rev 69: 1049-1169. https://doi.org/10.1152/physrev.1989.69.4.1049 ![]() |
[5] |
Peretto G, Sala S, Rizzo S, et al. (2019) Arrhythmias in myocarditis: state of the art. Heart Rhythm 16: 793-801. https://doi.org/10.1016/j.hrthm.2018.11.024 ![]() |
[6] |
Kumar S, Stevenson WG, John RM (2015) Arrhythmias in dilated cardiomyopathy. Card Electrophy Clin 7: 221-233. https://doi.org/10.1016/j.hrthm.2018.11.024 ![]() |
[7] |
Tisdale JE, Chung MK, Campbell KB, et al. (2020) Drug-induced arrhythmias: a scientific statement from the American Heart Association. Circulation 142: e214-233. https://doi.org/10.1161/CIR.0000000000000905 ![]() |
[8] |
Behere SP, Weindling SN (2015) Inherited arrhythmias: The cardiac channelopathies. Ann Pediat Cardiol 8: 210. https://doi.org/10.4103/0974-2069.164695 ![]() |
[9] |
FISCH C (1973) Relation of electrolyte disturbances to cardiac arrhythmias. Circulation 47: 408-419. https://doi.org/10.1161/01.CIR.47.2.408 ![]() |
[10] |
Tse G (2016) Mechanisms of cardiac arrhythmias. J Arrhythm 32: 75-81. https://doi.org/10.1016/j.joa.2015.11.003 ![]() |
[11] |
Antzelevitch C, Burashnikov A (2011) Overview of basic mechanisms of cardiac arrhythmia. Card Electrophy Clin 3: 23-45. https://doi.org/10.1016/j.ccep.2010.10.012 ![]() |
[12] |
Marbán E (2002) Cardiac channelopathies. Nature 415: 213-218. https://doi.org/10.1038/415213a ![]() |
[13] |
Franz MR, Cima R, Wang D, et al. (1992) Electrophysiological effects of myocardial stretch and mechanical determinants of stretch-activated arrhythmias. Circulation 86: 968-978. https://doi.org/10.1161/01.CIR.86.3.968 ![]() |
[14] | Morand J, Arnaud C, Pepin JL, et al. (2018) Chronic intermittent hypoxia promotes myocardial ischemia-related ventricular arrhythmias and sudden cardiac death. Sci Rep 8: 1-8. https://doi.org/10.1038/s41598-018-21064-y |
[15] |
Orchard CH, Cingolani HE (1994) Acidosis and arrhythmias in cardiac muscle. Card Res 28: 1312-1319. https://doi.org/10.1093/cvr/28.9.1312 ![]() |
[16] |
Morris CE (2011) Voltage-gated channel mechanosensitivity: fact or friction?. Front Physiol 2: 25. https://doi.org/10.3389/fphys.2011.00025 ![]() |
[17] | Dehghani-Samani A, Madreseh-Ghahfarokhi S, Dehghani-Samani A (2019) Mutations of voltage-gated ionic channels and risk of severe cardiac arrhythmias. Acta Cardiol Sin 35: 99. https://doi.org/10.6515%2FACS.201903_35(2).20181028A |
[18] |
Li Q, Huang H, Liu G, et al. (2009) Gain-of-function mutation of Nav1. 5 in atrial fibrillation enhances cellular excitability and lowers the threshold for action potential firing. Biochem Biophys Res Commun 380: 132-137. https://doi.org/10.1016/j.bbrc.2009.01.052 ![]() |
[19] | Moskalenko A (2014) Cardiac Arrhythmias Mechanisms, Pathophysiology, and Treatment: 1-162. https://doi.org/10.5772/57008 |
[20] | Cardiac Arrhythmia Suppression Trial (CAST) Investigators.Preliminary report: effect of encainide and flecainide on mortality in a randomized trial of arrhythmia suppression after myocardial infarction. N Engl J Med (1989) 321: 406-412. https://doi.org/10.1056/nejm198908103210629 |
[21] |
Brooks MM, Gorkin L, Schron EB, et al. (1994) Moricizine and quality of life in the Cardiac Arrhythmia Suppression Trial II (CAST II). Control Clin Trials 15: 437-449. https://doi.org/10.1016/0197-2456(94)90002-7 ![]() |
[22] |
Kurian TK, Efimov IR (2010) Mechanisms of fibrillation: Neurogenic or myogenic? reentrant or focal? multiple or single?: Still puzzling after 160 years of inquiry. J Card Electrophysiol 21: 1274. https://doi.org/10.1111%2Fj.1540-8167.2010.01820.x ![]() |
[23] |
Calvillo L, Redaelli V, Ludwig N, et al. (2022) Quantum biology research meets pathophysiology and therapeutic mechanisms: a biomedical perspective. Quantum Rep 4: 148-172. https://www.mdpi.com/2624-960X/4/2/11 ![]() |
[24] |
Kim Y, Bertagna F, D'souza EM, et al. (2021) Quantum biology: An update and perspective. Quantum Rep 3: 80-126. https://www.mdpi.com/2624-960X/3/1/6 ![]() |
[25] |
Cao J, Cogdell RJ, Coker DF, et al. (2020) Quantum biology revisited. Sci Adv 6: eaaz4888. https://doi.org/10.1126/sciadv.aaz4888 ![]() |
[26] |
Slocombe L, Sacchi M, Al-Khalili (2022) An open quantum systems approach to proton tunnelling in DNA. Commun Phys 5: 109. https://doi.org/10.1038/s42005-022-00881-8 ![]() |
[27] |
Sutcliffe MJ, Scrutton NS (2002) A new conceptual framework for enzyme catalysis: Hydrogen tunneling coupled to enzyme dynamics in flavoprotein and quinoprotein enzymes. Eur J Biochem 269: 3096-3102. https://doi.org/10.1046/j.1432-1033.2002.03020.x ![]() |
[28] |
Qaswal AB (2019) Quantum tunneling of ions through the closed voltage-gated channels of the biological membrane: A mathematical model and implications. Quantum Rep 1: 219-225. https://www.mdpi.com/2624-960X/1/2/19 ![]() |
[29] | Miller DA (2008). Quantum mechanics for scientists and engineers. Cambridge University Press |
[30] |
Aryal P, Sansom MS, Tucker SJ (2015) Hydrophobic gating in ion channels. J Mol Biol 427: 121-130. https://doi.org/10.1016/j.jmb.2014.07.030 ![]() |
[31] |
Oelstrom K, Goldschen-Ohm MP, Holmgren M, et al. (2014) Evolutionarily conserved intracellular gate of voltage-dependent sodium channels. Nat Commun 5: 3420. https://doi.org/10.1038/ncomms4420 ![]() |
[32] |
Jensen MØ, Borhani DW, Lindorff-Larsen K, et al. (2010) Principles of conduction and hydrophobic gating in K+ channels. Proceedings of the National Academy of Sciences 107: 5833-5838. https://doi.org/10.1073/pnas.0911691107 ![]() |
[33] |
Trick JL, Aryal P, Tucker SJ, et al. (2015) Molecular simulation studies of hydrophobic gating in nanopores and ion channels. Biochem Society Transact 43: 146-150. https://doi.org/10.1042/BST20140256 ![]() |
[34] |
Rao S, Klesse G, Lynch CI, et al. (2021) Molecular simulations of hydrophobic gating of pentameric ligand gated ion channels: insights into water and ions. J Phys Chem B 125: 981-994. https://doi.org/10.1021/acs.jpcb.0c09285 ![]() |
[35] |
Chandra AK (1974). |
[36] |
Miyazaki T (2004). |
[37] | Serway RA, Moses CJ, Moyer CA (2004). Modern physics |
[38] |
Eckart C (1930) The penetration of a potential barrier by electrons. Phys Rev 35: 1303. https://doi.org/10.1103/PhysRev.35.1303 ![]() |
[39] |
Zhu F, Hummer G (2012) Drying transition in the hydrophobic gate of the GLIC channel blocks ion conduction. Biophys J 103: 219-227. http://dx.doi.org/10.1016/j.bpj.2012.06.003 ![]() |
[40] |
Rao S, Lynch CI, Klesse G, et al. (2018) Water and hydrophobic gates in ion channels and nanopores. Faraday Discuss 209: 231-247. https://doi.org/10.1039/C8FD00013A ![]() |
[41] |
Neale C, Chakrabarti N, Pomorski P, et al. (2015) Hydrophobic gating of ion permeation in magnesium channel CorA. PLoS Comput Biol 11: e1004303. https://doi.org/10.1371/journal.pcbi.1004303 ![]() |
[42] |
Khavrutskii IV, Gorfe AA, Lu B, et al. (2009) Free energy for the permeation of Na+ and Cl− ions and their ion-pair through a zwitterionic dimyristoyl phosphatidylcholine lipid bilayer by umbrella integration with harmonic fourier beads. J Am Chem Society 131: 1706-1716. https://doi.org/10.1021/ja8081704 ![]() |
[43] |
Vorobyov I, Olson TE, Kim JH, et al. (2014) Ion-induced defect permeation of lipid membranes. Biophys J 106: 586-597. http://dx.doi.org/10.1016/j.bpj.2013.12.027 ![]() |
[44] |
Leontiadou H, Mark AE, Marrink SJ (2007) Ion transport across transmembrane pores. Biophys J 92: 4209-4215. http://dx.doi.org/10.1529/biophysj.106.101295 ![]() |
[45] |
Zhang HY, Xu Q, Wang YK, et al. (2016) Passive transmembrane permeation mechanisms of monovalent ions explored by molecular dynamics simulations. J Chem Theory Comput 12: 4959-4969. https://doi.org/10.1021/acs.jctc.6b00695 ![]() |
[46] |
Chen F, Hihath J, Huang Z, et al. (2007) Measurement of single-molecule conductance. Annu Rev Phys Chem 58: 535-564. https://doi.org/10.1146/annurev.physchem.58.032806.104523 ![]() |
[47] |
Qaswal AB (2020) Quantum electrochemical equilibrium: Quantum version of the Goldman–Hodgkin–Katz equation. Quantum Rep 2: 266-277. https://www.mdpi.com/2624-960X/2/2/17 ![]() |
[48] |
Qaswal AB (2021) The role of quantum tunneling of ions in the pathogenesis of the cardiac arrhythmias due to channelopathies, ischemia, and mechanical stretch. Biophysics 66: 637-641. https://doi.org/10.1134/S0006350921040072 ![]() |
[49] |
Ababneh O, Qaswal AB, Alelaumi A, et al. (2021) Proton quantum tunneling: Influence and relevance to acidosis-induced cardiac arrhythmias/cardiac arrest. Pathophysiology 28: 400-436. https://www.mdpi.com/1873-149X/28/3/27 ![]() |
[50] |
Zhang XC, Yang H, Liu Z, et al. (2018) Thermodynamics of voltage-gated ion channels. Biophys Rep 4: 300-319. https://doi.org/10.1016/j.celrep.2021.109931 ![]() |
[51] |
Summhammer J, Salari V, Bernroider G (2012) A quantum-mechanical description of ion motion within the confining potentials of voltage-gated ion channels. J Integr Neurosci 11: 123-135. https://doi.org/10.1142/S0219635212500094 ![]() |
[52] |
Summhammer J, Sulyok G, Bernroider G (2018) Quantum dynamics and non-local effects behind ion transition states during permeation in membrane channel proteins. Entropy 20: 558. https://doi.org/10.1142/S0219635212500094 ![]() |
[53] |
Summhammer J, Sulyok G, Bernroider G (2020) Quantum mechanical coherence of K+ ion wave packets increases conduction in the KcsA ion channel. Appl Sci 10: 4250. https://www.mdpi.com/2076-3417/10/12/4250 ![]() |
[54] |
Wang K, Wang S, Yang L, et al. (2021) THz trapped ion model and THz spectroscopy detection of potassium channels. Nano Res 15: 3825-3833. https://doi.org/10.1007/s12274-021-3965-z ![]() |
[55] |
Karandashev K, Xu ZH, Meuwly M, et al. (2017) Kinetic isotope effects and how to describe them. Struct Dynam 4: 061501. https://doi.org/10.1063/1.4996339 ![]() |
[56] |
Sen A, Kohen A (2010) Enzymatic tunneling and kinetic isotope effects: chemistry at the crossroads. J Phys Org Chem 23: 613-619. https://doi.org/10.1002/poc.1633 ![]() |
[57] |
Eckhardt AK, Gerbig D, Schreiner PR (2018) Heavy atom secondary kinetic isotope effect on H-tunneling. J Phys Chem A 122: 1488-1495. https://doi.org/10.1021/acs.jpca.7b12118 ![]() |
[58] |
Nappi P, Miceli F, Soldovieri MV, et al. (2020) Epileptic channelopathies caused by neuronal Kv7 (KCNQ) channel dysfunction. Pflüg Arch-Eur J Phy 472: 881-898. https://doi.org/10.1007/s00424-020-02404-2 ![]() |
[59] | Niday Z, Tzingounis AV (2018) Potassium channel gain of function in epilepsy: an unresolved paradox. Neurosci 24: 368-380. https://doi.org/10.1177/1073858418763752 |
[60] |
Miceli F, Soldovieri MV, Ambrosino P, et al. (2015) Early-onset epileptic encephalopathy caused by gain-of-function mutations in the voltage sensor of Kv7. 2 and Kv7. 3 potassium channel subunits. J Neurosci 35: 3782-3793. https://doi.org/10.1523/JNEUROSCI.4423-14.2015 ![]() |
[61] |
Du W, Bautista JF, Yang H, et al. (2005) Calcium-sensitive potassium channelopathy in human epilepsy and paroxysmal movement disorder. Nat Genet 37: 733-738. https://doi.org/10.1038/ng1585 ![]() |
[62] |
Robinson RB, Siegelbaum SA (2003) Hyperpolarization-activated cation currents: from molecules to physiological function. Annu Rev Physiol 65: 453-480. https://doi.org/10.1146/annurev.physiol.65.092101.142734 ![]() |
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