Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking

Progress in Biophysics and Molecular Biology xxx (2015) 1e17

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Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking E. Ravagli a, A. Bucchi b, C. Bartolucci a, M. Paina b, M. Baruscotti b, D. DiFrancesco b, S. Severi a, * a b

Computational Physiopathology Unit, Laboratory of Cellular and Molecular Engineering, D.E.I., University of Bologna, Via Venezia 52, 47521 Cesena, Italy The PaceLab, Department of Biosciences, University of Milan, Via Celoria 26, 20133 Milano, Italy

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 September 2015 Received in revised form 18 November 2015 Accepted 16 December 2015 Available online xxx

We used the Dynamic Clamp technique for i) comparative validation of conflicting computational models of the hyperpolarization-activated funny current, If, and ii) quantification of the role of If in mediating autonomic modulation of heart rate. Experimental protocols based on the injection of a real-time recalculated synthetic If current in sinoatrial rabbit cells were developed. Preliminary results of experiments mimicking the autonomic modulation of If demonstrated the need for a customization procedure to compensate for cellular heterogeneity. For this reason, we used a cellspecific approach, scaling the maximal conductance of the injected current based on the cell's spontaneous firing rate. The pacemaking rate, which was significantly reduced after application of Ivabradine, was restored by the injection of synthetic current based on the Severi-DiFrancesco formulation, while the injection of synthetic current based on the Maltsev-Lakatta formulation did not produce any significant variation. A positive virtual shift of the If activation curve, mimicking the Isoprenaline effects, led to a significant increase in pacemaking rate (þ17.3 ± 6.7%, p < 0.01), although of lower magnitude than that induced by real Isoprenaline (þ45.0 ± 26.1%). Similarly, a negative virtual shift of the activation curve significantly lowered the pacemaking rate (11.8 ± 1.9%, p < 0.001), as did the application of real Acetylcholine (20.5 ± 5.1%). The Dynamic Clamp approach, applied to the If study in cardiomyocytes for the first time and rateadapted to manage intercellular variability, indicated that: i) the quantitative description of the If current in the Severi-DiFrancesco model accurately reproduces the effects of the real current on rabbit sinoatrial cell pacemaking rate and ii) a significant portion (50e60%) of the physiological autonomic rate modulation is due to the shift of the If activation curve. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Dynamic Clamp Funny current Cardiac pacemaking Sinoatrial node Computational modeling Autonomic modulation

1. Introduction The role of the hyperpolarization-activated funny current, If, in sinoatrial node (SAN) activity and, ultimately, in the genesis and

Abbreviations: SAN, Sinoatrial node; AP, Action potential; DC, Dynamic clamp; DAQ, Data acquisition; MDP, Maximum diastolic potential; TOP, Take-off potential; CL, Cycle length; APD, Action potential duration; RyR, Ryanodine receptor; NCX, Sodium-calcium exchanger; DD, Diastolic Depolarization; DD1, Early diastolic depolarization slope; EDD, Early Diastolic Depolarization; LDD, Late Diastolic Depolarization; SDiF, Severi-DiFrancesco; ML, Maltsev Lakatta; IVA, Ivabradine; ISO, Isoprenaline; ACh, Acetylcholine. * Corresponding author. Computational Physiopathology Unit, Department of Electrical, Electronic and Information Engineering (DEI) “Guglielmo Marconi”, University of Bologna, Cesena, Italy Via Venezia 52; 47521 Cesena, (FC) Italy. E-mail address: [email protected] (S. Severi).

regulation of heart rhythm, has been studied extensively for many years, both in vivo and in silico, but remains a matter of intense debate. In particular, the contribution of If to pacemaking has been put into question by the development of mathematical models of SAN action potentials (APs) with very different If intensities. The problem is particularly relevant since in recent years If has become a target for pharmacological reduction of heart rate, which is beneficial in several pathologies, such as coronary artery disease and heart failure. In this work, we used the Dynamic Clamp (DC) technique for i) comparative validation of computational models of If and ii) quantification of the role of If in mediating autonomic modulation of heart rate. To achieve our aims we developed experimental protocols based on the injection of a real-time recalculated synthetic If current in

http://dx.doi.org/10.1016/j.pbiomolbio.2015.12.004 0079-6107/© 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Ravagli, E., et al., Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking, Progress in Biophysics and Molecular Biology (2015), http://dx.doi.org/10.1016/j.pbiomolbio.2015.12.004

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E. Ravagli et al. / Progress in Biophysics and Molecular Biology xxx (2015) 1e17

SAN rabbit cells, in conjunction with pacemaking-altering drugs. A particularly interesting point of this work is the cell-specific approach; indeed preliminary results in the autonomic modulation experiments demonstrated the need for a customization procedure to compensate for cellular heterogeneity. Before describing our experiments, we briefly introduce the topics of interest for our investigation. In the first subsection we summarize SAN pacemaking activity, its mechanisms and its connection with the If current. In the second subsection, mathematical models of SAN cells are introduced. The third subsection describes the general concept of Dynamic Clamp, the innovative experimental electrophysiology technique we used for our If investigation. Its history in cardiac electrophysiology, its variants, and the different technical implementations available are presented. 1.1. Cardiac pacemaker automatism: the role of funny If current In mammals, cardiac electrical activity originates in the SAN from specialized myocytes that rhythmically generate spontaneous APs. The most relevant functional feature of sinoatrial APs is the presence during diastole of a slow depolarization which acts as a clock to regulate the timing of consecutive action potentials. The duration of this pacemaker phase thus governs the cardiac chronotropism. In a healthy individual this process is repeated some 2.5 billion times over an average lifespan. One important physiological and clinical feature of a healthy SAN is its ability to cope with the constantly changing metabolic requirements of the organism, a feature which is reflected by the large range of the contraction rate (~40-~220 bpm) of the heart. This large variability is ensured by the continuous control of the slope of the diastolic depolarization by both circulating factors and neurotransmitters released by the autonomic branch of the nervous system. Sympathetic stimuli accelerate SAN rate by increasing the steepness of the pacemaker phase, while parasympathetic activation exerts the opposite action. Two main sets of molecular mechanisms are involved in generating the spontaneous depolarization: i) the “membrane clock”, which results from the combined activity of different membrane ion channels, among which the If current plays a central role; and ii) the “Ca2þ-clock”, which is sustained by the activity of ryanodine receptors (RyRs) and the Naþ/ Ca2þ exchange pump (NCX). These two mechanisms have been extensively investigated; however, their specific quantitative contributions, and relative importance, in controlling pacemaker activity are still debated (Mangoni and Nargeot, 2008; Lakatta and DiFrancesco, 2009). The membrane clock mechanism identifies with the rhythmic activity of voltage-gated ion channels, the molecular events that lead to charge movements (ionic fluxes) across the membrane. At the end of the action potential repolarization, around 55/-60 mV (Maximum Diastolic Potential, MDP) the net flow of membrane current reverses from outward to inward and this starts off the diastolic depolarization phase; this pacemaker phase brings the membrane voltage up to the Take-Off-Potential (TOP) where the fast upstroke of the action potential is initiated. A thorough comprehension of the ionic currents, pumps and exchangers playing a role during the diastolic depolarization must consider both outward and inward components. It has indeed been shown that both deactivating outward Kþ currents (IKr and IKs) and activating inward currents, such as the pacemaker current (If) and the T- and L-type Ca2þ currents, are dynamically involved during this phase (Mangoni and Nargeot, 2008; Dobrzynsky et al., 2013). Although the presence of INa in primary pacemaker cells is limited to peripheral SAN cells its contribution can be of relevance in the overall functional activity of the SAN (Milanesi et al., 2015). In

particular the If current (membrane clock) is responsible for the initiation of the diastolic depolarization (the Early Diastolic Depolarization, EDD), whereas the contribution of the NCX-based mechanism (calcium clock) is likely to be more relevant in the second part of the diastolic depolarization (Late Diastolic Depolarization, LDD) (Bucchi et al., 2007a). The If current (DiFrancesco, 1993; Baruscotti et al., 2010; DiFrancesco, 2010) is an inward current which activates in a time- and voltage-dependent manner at the end of the cell repolarization, and is modulated by direct interaction with the second messenger cAMP (DiFrancesco and Tortora, 1991). By increasing the cAMP content of SAN cells (via a mechanism mediated by adrenergic b-receptor activation), the sympathetic branch of the autonomic nervous system increases intracellular cAMP levels, and this in turn increases the availability of pacemaker f-channels; the opposite effect, i.e. a decrease in cAMP content and f-channel availability, occurs upon cholinergic stimulation of muscarinic M2 receptors. The mechanism by which cAMP levels control the f-channel availability relies upon the ability of cAMP molecules to lower the energy required for the closed-to-open transition when the molecules are bound to the channel. This causes the voltage dependence of the kinetic parameters (rate constants of the gating transition) to shift towards more positive potentials (see DiFrancesco, 1993; Altomare et al., 2001). The molecular determinants of pacemaker f-channels belong to the Hyperpolarization-activated Cyclic Nucleotide-gated channel family, which is part of the superfamily of Kþ channels. Of the four HCN isoforms (HCN1-4) known to be expressed in mammals, HCN4 is the one most expressed in mammalian SAN cells. The contribution of the If current to cardiac pacemaking in humans has been demonstrated by genetic and pharmacological studies (Baruscotti et al., 2005; DiFrancesco, 2010; Bucchi et al., 2012). In particular, mutations of the HCN4 gene have been associated with intrinsic arrhythmic behavior of the SAN (DiFrancesco, 2013; Milanesi et al., 2015). As a result, selective blockers of the If current have been developed for potential use in the clinic as heart rate-lowering agents. Currently, the only agent approved for clinical use is Ivabradine (IVA), available in several countries (Bucchi et al., 2007b). The proposed mechanism of the Ca2þ-clock relies on the spontaneous rhythmical release of small bursts of Ca2þ ions from the sarcoplasmic reticulum (SR) in SAN cells. These events, termed local diastolic Ca2þ releases (LCRs), determine the oscillation of subsarcolemmal Ca2þ content, which is coupled to the activation of the plasma membrane NCX. The electrogenic inward current generated at each NCX cycle ultimately acts in combination with the membrane-clock events to support the diastolic depolarization. 1.2. Numerical modeling The development of reliable mathematical models of the SAN AP may provide a deeper understanding of the “clocks” phenomenon than can be gained from experimental investigations alone. The first mathematical model reproducing pacemaker activity was created by Denis Noble in a notable paper in 1962 (Noble, 1962). This was followed by work by McAllister, Noble and Tsien in 1975 (McAllister et al., 1975), and then by other modeling studies a few years later (DiFrancesco and Noble, 1982; Noble and Noble, 1984; DiFrancesco and Noble, 1985). The historical perspective of SAN modeling has been reviewed few years ago (Wilders, 2007). It is worth mentioning that numerical cardiac modeling has received a prestigious recognition this year (2015). The Royal Society of London, to celebrate the 350th year of the Philosophical Transactions, selected a collection of the 33 most influential papers published since 1665, among which are papers by Newton, Joule,

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Maxwell, and Turing, to name a few. The list also includes the paper published in 1985 by DiFrancesco and Noble (DiFrancesco and Noble, 1985), the first numerical modeling of cardiac activity to include ion concentration changes. This recognition accurately expresses the general interest of the scientific community in biological numerical modeling in general, and cellular modeling in particular. One of the latest developments in SAN modeling is the addition of detailed calcium-handling dynamics, by Himeno (Himeno et al., 2008) and Maltsev and Lakatta (Maltsev and Lakatta, 2009). In particular, the latter developed a rabbit SAN model specifically addressing the interactions between intracellular calcium handling and membrane currents. Their model is mainly based on the Kurata model (Kurata et al., 2002). In 2012, a new rabbit SAN model was developed by Severi, DiFrancesco and collaborators (Severi et al., 2012), with the aim of improving the reproducibility of the available experimental data on the effects of If modifications. The SeveriDiFrancesco model, which includes updated descriptions of many membrane currents and intracellular mechanisms, is able to reproduce experimental data on pacemaking regulation due to neural modulation, If block, and inhibition of intracellular Ca2þ handling. 1.3. Applications of the Dynamic Clamp technique in cardiac electrophysiology The Dynamic Clamp (DC) technique is an evolution of the traditional current clamp. In its main configuration, used for the present study, a closed-loop control drives a current-clamp experiment. A myocyte is injected with a current whose amplitude and dynamics are constantly recalculated by an electronic system on the basis of a specific mathematical model. The model's input data is the voltage membrane potential of the cell, which is in turn sensitive to the current injection process, thus closing the loop. The investigator's control of the whole process is indirect; experiments are carried out by modifying the electrophysiological parameters of the mathematical model, possibly in conjunction with the perfusion of drugs into the investigated myocyte. The application of DC to the study of cardiac, endocrine and nervous cells has been previously reviewed in detail (Prinz et al., 2004; Goaillard and Marder, 2006; Wilders, 2006). We will summarize the recent DC cardiac applications and update past reviews with the more recent implementations. DC was introduced for the first time in cardiac electrophysiology by Scott (1979), who designed an analog circuit called Ersatz Nexus to electrically connect two independent groups of cardiomyocytes, without direct physical contact. It essentially functioned as a virtual gap junction. After a silent decade, at the beginning of the '90s, Joyner and coworkers (Joyner et al., 1990, 1991) implemented a coupling clamp circuit, with the same purpose of simulating intercellular electrical coupling through gap junctions. Although DC has existed in cardiac electrophysiology for well over 30 years now, it is more commonly used in neurophysiology. However, there is emerging interest in the potential of DC methodology in heart research. Different basic configurations of the DC technique are used in cardiac cellular electrophysiology: coupling clamp and model clamp, as well as some others such as dynamic AP clamp and celltype transforming clamp. The coupling clamp configuration (Fig. 1) simulates intercellular electrical coupling between myocytes through gap junctions. The membrane potentials of both cells are recorded in the current clamp mode. Based on the difference between Vm,1 and Vm,2 and a virtual conductance G, a personal computer (PC) computes the coupling current Ic flowing from myocyte 1 to myocyte 2 in real

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time. This configuration has been used by several groups, as listed in Fig. 1. The model clamp configuration (Fig. 2) is used to simulate the presence of an additional conductance on a cell membrane. In this case, a single isolated myocyte is involved in the DC measurement, and the Vm-dependent current Ix is injected into the cell. This configuration has been used to analyze the effect of several different currents, as detailed in Fig. 2. Recently, DC has also been applied in configurations different from the traditional coupling and model clamp. Instead of being computed, the virtual current may be recorded from a heterologous in vitro system, e.g. a HEK-293 cell, that expresses this current and is voltage-clamped by the free-running AP of the myocyte. Berecki et al. used this configuration, called the dynamic AP clamp (Wilders, 2006), to study the effect of hERG and SCN5A mutations identified in patients with long QT syndrome (Berecki et al., 2005, 2006, 2007). In the field of genetically engineered biopacemakers, Verkerk et al. (2008) used this technique to provide direct insight into the effects of introducing If current in a human atrial model; the current was generated by a transfected HEK293 cell, which was voltage-clamped by the AP generated in a realtime simulation of a human atrial cell model. Ahrens-Nicklas and Christini (2009) also introduced a new method, called the cell-type transforming clamp, allowing suppression of the interspecies differences of AP configurations in real time. The results were a change in AP morphology of the mouse cardiomyocyte to that typical of the human myocyte. Other applications of DC are related to the development of more complex networks involving two or more sheets of electrically coupled cells (Wagner et al., 1999; Joyner et al., 2000; Wang et al., 2000). The implementation aspects of DC were reviewed by Prinz et al. (2004) and Wilders (2006). In Table 1 we updated and integrated these reviews. Some of the earliest DC systems included hardware implementations with built-in analog devices. Instead of using dedicated hardware, the hardware available in most cardiac electrophysiology laboratories (e.g. a PC equipped with a multifunction data acquisition board (DAQ) and an electrophysiological amplifier) can be used as a DC system, with the help of dedicated software. As for the operating system, Table 1 reports the available software, which runs either on Windows or on real-time Linux (RT-Linux). All RT-Linux-based DC software requires a PC running the Linux operating system with one of the publicly available hard real-time extensions, e.g. RTAI (Real Time Application Interface, Department of Aerospace Science and Technologies, Polytechnic of Milano, Italy) or RTLinuxFree (FSMLabs, Socorro, NM, USA). RT-Linux, compared to Windows, has the advantage of running two processes, a realtime process (top priority, guaranteed timing) and the standard Linux operating system (low priority, interruptible by the real-time process), as set out in detail by Christini et al. (1999). The ‘Real-Time eXperiment Interface’ (RTXI, Lin et al., 2010; Ortega et al., 2014) was developed starting from RTLDC (Realtime Linux dynamic controller, Dorval et al., 2001) and MRCI (Model reference current injection, Raikov et al., 2004). RTXI is open-source and free; it uses a modular architecture, which allows the construction of complex experimental protocols using a combination of built-in, community-shared, and self-made modules. For these reasons RTXI was used in our experiments. Other platforms have also been used; Clausen et al. (2013) described a DC implementation in MATLAB designed to study different currents in cardiac electrophysiology, while Yang et al. (2015) have developed a new interface that uses a common personal computer platform, with National Instruments data acquisition and WaveMetrics IGOR, to provide a simple user interface in neurophysiology.

Please cite this article in press as: Ravagli, E., et al., Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking, Progress in Biophysics and Molecular Biology (2015), http://dx.doi.org/10.1016/j.pbiomolbio.2015.12.004

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Fig. 1. Coupling Clamp. Left panel: schematic of the connection between cells, amplifiers and computer in the coupling clamp DC configuration. The membrane potentials of two isolated myocytes (Vm,1 and Vm,2), both in current clamp mode, are sampled into a computer and a coupling current (Ic) is calculated. Command potentials (Vcmd,1,Vcmd,2) are then sent to the patch-clamp amplifiers to inject Ic into the myocytes as additional membrane current. Right panel: list of publications using the DC Coupling Clamp configuration for cardiac applications.

Fig. 2. Model Clamp. Left panel: schematic representation of the connection between cell, amplifier and computer in the model clamp DC configuration. The membrane potential of an isolated myocyte in current clamp mode (Vm) is sampled into a computer. An additional Vm-dependent membrane current (Ix) is computed and a command potential (Vcmd) is sent to the patch-clamp amplifier to inject Ix into the myocyte via the recording patch pipette. Right panel: list of publications using the DC Model Clamp configuration for cardiac applications. Ic ¼ coupling current; ISAC ¼ stretch-activated current.

Past applications of DC in cardiac cellular electrophysiology clearly indicate its valuable contribution to the investigation of many issues related to the basic cellular mechanisms of AP formation, propagation and synchronization, in both healthy and diseased myocardium. On the other hand, DC has some limitations, as does any experimental technique. Here is a short list. The glass microelectrode passes the correct electrical charge, but the charge-carrying ions are normally of a different species than the ones of the simulated current. Obvious examples are

calcium currents, which can only be simulated by DC on the electrical side, with no concurrent alterations in intracellular calcium concentration. An important technical issue to be addressed in order to inject specific ions into the cell is the availability of electrodes releasing such specific ions. In the case of calcium ions, moreover, perforated patch could not be used since it does not allow divalent ions such as Ca2þ to flow from the pipette to the cytosol. It is worth noting that, even when a virtual current is made of

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Table 1 Publicly available Dynamic Clamp implementations. This list updates and integrates the previous review work of Prinz et al. (2004) and Wilders (2006). See text for additional references. Name

References

NetClamp

Trexler et al. (2013)

Platform

URL and notes

Windows http://gothamsci.com/NetClamp/  Replaces the Dynamic Clamp by Manor and Nadim (2001)  Hardware requirements: E Series or M Series PCI boards from National Instruments. DYNCLAMP4 Pinto et al. (2001) Windows http://fge.if.usp.br/~reynaldo/dynclamp.html  Requires Axon Instruments Digidata 1200A data acquisition board G-clamp v2 Kullman et al. (2004) Windows http://hornlab.neurobio.pitt.edu/  Requires LabVIEW-RT 8.0 (or higher) hardware and software components, National Instrument DAQmx Advanced dynamic clamp Muniz et al. (2005) RT-Linux http://arantxa.ii.uam.es/~gnb/adclamp/ RTXI Lin et al. (2010) RT-Linux http://rtxi.org/  Merging of the Real-time experiment interface system (RTLab, Culianu and Christini, 2001e2002), Real-Time Linux Dynamic Clamp (RTLDC, Dorval et al., 2001), and Model Reference Current Injection (MRCI, Butera et al., 2001; Raikov et al., 2004) Yang et al. (2015) Windows http://www.biology.buffalo.edu/Faculty/Xu_Friedman/mafPC/sign_in.html  Requires hardware (PC and National Instruments) and software (Wavemetrics IGOR) interfaces.

the correct ion species, the injected current will always enter the cell through the glass microelectrode rather than through the real ionic channels. Thus the flow of current is concentrated in a very specific spot of the cellular membrane, rather than exhibiting the dispersed current flow associated with the overall surface distribution of a population of ion channels. This difference can affect the interaction between ion channels and transporters in the membrane microdomains (e.g. caveolae) and the ion kinetics in the different intracellular compartments, which in turn can influence the overall electrical excitation and contraction of the cell. Furthermore, errors may be introduced in the experiment by the limitations of the technical setup. One such example is latency, i.e. the time lag between measuring the voltage and applying the current based on that voltage. Real-time systems are built in a way that guarantees that required operations are carried out within a specific time limit or not at all; rather than slowing operations, the system would instead return an error message. There is no intrinsic limitation to the reproduction of the specific currents or models, but models with more mathematical complexity will need setups with more computational power to sustain the required update rate. This rate is, in turn, defined by the model dynamics. For example, in the case of INa, the time for the update of the model status variables must be very short, because of the very fast current dynamics. One Dynamic Clamp setup able to generate INa was developed by Clausen et al. (2013). Errors may be also introduced by the specific type of DC technique chosen for the experiment. In the case of a model clamp, for example, the mathematical description of the chosen ionic current needs to be sufficiently accurate to provide reliable results d unless, of course, the implemented mathematical model is itself the object of study. Moreover, model clamp experiments inherited a limitation of the computational approach to cardiac cell electrophysiology, which is usually focused on the average cell, discarding individual differences. In fact, the experimental results are often averaged in order to derive the computational model that describes the “typical” behavior of a cell. Although all experimentally measured APs are different, even within a homogeneous population, a single AP model is obtained from the data; information regarding individual variability is lost (Britton et al., 2013). Therefore, using the same mathematical model for each cell during model clamp experiments represents a limitation. This work addresses this limitation for the first time, by adapting the model of the virtual current to be injected into the specific single cell according to the characteristics of the electrical activity recorded in the cell itself in basal conditions.

2. Materials and Methods 2.1. Cell preparation Animal protocols conformed to the guidelines of the care and use of laboratory animals established by Italian (DL. 26/2014) and European (2010/63/UE) directives. Young white albino rabbits (0.8e1.2 Kg) were deeply anesthetized by intramuscular injection of Acepromazine (1 mg/kg) and euthanized with intravenous injection of sodium thiopental (60 mg/kg) and exsanguination. Single rabbit SAN cells were obtained by an enzymatic and mechanical procedure as reported in Bucchi et al. (2007a). Spontaneous activity was recorded by perforated-patch. The external (Tyrode) solution contained (mM): 140 NaCl, 5.4 KCl, 1.8 CaCl2, 1 MgCl2, 5 HEPESNaOH, 10 D-glucose, pH 7.4. The pipette solution contained (mM): 130 K-Aspartate, 10 NaCl, 2 CaCl2 (pCa ¼ 7), 2 MgCl2, 10 HEPES, 5 EGTA, 2 ATP(Na-salt), 0.1 GTP, 5 Creatine Phosphate, pH 7.2. Both solutions were prepared as previously reported in Bucchi et al. (2007a). Amphotericin B (100e250 mg/ml) was added to the pipette solution. T ¼ 37 ± 0.5  C. 2.2. Experimental setup The experimental setup consisted of traditional electrophysiology instrumentation, combined with additional hardware and software as needed for the Dynamic Clamp protocols. Fig. 3 shows a conceptual representation of our setup. An Axopatch 200B Amplifier (Molecular Devices, USA) was set in current-clamp mode, to inject a stimulation current Istim and record cellular activity in the form of membrane potential Vm. The External Command connector was used to pilot Istim shape and intensity in real time through an input voltage signal, VCmd. The current generated by the analog electronics in the amplifier is proportional to VCmd. The amplifier's Vm and VCmd channels were connected to a data acquisition board (DAQ NI-PCI-6221, National Instruments), outfitted with 16-bit resolution analog I/O channels. The board was mounted in a PCI slot of a PC running the RT-Linux Operative System. The RTXI (Real-Time eXperiment Interface (Lin et al., 2010; http://rtxi.org) software platform was used to implement and run the DC protocols, described in the following paragraphs. Different experimental protocols were designed and tested with this setup, each with its custom RTXI software code. Before providing the details of each protocol, we offer a general description here. The membrane potential Vm is acquired by the DAQ board input channel, then the protocol-specific model for the stimulus current is updated and a new VCmd value is returned to pilot the

Please cite this article in press as: Ravagli, E., et al., Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking, Progress in Biophysics and Molecular Biology (2015), http://dx.doi.org/10.1016/j.pbiomolbio.2015.12.004

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Fig. 3. Experimental Setup. A schematic representation of the most important components in our experimental setup and their interconnections. A PC running the RT-Linux OS and the RTXI software drives a DAQ card which is in turn connected to the amplifier. The amplifier is connected to the SAN cell under analysis through a headstage. A smoothing filter is placed between the DAQ output and the amplifier input. A secondary PC is used to record voltage and current tracings.

amplifier's headstage current injection. The system update frequency was set to 1 kHz, much faster than the simulated process. The updating process of the model-based current includes simple arithmetical operations and the integration of an ordinary differential equation, formulated as a gating variable. The forward-Eulero method was used for this task: between each Vm sampling step, 100 integration steps are performed. Some additional operations had to be carried out to adapt our command signal to the amplifier specifications. The DAQ board output channels have a fixed voltage range of ±10 V, and the amplifier has two gain options for the conversion of VCmd to IStim: 2 or 20 nA/V. Even with the adoption of the most favorable gain value, a direct board-to-amplifier connection would have prevented us from exploiting the board's high-resolution; since If is a very small current, the resulting IStim value would suffer from strong discretization due to the use of only a small number of digital levels. For this reason, the computed VCmd was multiplied by a factor of 100 before analog output, to exploit more discretization levels. After D/A conversion, the signal was processed by a passive first-order circuit to restore the correct level (100-factor attenuation) and provide low-pass filtering. The cut-off frequency of the filter was 40 Hz, higher than the relevant harmonics for the If current. Both Vm and VCmd signals were recorded by a PC running PCLAMP software (Molecular Devices) using signal-splitting connectors for the purpose of visualization and recording. The sampling rate for PCLAMP recordings was 2 KHz. The Vm signal, containing APs, was processed with custom software for pacemaking rate evaluation and extraction of relevant parameters. 2.3. Dynamic Clamp protocols Two different test protocols were implemented using custom RTXI modules. The fast closed-loop feedback mechanism was used in conjunction with Ivabradine (IVA protocol) and Acetylcholine or Isoprenaline (Ach/ISO protocol) in the bath. Before the start of each experiment, the membrane capacitance of the cell under examination was measured. The estimated value was used to scale the injected current amplitude and maintain the

same current density regardless of cell size. A second scaling factor was also added to the injected current after analyzing the results of the preliminary experiments. A detailed description, including the reasons for its inclusion, is provided in the Results section (Subsections 3.1 and 3.2). 2.3.1. IVA protocol This protocol was defined in order to investigate the effect on basal pacemaking rate of replacing the If current (blocked by Ivabradine) with a synthetic current, whose shape and intensity were computed with different mathematical formulations of If presented in the literature. Two different models were tested: the SDiF model (Severi et al., 2012) and the ML model (Maltsev and Lakatta, 2009). These single-cell SAN models differ greatly in their description of If; this difference is mainly expressed by the maximum current intensity reached during normal activity in the slow diastolic depolarization phase. The simulations were performed using the same ionic concentrations for both models ([Naþ]i ¼ 7.5 mM, [Naþ]o ¼ 140 mM, [Kþ]i ¼ 140 mM, [Kþ]o ¼ 5.4 mM), in order to evaluate reversal potential for the synthetic current. The protocol starts with the acquisition of control AP recordings to evaluate basal pacemaking rate, after which 3 mM Ivabradine is applied. At this concentration, the drug interacts with the cell by blocking the majority of If channels, thus slowing pacemaker activity. The subsequent step is the activation (via the Dynamic Clamp software interface) of the synthetic current injection, whose value is computed in real time using one of the two models. The current value is scaled to 66% to reproduce the extent of channel block caused by this concentration of Ivabradine (65.9 ± 2.4%, Bucchi et al., 2002). AP recording continues in this new condition for a time sufficient to detect any pacemaking rate change, and then current injection with the second model is carried out. Fig. 4 visually represents the IVA protocol timeline. A more detailed description of the computation of the updated synthetic current value is provided in Fig. 5. 2.3.2. ISO/Ach protocol This protocol (described in Fig. 6) was defined in order to

Please cite this article in press as: Ravagli, E., et al., Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking, Progress in Biophysics and Molecular Biology (2015), http://dx.doi.org/10.1016/j.pbiomolbio.2015.12.004

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Fig. 4. IVA Protocol Timeline. Control APs are recorded before and after the application of Ivabradine. The APs are also recorded after the injection of each of the two synthetic currents derived from the SDiF and ML models.

Fig. 5. Synthetic Current Computation for IVA Protocol. After each sampling of membrane potential Vm, the gating variable value is recalculated by numerical integration and the value for current injection is updated. y ¼ gating variable. y∞ ¼ steadystate curve for the gating variable y. ty ¼ time constant for the gating variable y.

investigate the effect on basal pacemaking rate of a “virtual shift” of the If activation curve, mimicking the autonomic modulation of If as reproduced in experiments with Isoprenaline (1 mM) and Acetylcholine (10 nM). In contrast to the previous protocol, the synthetic current effect and drug effect were evaluated separately, with no direct superposition in time. Since experiments with Ivabradine led to the conclusion that the SDiF model more adequately describes the quantitative contribution of If to SAN pacemaking (see the Results section), we chose this model for the ISO and ACh experiments. The simulations were performed using the same ionic concentration values used in the IVA protocol. As in the IVA protocol, control APs were acquired first. Synthetic current was then injected, and APs were recorded to quantify pacemaking rate changes. The influence of Isoprenaline and Acetylcholine on If is described as a shift in the voltage dependence of gating variable kinetics, specifically on the steady-state and time constant curves. The influence of Isoprenaline on If was modeled as

a þ7.5 mV shift and that of ACh as a 4.95 mV shift. The ISO and ACh effects on If activation kinetics were modeled according to the work of Severi et al. (2012), on the basis of the relations derived experimentally by Zaza et al. (1996). Specific values for the activation shifts were calculated by selecting the same concentrations used experimentally in the present study (1 mM ISO and 10 nM ACh). These values agree well with those reported in the literature for similar range of concentrations (Accili et al., 1997a; Accili et al., 1997b; Hagiwara and Irisawa, 1989; Zaza et al., 1996; Bucchi et al., 2003; Barbuti et al., 2007; Renaudon et al., 1997). The current and gating kinetics equations for the standard and voltage-shifted If currents were updated in real time by our custom software modules (Fig. 7). The first current value was then subtracted from the second, leading to the injection of a differential DIf value (Eq. (1)). Assuming the calculated control current value was roughly comparable to the real If in intensity and shape, what remained was equivalent to the shifted If current, simulating the drug's effect (Eq. (2)).

DIf ¼ If;shifted  If;Control

(1)

If ;real þ DIf ¼ If;real þIf;shifted  If;Control zIf;Shifted

(2)

After recording a sufficient number of APs, current injection was disabled, control APs were acquired again, and then the real drug was applied to compare its effect on pacemaking rate with our simulated drug effect on If.

2.4. Data processing and statistical analysis AP recordings were undersampled from 2 KHz to 500 Hz and analyzed with custom software to calculate pacemaking rate, Maximum Diastolic Potential, Take-Off Potential, and slope of the early Diastolic Depolarization (DD1), as described in Bucchi et al. (2007a). Briefly: action potential traces were digitally smoothed using a 10-point adjacent averaging smoothing procedure and then the time derivative (dV/dt) (Origin 9.1 OriginLab Corporation) was calculated. A customized software was then used to calculate the following parameters:

Fig. 6. ISO/ACh Protocol Timeline. APs are recorded in the control condition, and then a synthetic current simulating the effect of Isoprenaline or Acetylcholine is applied. APs are recorded in this new condition, then the synthetic current is switched off and the real drug is applied. APs during the drug effect are then recorded.

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Fig. 7. Synthetic Current Computation for ISO/Ach Protocol. Both control and shifted gating variable values are updated continuously based on membrane voltage potential. The difference between the shifted and control values of the If current is injected into the cell. y ¼ gating variable. y∞ ¼ steady-state curve for the gating variable y. ty ¼ time constant for the gating variable y.

(a) Maximum Diastolic Potential (MDP, mV), defined as the most negative potential reached during action potential repolarization; (b) Take-Off Potential (TOP, mV), defined as the voltage measured at the time when the voltage derivative (dV/dt) overtakes a given threshold, set to 0.5 mV/ms for all records; (c) slope of early (DD1, mV/ms) and late (DD2, mV/ms) Diastolic Depolarization. The diastolic depolarization (DD) was defined as the phase of the action potential comprised in the interval between MDP and TOP (Dt ¼ time of TOP  time of MDP); the DD1 was calculated as the slope of the early fraction of the DD interval Dt (defined as 0.1 Dt to 0.5 Dt); the DD2 was calculated as the slope of the late fraction of the DD interval Dt (defined as 0.5 Dt to 0.9 Dt). For each protocol the average values of the described parameters were calculated in different experimental conditions (control, current injection, drug application, etc.) and analyzed with the ANOVA test for repeated measures (Geisser-Greenhouse adjustment) and TukeyeKramer test for multiple comparisons (NCSS 2007, Kaysville, Utah, www.NCSS.com). All data results are reported as Mean ± Standard Deviation. 3. Results 3.1. Preliminary results with IVA protocol Results obtained with the Ivabradine protocol are shown in Fig. 8. The top panel shows representative APs recorded from one cell during different protocol conditions. The pacemaking rate was significantly reduced relative to control (2.77 ± 0.38 Hz) after application of 3 mM Ivabradine (2.20 ± 0.17 Hz, p < 0.05), and the rate decrease (20.6%) was comparable with values reported in the literature (23.8 ± 3.9 Hz, Thollon et al., 1994; 16.2 ± 1.5, Bucchi et al., 2007a). As described previously, the If conductance was scaled to 66% of the nominal value. The injection of the SDiF66 synthetic current increased the mean pacemaking rate in the presence of Ivabradine,

Fig. 8. Results of Ivabradine protocol early experiments. Top panel: superimposed AP traces from a representative cell. Bottom panel: mean results for pacemaking rate (n ¼ 9). * ¼ p < 0.05 vs Control.

restoring the frequency rate to a value close to that of the control (2.70 ± 0.27 Hz, N.S.). On the other hand, injection of ML66 synthetic current induced a smaller recovery, not sufficient to restore control rate (2.39 ± 0.30 Hz, p < 0.05 vs both Ivabradine and Control). An additional test with 100% of If conductance was carried out (ML100), equivalent to the injection of the total calculated synthetic If current, which adds to the current remaining after block. The increase in current intensity in ML100 led to results similar to the ML66 current injection d a rate value significantly different from the Ivabradine level (2.36 ± 0.25 Hz, p < 0.05 vs Ivabradine) but not high enough to reach the control value. For comparison, injection of 100% current was also tested with the SDiF model (SDiF100); this led to a slightly higher rate, albeit not significantly different from control (2.80 ± 0.28 Hz, N.S. vs Control). Based on these results, we chose to adopt the SDiF model as the mathematical basis for shift calculations in the ISO/ACh protocol.

3.2. Rate-adaptation of Dynamic Clamp for cell-specific experiments Initial experiments with the Acetylcholine protocol showed that, in some cells, injection of the differential synthetic current DIf led to a rapid hyperpolarization and excessive pacemaking rate reduction. These effects were stronger than those obtained during ACh perfusion, and sometimes even led to a complete stop of pacemaker activity. This phenomenon only occurred in some of the cells. On the contrary, some cells did not show any significant change in pacemaking rate after activation of our protocol. Rate response in our initial experiments is shown in Fig. 9 for both insensitive and hypersensitive cells. Hypersensitive cells clearly

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had a lower control rate with respect to insensitive ones (p < 0.001). Notice that shift protocol results were obtained by injecting the same amount of DIf current into all the cells, as calculated from the mean model (see Materials and Methods). The problem appears to be related to the magnitude of the injected current. In “fast” cells the current injected appears not to be large enough, whereas in “slow” cells too much current appears to be injected. For hypersensitive cells, the outward DIf current calculated by the DC module seemed to be excessive; it acted as a strong hyperpolarizing mechanism, causing a shift of the membrane voltage to highly negative levels. This, in turn, increased the intensity of the dynamically recalculated synthetic current; because it was calculated on the basis of the If activation curve, it was bound to increase at negative voltages. This positive feedback mechanism therefore led to a very long prolongation of the diastolic phase and even to a complete stop of the spontaneous activity, as shown in the example in Fig. 10. A similar effect was probably present for insensitive cells with a higher spontaneous pacemaking rate, but the injection of an inward current in that case led to a negative feedback, which prevented any instability. These findings can be explained if biological heterogeneity for ionic current density is taken into account. As each cell expresses an If current density that deviates from the average value due to biological heterogeneity, different cells will have different maximum conductance values for If due to variability in the channel population. Because of the If role in pacemaking, this will lead to variability in the pacemaking rate. In fact, the same effect may have been present in the early Isoprenaline experiments (not shown); it would have gone unnoticed because of the negative-feedback nature of the ISO experiment. To tune our model-based calculation and avoid injection of feedback current that was too high or too low, an additional scaling factor was defined for the output current. This scaling parameter was computed with a custom RTXI module that acquired control APs at the beginning of each test to estimate an average control cycle length (CL), returning the estimated scaling factor which was used for the rest of the experiment. The estimation was based on simulations with the SDiF model (Fig. 11, red points and black line). Modulating the maximum If conductance gf in the model by a variable gScaling factor, it is possible (for a reasonable frequency range) to map the relation between gf and the pacemaking

9

Fig. 10. Voltage and current recordings from a hypersensitive cell targeted with the ACh protocol. Top panel: membrane potential. Bottom panel: injected current. The current is recorded as negative due to the voltage sign convention on the Axon connector, but it is actually an outward current.

Fig. 11. Effect of If conductance scaling on SDiF and ML models' pacemaking rate. Behavior of the SDiF model (black points) fitted with an empirical equation to obtain a scaling computation equation (black line). Behavior of the ML model is also reported (black squares).

frequency. The ML model formulation of If was also taken into consideration for the development of the conductance-scaling equation, but as shown in Fig. 11 (black squares), the model only allowed the reproduction of very limited changes of rate by changing gf. This relationship can then be reversed to calculate the appropriate gScaling value, starting from the measured CL:

gScaling ¼ K1 þK2 $expð  ðCycle LengthÞ=ðtÞÞ

Fig. 9. Influence of control rate on pacemaking stability in the original ACh protocol. The effect of our original ACh protocol on rate is shown for insensitive cells (solid line) and hypersensitive (dashed black line) cells.

(3)

Using an error-minimization procedure, the parameter values were fitted to K1 ¼ 0.1605, K2 ¼ 294.3342 and t ¼ 60.2927. CL and t are expressed in milliseconds. Fig. 11 shows the results of fitting our equation (black line) to model-derived data (black dots). This equation was used to tune our IStim value for each cell. Results in the

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following sections refer to new experiments carried out with this cell-specific rate adaptation. Data from earlier experiments, in which no scaling was applied (gScaling ¼ 1), are included only for those cells which had a theoretical scaling factor (calculated from the control rate recorded during the experiment) close to unity. 3.3. Ivabradine results Table 2 reports numeric values for all analyzed variables. Fig. 12 reports the rate (left) and DD1 (right) results of our experiment with the IVA protocol. As expected, in this case the results with the rate-adapted DC were fully consistent with the preliminary ones. The pacemaking rate, which was significantly reduced after application of Ivabradine, was restored by the injection of the SDiF66 synthetic current, while the injection of the ML66 synthetic current did not produce any significant variation. No significant differences were found between MDPs in all groups. DD1 decreased when Ivabradine was applied (p < 0.001 vs Control). The injection of current calculated with the SDIF66 model was able to restore DD1 to the control value. Whereas the injection of ML66 current did not lead to any significant change from the value of DD1 under Ivabradine. DD1 values for SDiF100 and ML100 currents were consistent with the rate results: DD1 for SDiF100 was not significantly different from the control and SDiF66 values, and DD1 for ML100 was not significantly different from the Ivabradine and ML66 values. Regarding TOP, no significant difference was found from control value for any groups. Fig. 13 shows representative voltage and current traces from one of the analyzed cells, along with the corresponding rate analysis. Starting from control APs (upper right panel, dashed black line), the application of Ivabradine slowed the rate (dotted gray line). APs recorded during SDiF66 current injection returned to the control rate, whereas APs recorded during the ML66 phase did not. The recorded traces from current injection in the lower-right panel show how the two models follow a different dynamic, especially during depolarization; the SDiF66 current (solid black line) is clearly larger than the ML66 current (solid gray line). A typical rate signal is also reported (left panel), demonstrating a slow rate reduction due to Ivabradine, superimposed to some beatto-beat variability. Additionally, the effect of SDiF synthetic current injection can be clearly distinguished. 3.4. Isoprenaline results The results of the experiments with the Isoprenaline protocol are reported in Fig. 14 and Table 3. Table 3 also reports numeric values for all analyzed variables. We can see that injection of the synthetic ISO shift led to a significant (þ17.3 ± 6.7%) increase in pacemaking rate (p < 0.01 vs Control); applying real Isoprenaline Table 2 Numerical results for the IVA experiments. Group

Rate [Hz]

Control IVA SDif66 SDif100 ML66 ML100

2.91 2.34 2.76 2.87 2.40 2.46

± ± ± ± ± ±

0.37 0.37*** 0.34 0.36 0.34*** 0.35***

MDP [mV]

DD1 [mV/ms]

64.6 64.0 63.7 63.5 64.1 64.0

0.0737 0.0418 0.0706 0.0795 0.0464 0.0478

± ± ± ± ± ±

2.4 2.6 2.5 2.3 2.1 2.3

± ± ± ± ± ±

0.0215 0.0127*** 0.0103 0.0133 0.0122*** 0.0125***

TOP [mV] 45.1 45.9 43.9 44.0 45.6 45.5

Rate, MDP, DD1 and TOP values for all different experimental conditions. *** ¼ P < 0.001 vs Control (n ¼ 7).

± ± ± ± ± ±

3.6 4.5 4.0 3.6 4.2 3.9

also induced an increase in pacemaking rate (p < 0.001 vs Control), but of a higher magnitude (þ45.0 ± 26.1%). See Fig. 14, left panel. The pacemaking rate during current injection was significantly higher than that of the control, but lower than the value during perfusion with Isoprenaline (p < 0.01). The MDP was statistically different between groups (p < 0.05). As shown in Table 3, the maximum difference between values was less than 1 mV. Both ISO (p < 0.01) and Shift (p < 0.05) MDPs are different from control. An increase in DD1 was observed when both SDiF synthetic current and real Isoprenaline were applied (p < 0.01), with no significant difference between the two conditions (Fig. 14, right panel). On the contrary, DD2 in the presence of Isoprenaline was steeper than in the presence of the synthetic current. The TOP under Isoprenaline was lower (more negative) than after synthetic current injection by z 3 mV (p < 0.01). Rate analysis, AP and current traces from one of the analyzed cells are illustrated in Fig. 15. The application of the synthetic shift current caused a rise in pacemaking rate, as did Isoprenaline (Fig. 15, left panel). 3.5. Acetylcholine results Experiments with Acetylcholine were run with the same implementation used for the Isoprenaline experiments, and yielded conceptually similar results. Numeric values for all analyzed variables are reported in Table 4. Fig. 16 shows that all cells are, to some degree, sensitive to our new cell-specific version of the shift protocol. As shown in Fig. 17 (left panel), the injection of shift current significantly lowered the pacemaking rate (p < 0.001), as did the application of real Acetylcholine (p < 0.001). The resulting lowered pacemaking rate was also significantly different from the rate determined by the real drug action (p < 0.05). The shift-induced rate decrease amounted to 11.8 ± 1.9%. The ACh-induced rate decrease (20.5 ± 5.1%) was comparable to values reported in the literature (20.8 ± 3.2%, Bucchi et al., 2007a). No significant differences were found between groups in MDP and TOP. A decrease relative to the control value was observed in DD1 when SDiF synthetic current was applied (p < 0.001). DD1 also decreased when real Acetylcholine was applied (p < 0.001) with no significant difference between the two conditions. A decrease relative to control was also observed in DD2 in both conditions, with higher statistical significance in the case of real Ach application. Rate analysis, AP and current traces from one of the analyzed cells are illustrated in Fig. 18. 4. Discussion 4.1. Results analysis The experiments described in this work were developed to investigate the use of Dynamic Clamp for model validation as well as quantify the contribution of If during autonomic rate modulation. Our results demonstrate that the DC technique can be used as a model validation tool. Furthermore, the protocol we developed showed that the SDiF mathematical formulation of If is able to integrate itself with the physiological mechanisms of a real SAN cell. Further experiments led to an estimation of the contribution of the funny current to the total rate modulation effects. To the best of our knowledge, our protocol is the first of its kind to isolate and quantify the If contribution to autonomic rate modulation. Results obtained with the IVA protocol show that blocking a

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Fig. 12. IVA Protocol Results for Pacemaking Rate and DD1. Left: Mean Pacemaking Rate during different phases of the IVA protocol. Right: Average value of DD1 during various phases of the Ivabradine experiments. *** ¼ P < 0.001 vs Control (n ¼ 7).

Fig. 13. Example of IVA Protocol recorded signals. Left panel: Pacemaking rate during different phases of the Ivabradine Experiment. Right panel, upper: superimposed AP traces for control (dashed black line), Ivabradine (dotted gray line), SDiF model 66% (solid black line) and ML model 66% (solid gray line). Right panel, lower: corresponding current injection traces. Inward current is shown as positive due to a recording convention.

Fig. 14. ISO Protocol Rate Results. Left: Mean Pacemaking Rate during different phases of the ISO protocol. Right: DD1 value during various phases of the ISO experiments. ** ¼ P < 0.01 vs Control. *** ¼ P < 0.001 vs Control. x ¼ P < 0.01 vs ISO (n ¼ 6).

large fraction (z66%) of the physiological If current in a SAN cell and substituting it with a model-based current has different effects,

depending on the If mathematical formulation. Note that a total block of the physiological If would have required a higher

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Table 3 Numeric Results for the ISO experiments. Group

Rate [Hz]

MDP [mV]

DD1 [mV/ms]

DD2 [mV/ms]

TOP [mV]

Control ISO Shift þ7.5 mV

2.46 ± 0.47 3.43 ± 0.31*** 2.92 ± 0.62**xx

64.8 ± 3.0 63.9 ± 3.3** 64.1 ± 3.3*

0.067 ± 0.021 0.114 ± 0.023** 0.102 ± 0.041**

0.092 ± 0.028 0.200 ± 0.060** 0.125 ± 0.026x

44.5 ± 5.2 45.7 ± 5.3 42.7 ± 5.5xx

Rate, MDP, DD1 and TOP values for all different experimental conditions. * ¼ P < 0.05 vs Control. ** ¼ P < 0.01 vs Control. *** ¼ P < 0.001 vs Control. x ¼ P < 0.05 vs ISO. xx ¼ P < 0.01 vs ISO.

Fig. 15. Example of ISO Protocol recorded signals. Left panel: Pacemaking rate during different phases of the Isoprenaline Experiment. Right panel, upper: superimposed AP traces for control (dashed black line), Shift þ7.5 mV (solid black line) and Isoprenaline (solid gray line). Right panel, lower: corresponding current injection traces. Inward current is shown as positive due to a recording convention.

Table 4 Numeric Results for the ACh experiments. Group

Rate [Hz]

MDP [mV]

DD1 [mV/ms]

DD2 [mV/ms]

TOP [mV]

Control ACh Shift 4.95 mV

2.98 ± 0.72 2.37 ± 0.64*** 2.62 ± 0.64***,x

62.6 ± 3.9 62.7 ± 4.3 63.2 ± 3.7

0.0795 ± 0.0135 0.0560 ± 0.0141*** 0.0599 ± 0.0095***

0.116 ± 0.037 0.085 ± 0.038*** 0.092 ± 0.034**

41.9 ± 2.6 41.2 ± 3.7 43.0 ± 3.0

Rate, MDP, DD1 and TOP values for all different experimental conditions. ** ¼ P < 0.01 vs Control. *** ¼ P < 0.001 vs Control; x ¼ P < 0.05 vs ACh (n ¼ 6).

Fig. 16. Pacemaking stability in the cell-specific ACh experiment. Pacemaking rate behavior of cells under the new version of our shift protocol.

concentration of Ivabradine, with the side effect of influencing other cellular mechanisms in addition to the funny current, which would have invalidated the selectivity of our protocol. In our specific case, we chose to compare the effects of the SDiF and ML formulations of If on SAN cells. The SDiF formulation is associated with a significant role of If in diastolic depolarization, while the ML formulation assigns a smaller role to If. The If contribution is mostly related to the maximum current amplitude reached, rather than to the shape of the current time course, which is similar for the two formulations (see, e.g., Fig. 13, lower right panel). Our data show that the SDiF synthetic current is able to restore the original pacemaking rate of the cells prior to current blocking, while the ML-based current is not. Results obtained for the DD1 parameter are consistent with rate results: SDiF current injection also restores the original early depolarization slope, while ML current injection does not. While the lack of meaningful differences in TOP values is expected, since If is obviously very small at these membrane potentials, the lack of influence of different If formulations on MDP means that neither model provides much current at that specific point. Overall, our IVA experiment results suggest that the SDiF If formulation is able to sustain physiological pacemaking in experimental conditions, while the ML formulation is not.

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Fig. 17. ACh Protocol Rate Results. Left: Mean Pacemaking Rate during different phases of the ACh protocol. Right: Mean value of DD1 during various phases of the Acetylcholine experiments. *** ¼ P < 0.001 vs Control; x ¼ P < 0.05 vs ACh (n ¼ 6).

Fig. 18. Example of ACh Protocol results. Left panel: Pacemaking rate during different phases of the Acetylcholine experiment. Right panel, upper: superimposed AP traces for Control (dashed black line), Acetylcholine (solid gray line) and Shift current (solid black line). Right panel, lower: corresponding current injection traces. Outward current is shown as negative due to a recording convention.

The effect on pacing rate of injecting 100% synthetic If current was not significantly different from injecting 66% current. There are many possible reasons why no differences were found. For the ML model the simplest explanation is that the current magnitude is so low that neither 66% or 100% is enough to provide any significant effect. For the SDiF model, in which the injection of a 66% If model current leads to a significant rate recovery, it is possible to formulate an explanation based on the presence of a natural negative feedback on If effects. A higher If magnitude allows the membrane potential to depolarize faster, which in turn leads to more positive voltages causing faster If inhibition. This mechanism limits the effect of a conductance increase from 66% to 100%. Another possible reason is that the late diastolic depolarization is influenced by factors other than If, which means that the relation between If and rate is not expected to be linear. Fig. 11 demonstrates this concept for simulations with the SDiF model: injecting 66% or 100% If model current into a cell which still has 34% If unblocked is equivalent to setting gScale ¼ 1 (34% þ 66%) or gScale ¼ 1.34 (34% þ 100%), which leads to a rate increase of only z3.5% (from 2.9 Hz to 3 Hz). On the basis of this observation, we analyzed the injected current peaks for the IVA experiments during application of the SDiF model current. The ratio between the SDiF100 and SDiF66 peaks is 1.25 ± 0.18, confirming that our setup was correctly injecting a higher current, but other natural cell mechanisms intervened to reduce its effect on rate. In a recent study with both experimental and modeling

components, Yaniv et al. (2013a) propose the existence of a feedback mechanism between membrane and calcium clocks to explain the effect of Ivabradine in terms of intracellular Ca2þ depletion, in addition to its already known partial If block. Whether or not such a mechanism can affect the interpretation of our data is an interesting question that requires specific investigation. In any case, the difference in DD1 values for the SDiF and ML models suggest that the two models have different behaviors regardless of their influence on Ca2þ, which is expected to affect the late phase of depolarization. A later version of the ML model (Yaniv et al., 2013b) recently updated the balance between the relative weights of different ionic currents during diastole, resulting in a more relevant contribution of If, but its specific formulation was not changed. Our results suggest that the ML If formulation is not adequate from a quantitative point of view, independently of the description of other currents. Verkerk and Wilders (2013) recently published a detailed review of the various mathematical descriptions of If and compared the different characteristics with their experimental data. Based on their analysis they suggested that both SDiF and ML models have caveats and proposed a novel model that lies between the two in terms of the amount of current flowing during diastolic depolarization. While our results with the ML model are fully consistent with their analysis, which indicated an underestimation of If with this model, the results we obtained with the SDiF model are not

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fully explained by their analysis. The lower amount of current in the Verkerk and Wilders model could be due to differences in the experimental conditions, since the SDiF model was largely based on data from the same lab in which our present results have been obtained. On the other hand, some overestimation of the current with the SDiF model could be masked in our experiments due to secondary effects of If block on ion concentrations that cannot be actually reproduced by the DC technique. This aspect deserves further investigation. After model validation, we investigated the importance of If in autonomic modulation, developing a novel protocol to simulate shifting effects of specific drugs on current kinetics. The SDiF If model, validated with the IVA protocol, was used for these ISO/ACh experiments. Regarding the simulation of the effects of Isoprenaline, our ISO protocol results show that a shift in SDiF kinetics leads to a þ17.3 ± 6.7% increase in pacemaking rate versus a þ45.0 ± 26.1% effect obtained during perfusion with Isoprenaline. In interpreting this result, one should keep in mind that Isoprenaline does not affect If only, although our protocol only reproduces the effects of Isoprenaline on If. Thus what we are observing is the isolated contribution of If to the phenomenon of autonomic increase of pacemaking rate, as predicted by the model. Results from the analysis of DD1 and DD2 support this view; while Isoprenaline and our synthetic shift have different global effects on pacemaking rate, their effect on early diastolic depolarization is the same. This is consistent with the work of Bucchi et al. (2007a), who determined that in the EDD phase only If is responsible for pacemaking rate modulation, while in LDD more than one mechanism is involved. Thus part of the rate increase caused by Isoprenaline is attributable to other cellular mechanisms acting outside the early phase of diastolic depolarization, in particular the ICaL, INCX, and IKs currents (see Severi et al., 2012 for a list of experimental references). Part of the rate increase caused by Isoprenaline is attributable to its ability to modulate other currents such as ICaL, INCX, IKs (see Severi et al., 2012). In particular it is known that catecholamine modulation increases ICaL (Zaza et al., 1996; Mangoni et al., 2003), enhances the NCX activity (Ca2þ-clock mechanism) by increasing the SR Ca2þ release (Vinogradova et al., 2002), and increases the IKs current (Lei et al., 2000). TOP analysis is consistent with this hypothesis. There are significant differences in TOP values between the ISO and Shift groups. TOP's value under Isoprenaline is z3 mV more negative than its value under Shift conditions. Therefore a lower trigger threshold for AP firing could account for part of the larger rate increase obtained with Isoprenaline. In the study by Severi et al. (2012) which formulated the original SDiF model, the overall effect of simulated Isoprenaline was a þ28.2% rate increase. Simulations performed to determine If's contribution to the Iso-dependent rate increase (i.e. by specifically applying the phenomenological Iso effect only on If or on all the targets but If) showed that changes in If are dominant, but the contribution from other components is not negligible. In that work, the If contribution ranged between þ17.2% and þ26.7%; our experimental finding of a þ17.3 ± 6.7% rate increase after virtual shift mimicking ISO effects on If is consistent with that prediction. Regarding Acetylcholine, our ACh protocol resulted in a 11.8 ± 1.9% rate decrease, while drug effect led to a 20.5 ± 5.1% rate decrease. As in the case with ISO, the difference between the drug and synthetic effects is significant. Analysis of DD1 shows that Acetylcholine and current injection have the same effect in early diastolic depolarization, suggesting that the observed 11.8 ± 1.9% rate decrease is due to the

contribution of If only. In the case of Acetylcholine, results cannot be so easily interpreted, since there were no significant differences in MDP, TOP, DD1 or DD2 between drug and synthetic-current conditions. Therefore, to further investigate the effects of Ach, we also analyzed the total duration of the DD (Dt, see the Data analysis subsection in Methods) and the action potential duration (APD). DD was 266 ± 119 ms for the ACh group and 220 ± 93 ms for the Shift group (p < 0.05). APD values were 175 ± 36 ms for the ACh group and 169 ± 42 ms for the Shift group (NS). We believe that these data can be explained on the basis that changes in AP rate integrate changes in many parameters of the AP (TOP, MDP DD1 and DD2). Indeed our data indicate for DD2 and TOP small, though not significant, differences, which together may sum up to a significant rate lengthening. The difference in CL seems once again associated with the late phase of diastolic depolarization. ACh is known to activate the IKACh current and to negatively modulate both the ICaL and the INCX currents (Zaza et al., 1996; Petit-Jacques et al., 1993; Lyashkov et al., 2009). Activation of the KACh conductance is expected to decrease both the early and late diastolic depolarization phase as well as to negatively shift the MDP. In our experiments however we chose to use an ACh concentration of 10 nM which is below the threshold for the activation of the IKACh current (DiFrancesco et al., 1989; Osterrieder et al., 1980). In agreement with this, data analysis show that MDP is not changed and therefore we can reasonably conclude that IKACh does not play a role in the negative chronotropic modulation observed in our experiments. ICaL provides a substantial contribution to the second part of the diastolic depolarization. However, since the concentration threshold of ACh necessary to elicit a negative modulation of ICaL is >10 nM (Zaza et al., 1996; Petit-Jacques et al., 1993) we can assume that a contribution of ICaL to the negative chronotropic effect studied in our experiments is negligible. Muscarinic stimuli also negatively modulate the Ca2þ clock mechanism as shown by Lyashkov et al., 2009 and it is therefore possible that this mechanism may contribute together with the If reduction to lengthen the DD as observed in our experiments. The SDiF SAN cell model of Severi et al. (2012) predicts, for 10 nM ACh, a reduction in spontaneous rate of 19.6%, similar to the reported experimental value of 20.8 ± 3.2% (Bucchi et al., 2007a). Modification of If only led to a 13% rate decrease, similar to our 11.8 ± 1.9% shift effect, while modification of all other targets except If led to a rate decrease of 18%. 4.2. Innovative aspects of Dynamic Clamp experiments Our work contains innovations in the use of the DC clamp technique. The most important is the cell-specific customization procedure, which represents a first step in the development of cellspecific experimental Dynamic-Clamp protocols. This procedure was developed as a response to unexpected preliminary findings, which could be due to an intrinsic limitation of the Dynamic Clamp approach; the mathematical model does not take individual differences into account, assuming average cell behavior instead, with a fixed (average) beating rate and fixed (average) values for the conductance of ionic current. However, cells actually have very different beating rates (e.g. from about 1 to 4 Hz in our experiments), and cells with higher spontaneous rates probably express a higher If. For this reason the customization aspect of our work addresses the need, clearly felt in cardiac electrophysiology, to include inter-subject variability in the computational approach. The DC current-replacement approach is used in our work for the first time to replace the If pacemaker current in SAN cells. The If current has already been investigated using DC (Verkerk et al., 2008), but that study involved expression of If in HEK-293 cells,

Please cite this article in press as: Ravagli, E., et al., Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking, Progress in Biophysics and Molecular Biology (2015), http://dx.doi.org/10.1016/j.pbiomolbio.2015.12.004

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while in our case If is studied in its natural environment of SAN cells. Working with currents on the order of a few picoAmperes in beating SAN cells is technically demanding, but this approach allowed us to obtain and analyze reliable, repetitive results. Another innovation of our work is the development of the shift protocol, which mimics the effects of shifting the kinetics of a current, without the use of a drug. In fact, the solution we adopted could be applied to reproduce the effects of any other kind of variation in gating kinetics, provided such variation can be mathematically described as a voltage shift. 4.3. Limitations The computation of the cell-specific scaling factor is based on several assumptions and approximations. Current scaling as a function of capacitance is common in AP mathematical models, where current density is often directly employed in place of current. Consequently, it is straightforward to translate this concept into an experimental process in which current injection is model-based. However, other properties of the cell are less easily exploited for customization. Many studies have highlighted the fact that SAN cells are strongly heterogeneous in their properties (see the modeling work of Zhang et al. (2000) for detailed experimental references), such as those associated with their location in the nodal geometry. For this reason a customization-based investigation adds value compared to traditional results based on averaged measurements. What remains is the need to establish a precise customization procedure. For our purposes, this customization criterion is the scaling of If maximal amplitude as a function of control pacemaking rate, based on the assumption that heterogeneity in the membrane density of If channel expression is the principal cause for different basal rates. The rationale for this approach is that spontaneous frequency of a single cell, belonging to a given population, is proportional to the size of If. This rationale is based on the very properties of funny channels and is supported by the overall evidence indicating a role of the If current in pacemaking, including autonomic regulation of rate, the action of If blockers like Ivabradine, the rate slowing in HCN4 KO mice, the bradyarrhythmias of individuals carrying a lossof-function HCN4 mutations and more (see DiFrancesco, 2010; Bucchi et al., 2012); specific evidence is also available, such as for example the one provided by Boyett et al. showing that SAN cells endowed with faster spontaneous rates also have higher If current density (Boyett et al., 2000). Although If channels also express variability in voltage dependence of kinetic rates and steady-state activation, we still consider conductance variations to be the major source of rate variation, based on the assumption that variability is mostly depending on the difference in the number of ionic channels from cell to cell, as recently suggested also by others (e.g.: Groenendaal et al., 2015; Sarkar and Sobie, 2011). This assumption represents only a first approximation, but nevertheless the results we obtained are encouraging. In support of our approach, it should also be highlighted that the original IVA protocol, without customization features, had already led to significant results; the conclusions regarding model validation were the same as those obtained later. With the updated protocol. Thus, adding customization only increased the significance of the results. Recall that in the IVA protocol the injected current is inward, so that a negative (stable) feedback mechanism is created; the injected current causes potential depolarization, which in turn causes current decrease. It is clear that the customization procedure was not essential in this case. In other words, the average behavior does not seem to be dramatically dependent upon the features of the specific cells. Instead In contrast, in the ACh protocol,

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in which a positive feedback mechanism causes potential instability or insensitivity, the adaptation turns out to be crucial. Future experimental protocols may also improve this aspect by including other AP features in the current-tuning procedure. A second limitation of our work is the approximation at the core of the shift protocols, where a differential current is injected with the assumption that it will cancel the physiological current and replace it with our shifted model-based current. Admittedly this is an imperfect process, as the differential current is calculated by a mathematical model and does not completely correspond to physiological If. On the other hand, the shift experiments were carried out only after experimental model validation by the IVA protocol, so a good degree of similarity had already been ascertained. A third limitation, inherent to the DC technique, is that the ions flowing through the cell membrane during current injection are not the Naþ and Kþ ions of the physiological If current, but are related to the composition of the solution in the pipette microelectrode. This is particularly relevant because of the possible effects of changes in intracellular sodium concentrations on the calcium-handling system. It should be taken into account, in any case, that the continuity of the patch-clamp with the pipette should guarantee an almost constant intracellular sodium concentration. A fourth possible limitation is linked to experiment duration; even using the perforated-patch technique, the cell is prone to the effects of run-down in experiments longer than a few minutes. For this reason we carefully timed our acquisitions to complete the protocol on each cell within approximately 5 min. 4.4. Conclusions In conclusion, we applied the DC technique to the investigation of If current in two different ways. Firstly, we used a DC replacement protocol and showed that the SDiF mathematical formulation of If is able to restore physiological pacemaking in SAN cells under the effect of Ivabradine, whereas the ML formulation is not. Secondly, we used the SDiF model in conjunction with our newly-developed virtual shift DC protocol to study and quantify the contribution of If to autonomic modulation of rate. An important factor in obtaining our results was the development of a cell-specific customization procedure which allowed us to take into account the biological heterogeneity in our experimental protocols. Funding sources This work was supported by the Cariplo Foundation grants 2014-0728 (ACROSS) to DD and 2014-0822 (CLARIFY) to MB. Disclosures The authors have nothing to disclose. References Accili, E.A., Robinson, R.B., DiFrancesco, D., Mar 1997a. Properties and modulation of If in newborn versus adult cardiac SA node. Am. J. Physiol. 272 (3 Pt 2), H1549eH1552. Accili, E.A.1, Redaelli, G., DiFrancesco, D., May 1 1997b. Differential control of the hyperpolarization-activated current (i(f)) by cAMP gating and phosphatase inhibition in rabbit sino-atrial node myocytes. J. Physiol. 500 (Pt 3), 643e651. Ahrens-Nicklas, R.C., Christini, D.J., 2009. Anthropomorphizing the mouse cardiac action potential via a novel dynamic clamp method. Biophys. J. 97, 2684e2692. Altomare, C., Bucchi, A., Camatini, E., Baruscotti, M., Viscomi, C., Moroni, A., DiFrancesco, D., 2001 Jun. Integrated allosteric model of voltage gating of HCN channels. J. Gen. Physiol. 117 (6), 519e532. Altomare, C., Bartolucci, C., Sala, L., Bernardi, J., Mostacciuolo, G., Rocchetti, M., Severi, S., Zaza, A., 2015. IKr impact on repolarization and its variability assessed

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Please cite this article in press as: Ravagli, E., et al., Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking, Progress in Biophysics and Molecular Biology (2015), http://dx.doi.org/10.1016/j.pbiomolbio.2015.12.004