Bottom-Up Self-Organization in Supramolecular Soft Matter Principles and Prototypical Examples of...

Springer Series in Materials Science 217

Stefan C. MüllerJürgen Parisi Editors

Bottom-Up Self-Organization in Supramolecular Soft MatterPrinciples and Prototypical Examplesof Recent Advances

Chapter 10Negative Curvature and Controlof Excitable Biological Media

Marcel Hörning and Emilia Entcheva

Abstract Biological media studied in controlled in-vitro conditions are sensitive totheir environment, including the materials which shape their development and func-tionality. We discuss the importance of the factors that can significantly influencetissue morphology and dynamics in biological excitable media. Active and passivecontrol of excitability in cardiac tissue are exemplarily reviewed by using rigiditycontrollable gels and tissue boundary shaping polymers. In particular, we illustratehow the knowledge of tissue boundaries can be utilized to control excitation patterns,with relevance to the treatment of cardiac diseases. Further, we discuss new optoge-netic ways for active control of excitation patterns by light, offering higher versatilitycompared to traditional electrical means of control. Finally, we discuss the influenceof the substrate rigidity on the tissue morphology and signaling dynamics duringdevelopment of cardiac tissue, and provide evidence that the smart use of materialscan significantly alter the morphology and functionality of the assembled tissue.

10.1 Introduction

Dynamics of excitable media are observed and studied in a range of living systems,such asmammalian heartmuscles [1, 2], Xenopus eggs [3, 4], Physarumplasmodium[5, 6], and Dictyostelium cells [7, 8] (see some examples in Fig. 10.1). Generally,excitability provides cells with a mechanism to amplify and synchronize molecularevents/noise and achieve time- and space-coordinated phase transitions, transforming

M. Hörning (B)Institute for Integrated Cell-Material Sciences (iCeMS), Kyoto University, Kyoto, Japane-mail: [email protected]

M. HörningRIKEN Center for Developmental Biology, Kobe, Japan

E. EntchevaStony Brook University, Department of Biomedical Engineering, New York, USAe-mail: [email protected]

© Springer International Publishing Switzerland 2015S.C. Müller and J. Parisi (eds.), Bottom-Up Self-Organizationin Supramolecular Soft Matter, Springer Series in Materials Science 217,DOI 10.1007/978-3-319-19410-3_10

237

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238 M. Hörning and E. Entcheva

(a)

(d)

(b) (c)

Fig. 10.1 Examples of pattern formation in excitable media. a Shows an oil-droplet anchoredspiral wave in photosensitive ruthenium based Belousov-Zhabotinsky reaction on a cellulose nitratemembrane filter (see also [12]). b Shows a target wave and non-excitable obstacle anchored spiralwave in engineered cardiac tissue (confluent primary culture of rat cardiomyocytes) visualizedby activation time mapping, where red color indicate the wave fronts [13]. c Shows two counterrotating waves in a protoplasmic droplet of the Physarum plasmodium. The color code indicatesthe phases in the contraction relaxation cycle, where red and cyan indicates maximum contractionand relaxation, respectively, similar as shown in [6] (courtesy of Dr. Seiji Takagi). d Shows rotatingwaves of phosphatidylinositol lipids on the membrane of Dictyostelium cells (left pannel) and thecorresponding kymograph along the membrane at constant focal plane (right pannel), similarly asshown in [7, 8]

these into a macroscopic cellular response [9], e.g. response to DNA damage inhuman cells [10] and differentiation priming in embryonic stem cells [11].

The chemical Belousov-Zhabotinsky reaction is the simplest and best studiedexample of an excitable reaction-diffusion medium that exhibits functional dynam-ics similar to that observed in other more complex living excitable systems [14–17].However, it does not provide an understanding of the molecular underpinnings ofbiological phenomena [18]. Though, in the last couple of decades a lot of progresshas been made to describe and understand the underlying dynamics of typical pat-terns in generic excitable media, recently, there is increasing interest in the study andcontrol of specific biological excitable media. Continuing the tradition of as Hodgkinand Huxley [19] or Winfree [20, 21], who brought mathematics and biology closertogether, contemporary biological research is impossible without drawing on thesophisticated tools by other disciplines, including the application of novel materi-als, quantitative methods and image processing etc. Materials science, in particular,has facilitated the more realistic and physiologically-relevant experimentation in

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10 Negative Curvature and Control of Excitable Biological Media 239

biological systems in-vitro, specifically allowing for controlled guidance and provi-sion of external cues during the development and maintenance of engineered tissues.

In this chapter, we provide an overview on approaches to control wave dynamicsin excitable systems with focus on cardiomyocyte culture by investigating the pos-sibility of active control by electric and optical stimuli as well as the importance ofthe microenvironment to the tissue, which is discussed in terms of active and passivecontrol and influence onwave dynamics. In particular, Sect. 10.3 describes the impor-tance of the shape of non-excitable boundaries, e.g. non-conducting boundaries, inthemyocardium (such as occurring at blood vessel walls or as seen in the infarct zonein the real heart). The ability of low-amplitude electric fields to activate excitationwaves utilizing information about the curvature of those boundaries is investigated.In Sect. 10.4, we discuss new optogenetic means of stimulating excitable (cardiac)tissue by light as well as the unique features and control possibilities offered bysuch optical stimulation compared to traditional electrical stimulation. Finally, inSect. 10.5 the passive control of excitable media is discussed and exemplified bymodulation of the cell microenvironment using materials with controllable rigidityto influence myocardium development.

10.2 Characteristics of Wave Propagationin Excitable Media

Successful control of excitable waves in two-and three-dimensional media, such as incardiac monolayer syncytia in vitro or in the human heart, respectively, necessitatesdetailed knowledge of active and passive characteristic tissue properties and dynam-ics. In this section we briefly introduce important properties of excitable media, witha particular focus on cardiac tissue.

Impulse propagation (the spread of excitation waves) depends on various charac-teristics of the tissue and its environment. Active electrical properties are regulatedby individual cardiac cells, i.e. cell distribution, conductances and kinetics charac-teristics of ion channels. Thus, the ionic dynamics of individual cells is generallycaptured by the membrane action potential (AP)—the excitation event occurringat the cellular level. For example, an electrocardiogram (ECG) records the electricpotential of the heart surface as an integral representation of the cellular APs, whichare generated over the tissue during a full cardiac cycle, as P-wave, QRS-complex,T-wave and U-wave. Each cell exhibits unique AP depending on cell type, i.e. itsposition and function within the heart. ECG diagnosis is based on extracting quanti-tative information from the ECG records regarding AP changes in different regionsof the heart and altered propagation patterns, i.e. a shortened QT interval may bean indicator of a hypercalcemia (which also leads to a general AP shortening) [23]or a prominent T-wave may be an indication for myocardial infarction [24]. In con-trast, passive electrical characteristics are determined at the cell network level, suchas structural (tissue) details, i.e. anatomical obstacles (blood vessels, scars, etc.),

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cell-cell communication details (distribution of gap junctions), rigidity of non-myocytes [25] etc.

Although, the characteristics of excitation waves are influenced by intrinsic cellproperties and the cellular environment, biological excitable media obey similar gen-eral principles as non-biological excitable media as well. One of the most prominentcharacteristics is the relationship between wave front curvature and wave propaga-tion velocity. Considering a two-dimensional isotropic medium, a flat wave frontexhibits the same speed, Θ0, as a wave in one-dimensional medium. When the wavefront curves outward (convex) the speed decreases (Θ < Θ0), and when it curvesinward (concave) the speed increases (Θ > Θ0). Curvature of the wave front can beinfluenced by local tissue heterogeneities or curved obstacles (non-excitable regionswithin the tissue), i.e. scars and blood vessels, respectively. The above relationshipbetween the wave front curvature and the wave speed can be explained by the localexcitatory current supplied by the cells at the front of the wave and the area that itneeds to excite, i.e. the electrotonic load (large for convex and small for concavewaves), leading to change in the wave front speed [25]. This effect can be mathe-matically described by the linearized Eikonal equation

Θ = Θ0 + κD (10.1)

where Θ depends on the wave front curvature κ and the diffusion of the mediumD. Wave front curvature plays an important role in the formation and dynamics ofspiral waves, observed in various excitable media, as illustrated for a few examplesin Fig. 10.1. The periphery of a spiral wave can be mathematically described by anArchimedean spiral, because the wave front cannot exceed the speed of flat waves(Θ0). Importantly, the complex dynamics of the spiral core strongly depend on theproperties of the medium [26] and can be approximated mathematically consideringthe excitability of the medium [27, 28].

A critical mass (minimum number of cells) is needed for the successful initiationand subsequent spread of excitation within tissue. This area is generally known asliminal area or liminal length in one-dimensional medium. It has been measuredexperimentally to be approx. rc = 0.2mm in adult ventricular myocardium by esti-mating the critical electrode radius that initiates an excitation wave [29]. Generally,the liminal area depends on the maximal sodium conductance of the myocardium[30], andmay vary depending on the cell type and density of coexisting non-excitablecells, such as fibroblasts [31, 32]. In addition to direct stimulation by a localizedelectrode, the initiation of waves can be also achieved by externally applied electricfar-fields. An example of far-field effects in the human heart is the application ofautomated external defibrillators (AED)—electronic devices delivering life-savinghigh-magnitude electric fields to terminate an ongoing arrhythmia (fibrillation). Gen-erally, such devices apply up to 5000V, necessary to ensure the excitation of the entiremyocardium to terminate undesired potentially lethal patterns of excitation. The hugevoltage is necessary to overcome the high resistance of the human skin, skeletal mus-cle, fat and other tissue structures on the way of the electric field applied across thechest. In contrast, lower voltages may be sufficient to specifically trigger waves at a

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desired location within the myocardium utilizing local tissue heterogeneities. Thismechanism is explained in detail in Sect. 10.3, focusing on the importance of theshape of non-conductive boundaries that define the minimum electric field strengthnecessary to initiate a spreading wave.

Alternative means of stimulating excitable (cardiac) tissue, using light instead ofelectrical current injection or electrical fields, is discussed in Sect. 10.4. Such “opto-genetic” actuation (stimulation or suppression of activity by light) can be achievedafter genetic modification of the tissue using light-sensitive ion channels or pumps,reviewed in [33, 34]. Optogenetic perturbation offers superior options for active con-trol of cardiac dynamics compared to electrical or chemical means of control, as itcan achieve better spatiotemporal resolution, can be cell-specific (by the virtue ofgenetic targeting of a particular cell type), and can be bi-directional in terms of polar-ity of the induced changes in membrane voltage, i.e. depolarizing or hyperpolarizingresponses can be induced depending on the expressed optogenetic tools. This newoptogenetic perturbation can selectively create, modify and control excitation wave-fronts with unprecedented precision for better understanding of cardiac dynamicsand arrhythmias.

The ability to respond to an external stimulus is generally described by theexcitability of the medium, i.e. an electric (or optogenetic) stimulus applied to a cellthat can produce excitation. Response to external stimuli is frequency-dependent, i.e.excitable tissues exhibit restitution properties. Restitution describes the response ofthe action potential in a high-frequency entrainedmedium or single cell with constantperiod T . The change in the action potential duration (APDn+1) is determined as afunction of the previous diastolic (resting) interval (DIn), as

APDn+1 = f (DIn) (10.2)

withAPDn + DIn = T , (10.3)

where f is a function of the restitution properties [35]. Generally, f is a monotonicincreasing function (monophasic) of DI with a minimum DI that sets the mini-mum distance of two subsequently occurring action potentials [36], though it hasbeen shown that f can be biphasic in non-equilibrium conditions in human ven-tricles [37, 38]. The excitation dynamics can be studied by analyzing the slope off (d f/dDI). Slope smaller than one has an equilibrium point that corresponds to aperiodic response of the excitable medium, whereas the equilibrium becomes theo-retically unstable for |d f/dDI| > 1 [35]. The latter is known as alternans instability,where instead of a periodic response to the constant (periodic) stimulation, the actionpotentials begin to alternate in duration (e.g. APDlong-APDshort -APDlong-APDshort ,etc.) [39]. This phenomenon has been linked to instabilities and arrhythmia initia-tion in the human heart [40]. In addition to AP-alternans, this type of instabili-ties are observed also in calcium dynamics in cardiac cells (Fig. 10.2), where thecalcium transient duration (CTD) as a function of the previous calcium transientinterval (CTI) can be measured similar to APD and DI. Alternatively, the calcium

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Fig. 10.2 Dynamics of alternans instability in cardiac tissue culture. a Shows the calcium transientduration (CTDn+1) as a function of the previous calcium transient interval (CTIn) for differentpacing periods. CTD and CTI is measured at the half-width of intensity change. The critical periodthat initiates alternans instability is T≈286ms. b Shows two time series of stable and unstablecalcium intensity dynamics for pacing periods of 700 and 280ms, respectively [22]

transient amplitude (not duration) can be analyzed to obtain similar outcomes [22].The critical pacing period of producing alternans instability is indicative of the stateof cells, including their maturity, and has been found to be sensitive to the rigidityof the extracellular environment [22], which affects developing myocytes [41, 42]as well as coexisting non-myocytes, i.e. fibroblasts [43, 44]. The importance of suchmicroenvironment effects on cardiac tissue is discussed in detail in Sect. 10.5 withfocus on cell morphological changes.

10.3 Active Control of Heart Tissue and the Roleof Negative Curvature

Methods based on electrical stimulation to actively control undesired pattern for-mation in heart tissue have been suggested and intensively investigated in vitro andex-vivo over the last decades. Generally, two electrical cardioversion methods areinvestigated, i.e., high-frequencypacing (HFP) [13, 45–48] and far-field pacing (FFP)[49–51]. The latter is known under various synonyms, such as secondary sources[52–54], wave emission from heterogeneities (WEH) [31, 55], virtual electrodes[56, 57] and low-energy antifibrillation pacing (LEAP) [58, 59].

The termination dynamics of obstacle anchored spiral waves by HFP has beeninvestigated widely and shown to be valid not only in cardiac tissue but also in non-biological excitable media, such as in a Belousov-Zhabotinsky medium [12]. Briefly,the terminationmechanismcanbe summarized as depicted inFig. 10.3a,which showsthe mechanism in cardiac monolayer syncytia. The high-frequency stimulated waves

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approach the obstacle, collide with and annihilate the pinned spiral (Fig. 10.3a; whitedashed line). A new spiral is formed by the lower arm of the initially approachingwave. This cycle (Fig. 10.3a; upper row) repeats and eventually leads to the detach-ment of the spiral due to a local conduction block on the obstacle. The detachedspiral wave drifts toward the boundary forced by subsequently approaching wavesand eventually terminates [13].Whether a spiralwave can be detached and terminatedby HFP depends strongly on the obstacle size and shape, pacing period, tissue mor-phology and the excitability of the medium [46, 48, 60, 61]. Though, HFP is alreadysuccessfully applied as clinical treatment by implantable cardioverter-defibrillator(ICD) in the form of anti-tachycardia pacing (ATP), recent studies indicate that FFPmight be a promising novel cardioversion procedure [58, 59, 62]. Therefore fromhereon we will focus on the electrical far-field based cardioversion procedure.

Understanding the basic mechanism of an applied electric far-field to excitabletissue is essential to control the activation patterns in themyocardium.Generally, FFPgenerates a nonuniform distribution of transmembrane potentials consisting of largeadjacent areas of depolarization and hyperpolarization of themembrane potential, Vm[56] near an intercellular cleft (nonconducting inclusion) [52] or tissue heterogeneity[55, 58] that aremediated by a spatial change in the tissue conductivity [51]. A simpleillustrative example can be given considering one dimensional chain of excitable cells(intracellular space) embedded in a conductive extracellular medium, which is oftenreferred as bidomain model [63, 64]. The external applied electric field leads to anion flux in the intracellular and extracellular space. The ion flux outward from theintracellular space near an intracellular cleft (missing chain) leads to a local decreasein the membrane potential (hyperpolarization). Since the total current of both spacesis conserved (Ohm’s law), on the opposite side of the intracellular cleft an inwardflux of current can be observed leading to an increase in the membrane potential(depolarization). This localized polarization can lead to a propagating excitationwave [31].

The electric field necessary to excite a wave at an intracellular cleft is mediated bythe spatial distribution of excitation [65] and the geometry of the tissue boundary nearthe intercellular cleft when considering higher dimensions, i.e. 2D and 3D [55, 58,59, 66]. The electric field distribution on an intracellular cleft in a 2D tissue can bederived by the bidomain equations, which describe the dynamics of the extracellularand intracellular potentials [64]. When considering isotropic tissue, those can bereduced to the monodomain equations [67]

∂Vm∂t

= g(Vm,h)+ D∇2m (10.4)

∂h∂t

= H(Vm,h) (10.5)

where Vm is the difference in the extracellular and intracellular potentials, D isthe diffusion, and H describes the ion channel dynamics [58]. Solving (10.4) bylinearizing around the resting potential, Vrest for a homogenous applied electric

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Fig. 10.3 Termination of pinned spiral wave (anatomical reentries) and the effect of low electricfields on negative curved intercellular clefts in cardiac tissue. a Example of the termination of anobstacle pinned spiral wave via high-frequency pacing. The annihilation line is marked by the whitedashed line. b Analytical and semi-analytical solution of the maximum polarization for circularpositive, circular negative and parabolic negative curved intracellular clefts, shown in red, blue andgreen lines, respectively (courtesy of Dr. Philip Bitthin). c Shows the comparison of the electricfield-strengths necessary to excite waves on flat (κ = 0) and concave, parabolic curved (κ < 0)tissue boundaries in cardiac tissue (N = 19). The median electric field-strength ratio is shown in(a), as Econcave/E f lat = 1.35. Two examples are shown for E = 0.91 and E = 1.37V/cm. Thewhite arrow indicates the direction of the electric field. Images were analyzed using activation timemapping [13]

field, E, and considering that H is independent of Vm below some finite threshold[58, 68–70], (10.4) can be simplified to

∇2e − eλ2

= 0 (10.6)

n · (∇e − E) = 0 (10.7)

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where e is the difference in Vm and the resting potential of the medium, and λ isthe electronic constant (length), which is approximately λ ≈ 1mm for cardiac tissue[55, 58]. The general solution of (10.6) and (10.7) is the linear combination of themodified Bessel functions of first and second kind, respectively (10.8),

e = α I1 (r/λ)+ βK1 (r/λ) (10.8)

where α and β are constants (see [71]). In the case of intracellular clefts that havecircular geometries (positive curvature), an explicit solution can be determined usingthe modified Bessel functions of the second kind (α = 0). Since I1 is divergent forr → ∞, the theoretical limit to excite awaveona circular cleftwith positive curvaturecan be approximated as λE [71]. Thus, the applied field-strength E ∝ R−1. In otherwords, the smaller the obstacle the larger the electric field necessary to trigger a wave(Fig. 10.3b; red line).

Recently, Bitthin et al. [58] extended the theory considering intracellular cleftswith negative curvature. For the special case of round clefts the relation can be derivedsimilarly, as for the case of positive curved clefts, by the modified Bessel functionsof the first kind (β = 0), since in this case K1 is divergent for r = 0. Worth notingis that the solution of epeak(κλ < 0) exhibits a maximum at κλ ≈ −0.2 (Fig. 10.3b;blue line) and it approaches λE for larger clefts. The strongest effect of concaveboundaries has been semi-analytically derived for parabolic clefts. In contrast tocircular clefts it increases monotonically instead of approaching a smaller limitingvalue (Fig. 10.3b; green line).

Experiments in cardiac monolayer syncytia have revealed the effect of negativecurvature on an externally applied electric field by employing PDMS (Polydimethyl-siloxane), as artificially introduced intracellular clefts (see grey area in inlets ofFig. 10.3c) [13, 31, 58]. Here, the shape of the tissue-void clefts is chosen to haveparabolic and flat interfaces. By tuning the externally applied electric field to excite awave on the respective interface are obtained. Figure10.3c) shows the result of N=19experiments. The median electric field-strength ratio is approx. 1.35 at κλ ≈ −1.5,which iswell approximated by the semi-analytical solution of parabolic-curved clefts(Fig. 10.3b).

Experiments that show these effects in three-dimensional cardiac tissue are per-formed using isolated perfused animal preparations [50, 59]. The termination ofatrial fibrillation was achieved using low-pulsed field-stimulation with only 13%of the energy required for cardioversion at a success rate of 97% [50], where theentrainment dynamics of wave emission sites on intracellular clefts were utilized tosynchronize the tissue dynamics with the applied electric field. This is independentlyverified by a comprehensive investigation which aimed to study the selective recruit-ment of wave emitting sites to treat more efficiently cardiac fibrillation showing thatthe response of quiescent atrial and ventricular tissue to a homogeneous, pulsed elec-tric field increases with increasing electric field-strength, as well as the number ofactivation sites [59]. Further, an estimation of the wave emission site density, ρ, asfunction of the present blood vessels was theoretically derived and experimentallyverified as

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ρ(E) = NV

! Rmax

Rmin(E)p(R)dR (10.9)

whereN is the total number of blood vessels in the tissue volumeV and p(R) ≈ R2.75

is the size distribution of vessels that has been determined by micro-CT measure-ments.

These studies show that FFP is a promising electrical cardioversion method asan alternative to implantable cardiac pacemaker or even automated external defib-rillators (AEDs). Novel concepts for further improvements are suggested, such asthe implementation of circularly polarized electric fields [72], which may furtherincrease the effectiveness and applicability on hearts in-vivo toward translation ofthis technology in humans.

10.4 Active Control of Heart Tissue by Optogenetic Means

An alternative to electrical stimulation to control excitation patterns is offered by thenewly emerging field of optogenetics. Optogenetics relies on genetic expression ofmicrobial opsins (light-sensitive ion channels and pumps) in mammalian cells andtissues, e.g. brain, heart. Then light with a specific wavelength is used to modulatemembrane voltage in a cell-specific and precisemanner by activating these opsins andgenerating either depolarizing (excitatory) or hyperpolarizing (inhibitory) currents.Excitatory opsins, e.g. channelrhodopsin-2 (ChR2) [73], provide currents sufficientto trigger action potentials in neurons and cardiomyocytes,whereas inhibitory opsins,such as Archaerhodopsin (Arch) and Halorhodopsin (Halo), can inhibit activity [74].Opsin responses are fast (in the milisecond range), and spatial targeting by light canbe done at very high resolution. New developments include the design of betteroptogenetic tools [34, 75], i.e.. optimization of light sensitivity, speed, and spectralresponse. For example, ChR2 mutants with higher conductance and hence requiringlower energy to excite include the H134Rmutant [76] and T159C [77]), mutants withenhanced calcium permeability (CatCh [78]) control preferentially calcium influx,and faster response time mutants (ChETA [79]) improve the frequency response ofoptical stimulation. Furthermore, mutants with red-shifted excitation spectra [80] areconsidered for deeper light penetration in in vivo applications.

Unlike neurosceince applications [75], cardiac applications of optogenetics havebeen slow to emerge—see recent reviews [33, 34]. Important advances were madeby Bruegmann et al., who generated transgenic mice with ChR2 expression, anddemonstrated optical cardiac pacing and the induction of cardiac arrhythmias inopen-chest hearts [81]. In vitro uses have included viral expression of ChR2 at theembryonic stage [81, 82], viral transduction of neonatal and adult cardiomyocytes[33, 34, 83], as well as a cell-delivery approach where nonexcitable cells, express-ing ChR2, are coupled to cardiomyocytes (CMs) thus inscribing light sensitivityto the cardiac syncytium [84]. Computational tools have been developed to better

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Fig. 10.4 Combining optical actuation with optical imaging: a Experimental setup for high-resolution, high-speed optical imaging and optical control of cardiac syncytia. b Activation maps incardiac syncytia by electrical and optical pacing at 0.5Hz. Normalized calcium transients (acquiredwith Rhod 4 staining) are shown from two locations—A and B. Reproduced from Jia et al.[84] with permission from the American Heart Association (Circulation: Electrophysiology andArrhythmias) [84]

understand optogenetic perturbation of excitation and the action of ChR2 (i.e.voltage- and light-sensitivities) in a variety of cardiac cell types (i.e. atrial, ven-tricular, and Purkinje), [83, 85] as well as in whole heart models [82, 83, 86, 87].It is important to note that optogenetic stimulation (with ChR2) triggers similarconduction patterns to electrical stimulation without undesired alterations in theelectrophysiological response (action potentials or calcium transients), Fig. 10.4.

As a new basic science tool in cardiac research, optogenetic stimulation offersunique advantages. Compared to classical electric field stimulation (discussed inSect. 10.3), optogenetics yields better spatiotemporal addressing (cellular and sub-cellular) due to a combination of factors: (1) selective cell type expression by genetictargeting using cell-specific promoters, and (2) superior light focusing and con-trolled delivery of desired and well-localized action unlike the typical complexpolarization induced by an electric field with islands of opposite polarity (virtual

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electrodes) around the target spot(s); (3) bi-directional control (excitatory orinhibitory) depending on the type of opsins expressed. Truly dynamic spatiotem-poral patterns of optical stimulation can be imposed to directly control wavefrontsindependent of structural features. For example, recently ”shaped” or ”sculptured”illumination has been demonstrated [88–90]. Using an optical system with a digitalmicromirror device (DMD), arbitrary computer-generated optical patterns of stimu-lation can be projected at high speed (in real time) onto the tissue to trigger or perturbongoing excitation waves with unprecedented precision. Such robustness offered byoptical actuation essentially allows in vitro experimentation to be done with a levelof control only seen before in computer simulations. This makes optogenetics idealfor in vitro investigations into the mechanisms of excitation, reentrant arrhythmiasand their termination. Precise dynamic optical probing can be used to quantify limi-nal area, for example, by projecting gradually expanding circular patterns of opticalstimulation until a propagating excitation wave is induced. Controlled induction ofreentrant waves in vitro can be achieved by imposing precise spatial patterns of depo-larization to create critical points, as outlined theoretically by Wiener [91], Frazer[92] and Winfree [20]—conditions that are much harder to achieve by electricalstimuli. Furthermore, the exact nature of reentrant activation and the state of thereentrant core—spiral wave vs. leading circle [93] can be probed optically even inthe absence of structural heterogeneities. In fact, similar to setting initial conditionsin computer simulations, optogenetically (using a DMD), one can generate arbitraryshape wavefronts of excitation, including the circular or parabolic ones discussed inSect. 10.3., and curvature of the wavefront can be gradually varied from positive tonegative for detailed experimental validation of the eikonal theory.

The search for mechanisms of atrial fibrillation [94] or ventricular fibrillation[95]—mother rotor, wandering wavelets or other, can be tackled to quantify thevulnerability of the reentrant wave(s) to external perturbations, and may have realimpact on devising new defibrillation strategies. Compared to the low-energy strate-gies for termination of arrhythmias using electric fields, discussed in the previoussection, optogenetic perturbation is far more versatile. Specifically, any spatial loca-tion is optically addressable, unlike far-field effects that are tied to gradients in tissueconductivity. Moreover, global hyperpolarization (or global forced repolarization) ishard to achieve by electric fields, thus optical suppression of activity using inhibitoryopsins, offers a new tool. For example, it is interesting to point out a successful ter-mination of epileptic seizure activity by light (using inhibitory Halorhodopsin) inhippocampal tissue slices in vitro [96], as epilepsy and cardiac arrhythmias sharesome mechanistic similarities.

For in vivo use of optogenetics, several challenges need to be addressed, includ-ing direct light access into the dense cardiac muscle, penetration depth and spectralchoices [97]. Questions that are amenable to optogenetic probing in vivo include thestudy of focal arrhythmias. Suspected common sites, e.g. automaticity at endocardialPurkinje network locations [98, 99] can be systematically examined by cell-specificexpression and perturbation by light to induce or suppress such activity. Criticalcontributions of different parts of the pacemaking and conduction system can beprobed, especially by inhibitory opsins, as demonstrated in zebra fish [88]. Such

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approaches may not only help understand arrhythmia induction but may offer newanti-arrhythmic strategies. Due to its completely contactless nature, optogenetics nat-urally lends itself to parallelization and scalability, as well as closed-loop feedbackcontrol when combined with optical sensing/imaging. This makes it a highly attrac-tive tool not only for basic research in excitable media, but also for high-throughputscreening of anti-arrhythmic drugs, where the contact-requiring nature of electro-physiological testing has been a major obstacle.

10.5 Passive Control of Heart Tissue by Soft Materials

Most investigations aim to actively control spatiotemporal patterns in cardiac tis-sue in-vitro and in-vivo in order to improve maintenance of cardiac diseases, i.e.arrhythmia and fibrillation, either by the application of electric shocks [13, 50, 58]or by pharmacological means [100–102]. An alternative approach is based on theunderstanding of tissue growth and function depending on external cues, i.e. micro-environment for the ultimate goal to develop cardiac tissue constructs for regenerativepurposes.

The extracellular matrix (ECM) regulates mechanotransduction, including thetransmission of mechanical stress during contraction, cell shape, and cytoskeletalarchitecture [105] and thus can regulate the cell fate of embryonic stem cells [106].For muscle cells, this effect is even more pronounced since they can respond to theirenvironment by actively contracting and regulating their cytoskeletal architecture,i.e. adjusting their contact area respectively to the rigidity of the ECM [107]. Thedifference in the actomyosin organization can be seenwhen comparing layered tissuecultured on glass, where the actomyosin striation between cells that are in directcontact with glass (E ∼ GPa) is less prominent compared to cells that are in contactwith other cells only [108]. Furthermore, surface topographic cues can guide cellshape and orientation via cues by the ECM. Aligned nano-fibers may increasesthe structural cell anisotropy [109] and groves in the ECM can lead to bipennate(fishbone-like) tissue formation [110].

The particular choice of rigidity in cardiac tissue has been regulated and adjustedduring evolution. Thus, an optimal rigidity is observed not only during the devel-opment [106] and the proliferation, differentiation, and morphogenesis of cardiactissue [111], but can also be observed as an enhancement of the electrophysiologicaldynamics in confluent cardiac tissue [22]. In particular, higher degree of synchro-nization in the spontaneous beating and increase in the critical bifurcation period toinduce wave alternans have been observed when the substrate rigidity matches thatof the cardiac cell rigidity (∼11kPa). Here it is important to note that both, wavealternans and local changes in the rigidity, are known to contribute to severe and fatalheart diseases [112].

The optimum ECM rigidity for mimicking myocardium is around 11kPa[22, 106, 111, 113]. Though, it is interesting to analyze the role of the ECM rigidityon a single cell, cell-to-cell interactions play a crucial role in the development of

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4 kPa 12 kPa 25 kPa glass (GPa)+90o

-90o

0o

fiber orientation

ROI

θ

2D-FFT

x = N/λ

intensity

FTT-profile

λ = 1.87 µm (glass) 1.6

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1

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omer

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ngth

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r pa

ram

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52

S=0.

63

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61

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52

(a)

(b) (c)

Fig. 10.5 Quantitative analysis of fiber orientation and sarcomeric structure in confluent cardiomy-ocyte tissue on rigid hydrogels (Matrigen Life Technologies) with 4, 12 and 25kPa, and glasssubstrate. a Phalloidin stained cardiac tissue highlighted by the local fiber orientation [103]. b Illus-trative example on the 2D-FFT based extraction of sarcomeric length. A ROI was selected, analyzedby 2D-FTT, and the sarcomeric length was extracted from the frequency domain perpendicular tothe zero-mode in the FTT-space following (10.10). cQuantification of the average sarcomeric length(red bars) and the order parameter (green bars) (10.11) as a function of the substrate rigidity. Con-fluent rat-neonatal cardiomyocyte tissue is obtained using isolated hearts of two-day old Wistarrats. The tissue is analyzed on the 5th culture day using a standard protocol [13, 31, 51, 58], whichincludes Cytosine Arabino-Furanoside from the second culture day to prevent overproliferation ofcontaminating nonmyocytes [104]

tissue and lead to a change in actin organization (Fig. 10.5a), as observed also forsingle cardiomyocytes with spatially constraining boundaries [114]. The culture ofsingle premature cardiac cells on substrates exhibiting different rigidities does notinfluence the sarcomeric length (∼1.9µm) [115], which is confirmed [116] to beshorter than in mature sarcomeres (2–2.5µm) for cardiac tissue [117]. However,the sarcomeric length exhibits structural differences when those cells are culturedunder confluent conditions on soft substrates with various rigidities. To quantify thisdifference in the sarcomeric organization, regions of interests (ROI) are analyzedusing spatial 2D-FFT approach with ImageJ to uncover fine spatial periodicities(Fig. 10.5b). The intensity profile of the spatial frequency domain perpendicular tothe main mode in the FFT-space is used to extract the average sarcomeric length ineach ROI. The distance x is defined between the zero-order and first-order harmonicin the spatial frequency domain, which is the sarcomere-related peak, as

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x = N/λ (10.10)

where N is the number of pixels along the dimension in the FFT-space, and λ [µm]is the actual sarcomere spacing [110]. Using this method the sarcomeric length isextracted for cells cultured in confluent cardiac tissue on soft matrigels (4, 12 and25kPa) and glass coverslips as a control. A decrease of the sarcomeric length withincreasing rigidity is observed (Fig. 10.5c). Cardiac tissue cultured on glass and25kPa rigid matrigels exhibit sarcomeric lengths comparable to that of single cellson rigid substrates [115, 116], whereas softer substrates exhibited sarcomeric lengthmore similar to that observed inmature cardiac cultures [117]. Thus, the combinationof soft ECM that mimics the cellular environment and the spatial constraints of cellsappears to lead to an increase in cellular (tissue) maturity. While it is sufficient toaffect cellular function and morphology, it may not be sufficient to mimic all aspectsof native tissue development. An alternative interpretation could be difference in therelative development time of tissue toward full maturity, i.e. the harder ECMs mayonly slow down the developmental processes of cells. The results shown in Fig. 10.5are obtained on the 4th day after seeding. Observation at a later stage may revealsynchronization of tissue maturity regardless of the rigidity of the ECM. The latter,however, is unlikely considering the structural order of cell alignment, which can bequantified by the order parameter

S = ⟨cos 2θ⟩ (10.11)

where θ is the directional angle of local actin filaments (ROI: 8× 8µm2) relative tothe main orientation axis that is extracted by 2D fourier transformation (Fig. 10.5b).The order parameter is defined between +1 (perfect alignment) and −1, and is usedfor the characterization of liquid-crystals [118] and actin fibers of single cells [42,119]. Confluent cardiac tissue on rigid gels showhigher anisotropy on gel with 12 and25kPa, lower and larger substrate rigidities lead to higher isotropy (S=0, completeisotropy) (Fig. 10.5c), respectively.

Though a considerable progress has been made in successfully capturing three-dimensional tissue architectures in-vitro [120–123], such approaches are still in arudimentary stage, and much has to be improved toward developing more relevantexperimental systems for medical applications. Different aspects of the intricate tis-sue architecture have been revealed in a greater detail recently, including the roleof vascularization of tissue [124], fiber orientation [109, 125, 126], nonmyocyte-myocyte ratios [104], mechanical cues during development [120, 127], etc., how-ever, much remains to be done to integrate knowledge and develop better controlstrategies to engineer physiologically relevant tissues and to apply these principlesin controlling tissue function in vivo.

Conclusively we can say that mechano-sensory response phenomena are sharedby other biological systems, where similar or even more pronounced functionaldependencies can be found, as the stress sensitivity to the extracellular matrix guidesdevelopmental processes of single cells and tissues [43, 44, 128–130]. An interesting

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example, which is still not well understood, is the biomineralization process ofcalcium carbonates, as found inmany invertebrate biominerals such as alveolar platesof ciliates (single-cell eukaryotic micro-organism) [131] and mollusk shells. The lat-ter in particular is still not understood in terms of mechano-sensory response to theextremely hard shell (∼GPa).A soft tissue (∼kPa) controls the formation of a fine tex-tured 3D structure (polysaccharide-containing ECM) into whichmineral is deposited[130], mediated by local transmembrane proteins and myosin motor domains [129].Mechanical sensing has been suggested to include a myosin chitin synthase withdirect cytoskeletal interaction [132], similar as actin-myosin mechanosensing feed-back found in vertebrate cardiac cells. The difference between the two systems is theresponse of chitin synthesis and sarcomeric contraction.

10.6 Summary

In this chapter, we reviewed active control mechanism utilizing externally appliedelectric and optical stimulation to control assembled excitable cardiac tissues withrespect to their microenvironment, such as the tissue boundary shape on the inducedexcitation patterns. The effect of unpinning anchored spiral waves (anatomical reen-tries) is explained and an alternative way of termination via low electrical far-fieldstimulation is discussed and explained in detail. The unique advantage and possi-ble obstacle that have to be overcome to control excitable cardiac tissue via opticalstimulation are discussed in comparison with electrical stimulation.

Furthermore, control of tissue growth and functionality through themicroenviron-ment is discussed. In particular we focused on the importance of the ECM rigidity,which not only can control the embryonic cell fate [41], but also can influence tis-sue morphology and signaling dynamics during development, i.e. sarcomeric lengthof actin fibers and excitation dynamics that are associated with cell-to-cell couplingproperties [22]. Here we focused on the direct influence of electrophysiological wavedynamics and cellular morphology, which can be altered during the development dueto the stress-sensitivity of the premature cells [133–136].

Appendix

The authors thank Dr. Torsten Bullmann (CDB, RIKEN, Japan) for his help on theobservation of cardiac tissue cultures, Dr. Ingrid Weiss (Leibniz Institute for NewMaterials, Germany), Dr. Philip Bitthin (BioCircuits Institute, University of Cali-fornia, USA) and Prof. Motomu Tanaka (Heidelberg University, Germany; iCeMS,Kyoto University, Japan) for their helpful comments.

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References

1. W. Bian, L. Tung, Structure-related initiation of reentry by Rapid pacing in monolayers ofcardiac cells. Circ. Res. 98, 29–38 (2006)

2. A.T. Winfree, Electrical turbulence in three-dimensional heart muscle. Science 266, 1003–1006 (2004)

3. C. Baud, R.T. Kado, Induction and disappearance of excitability in the oocyte of Xenopuslaevis: a voltage-clamp study. J. Physiol. 356, 275–289 (1984)

4. G. Charpentier, Effect of Lidocaine on the slow Na+ channels of Xenopus oocytes. Gen.Physiol. Biophys. 21, 355–365 (2002)

5. A. Adamatzky, Routing Physarum with repellents. Eur. Phys. J. E Soft. Matter. 31, 403–410(2010)

6. S. Takagi, T. Ueda, Annihilation and creation of rotating waves by a local light pulse in aprotoplasmic droplet of the Physarum plasmodium. Phys. D 239, 873–878 (2010)

7. Y. Arai, T. Shibata, S. Matsuoka et al., Self-organization of the phosphatidylinositol lipidssignaling system for random cell migration. Proc. Natl. Acad. Sci. U.S.A. 107, 12399–12404(2010)

8. D. Taniguchi, S. Ishihara, T. Oonuki et al., Phase geometries of two-dimensional excitablewaves govern self-organized morphodynamics of amoeboid cells. Proc. Natl. Acad. Sci. USA110, 5016–5021 (2013)

9. P. Rué, J. Garcia-Ojalvo, Gene circuit designs for noisy excitable dynamics. Math. Biosci.231, 90–97 (2011)

10. G.Lahav,N.Rosenfeld,A. Sigal et al., Dynamics of the p53-mdm2 feedback loop in individualcells. Nat. Genet. 36, 147–150 (2004)

11. T. Kalmar, C. Lim, P. Hayward et al., Regulated fluctuations in Nanog expression mediatecell fate decisions in embryonic stem cells. PLoS Biol. 7, e1000149 (2009)

12. M. Tanaka, A. Isomura, M. Hörning et al., Unpinning of a spiral wave anchored arounda circular obstacle by an external wave train: common aspects of a chemical reaction andcardiomyocyte tissue. Chaos 19, 043114 (2009)

13. A. Isomura, M. Hörning, A. Agladze et al., Eliminating spiral waves pinned to an anatomicalobstacle in cardiac myocytes by high-frequency stimuli. Phys. Rev. E 87, (2008)

14. A.T. Winfree, S.H. Strogatz, Singular filaments organize chemical waves in three dimensionsI. Geometrically simple waves. Phys. D 8, 35–49 (1983)

15. A.T. Winfree, S.H. Strogatz, Singular filaments organize chemical waves in three dimensionsII. Twisted waves. Phys. D 9, 65–80 (1983)

16. A.T. Winfree, S.H. Strogatz, Singular filaments organize chemical waves in three dimensionsIII. Knotted waves. Phys. D 9, 333–345 (1983)

17. A.T. Winfree, S.H. Strogatz, Singular filaments organize chemical waves in three dimensionsIV. Wave taxonomy. Phys. D 13, 221–233 (1984)

18. N. Shanks, Modeling biological systems: the belousov-zhabotinsky reaction. Found. Chem.3, 33–53 (2001)

19. A.L.Hodgkin,A.F.Huxley,Aquantitative description ofmembrane current and its applicationto conduction and excitation in nerve. J. Physiol. 117, 500–540 (1952)

20. A.T. Winfree, When Time Breaks Down: The Three-Dimensional Dynamics of Electrochem-ical Waves and Cardiac Arrhythmias. (Princeton University Press, Princeton, 1987), ISBN0-691-02402-2

21. A.T.Winfree,TheGeometry of Biological Time (Springer, Berlin, 2001), ISBN0-387-98992-722. M.Hörning, S.Kidoaki, T.Kawanoet al., Rigiditymatchingbetween cells and the extracellular

matrix leads to the stabilization of cardiac conduction. Biophys. J. 102, 379–387 (2012)23. R. Ahmed, K. Hashiba, Reliability of QT intervals as indicators of clinical hypercalcemia.

Clin. Cardiol. 11(395), 400 (1988)24. F. Morris, W.J. Brady, Acute myocardial infarction—part 1. Br. Med. J. 324, 831–834 (2002)25. V.G. Fast, A.G. Kleber, Role of wavefront curvature in propagation of cardiac impulse. Car-

diovasc Res. 33, 258–271 (1996)

[email protected]


26. S. Alonso, A.V. Panfilov, Phys. Rev. Lett. 100, 218101 (2008)27. J.J. Tyson, J.P. Keener, Singular perturbation theory of traveling waves in excitable media.

Phys. D 32, 327–361 (1988)28. V.S. Zykov, Kinematics of rigidly rotating spiral waves. Phys. D 238, 931–940 (2009)29. F.W. Lindemans, J.J.D. van der Gon, Current thresholds and liminal size in excitation of heart

muscle. Cardiovasc. Res. 12, 477–485 (1978)30. G.W.Beeler, H. Reuter, Reconstruction of the action potential of ventricularmyocardial fibres.

J. Physiol. 268, 177–210 (1977)31. M. Hörning, S. Takagi, Yoshikawa, wave emission on interacting heterogeneities in cardiac

tissue. Phys. Rev. E 82, 021926 (2010)32. S. Zlochiver, V.Munoz, K.L. Vikstrom et al., Electrotonicmyofibroblast-to-myocyte coupling

increases propensity to reentrant arrhythmias in 2-dimensional cardiac monolayers. Biophys.J. 95, 4469–4480 (2008)

33. C.M. Ambrosi, A. Klimas, J. Yu et al., Cardiac applications of optogenetics. Prog. Biophys.Mol. Biol. [Epub ahead of print], PMID 25035999 (2014)

34. E. Entcheva, Cardiac optogenetics. Am. J. Physiol. Heart Circ. Physiol. 304, H1179–1191(2013)

35. A.V. Panfilov, C.W. Zemlin, Wave propagation in an excitable medium with a negativelysloped restitution curve. Chaos 12, 800–806 (2002)

36. F. Fenton, A. Karma, Vortex dynamics in three-dimensional continuous myocardium withfiber rotation: filament instability and fibrillation. Chaos 8, 20–47 (1998)

37. J.M. Morgan, D. Cunninggham, E. Rowland, Electrical restitution in the endocardium of theintact human right ventricule. Br. Heart J. 67, 42–46 (1992)

38. J.M. Morgan, D. Cunningham, E. Rowland, Dispersion of monophasic action potential dura-tion: demonstrable in humans after premature ventricular extrastimulation but not in steadystate. J. Am. Coll. Cardiol. 19, 1244–1253 (1992)

39. W.T. Clusin, Mechanisms of calcium transient and action potential alternans in cardiac cellsand tissues. Am. J. Physiol. Heart Circ. Physiol. 294, 1–10 (2008)

40. L.D. Wilson, D. Jeyaraj, W. Xiaoping et al., Heart failure enhances susceptibility to arrhyth-mogenic cardiac alternans. Heart Rhythm 6, 251–259 (2009)

41. A.J. Engler, C. Carag-Krieger, C.P. Johnson et al., Embryonic cardiomyocytes beat best on amatrix with heart-like elasticity: scar-like rigidity inhibits beating, J. Cell Sci. 121, 3794–3802(2008)

42. H.Y.Yoshikawa, T. Kawano, T.Matsuda et al.,Morphology and adhesion strength ofmyoblastcells on photocurable gelatin under native and non-native micromechanical environments. J.Phys. Chem. 117, 4081–4088 (2013)

43. T. Kawano, S. Kidoaki, Elasticity boundary conditions required for cell mechanotaxis onmicroelastically-patterned gels. Biomaterials 32, 2725–2733 (2011)

44. S. Kidoaki, T.Matsuda,Microelastic gradient gelatinous gels to induce cellularmechanotaxis.J. Biotechnol. 133, 225–230 (2008)

45. C. Cherubini, S. Filippi, A. Gizzi, Electroelastic unpinning of rotating vortices in biologicalexcitable media. Phys. Rev. E 85, 031915 (2012)

46. M. Hörning, Termination of pinned vortices by high-frequency wave trains in heartlikeexcitable media with anisotropic fiber orientation. Phys. Rev. E 86, 031912 (2012)

47. J. Jalife, R. Gray, Drifting vortices of electrical waves underlie ventricular fibrillation in therabbit heart. Acta Physiol. Scand. 157, 123–131 (2009)

48. A.V. Panfilov, J. Keener, Effects of high frequency stimulation on cardiac tissue with aninexcitable obstacle. J. Theor. Biol. 163, 439–448 (2009)

49. J. Cysyk, L. Tung, Electric field perturbations of spiral waves attached to millimeter-sizeobstacles. Biophys. J. 94, 1533–1541 (2008)

50. F. Fenton, S. Luther, E.M. Cherry et al., Termination of atrial fibrillation using pulsed low-energy far-field stimulation. Circulation 120, 467–476 (2009)

51. M. Hörning, S. Takagi, K. Yoshikawa, Controlling activation site density by low-energy far-field stimulation in cardiac tissue. Phys. Rev. E 85, 061906 (2012)

[email protected]


52. V.G. Fast, S. Rohr, A.M. Gillis et al., Activation of cardiac tissue by extracellular electri-cal shocks: formation of secondary sources at intercellular clefts in monolayers of culturedmyocytes. Circ. Res. 82, 375–385 (1998)

53. R. Plonsey, R.C. Barr, Inclusion of junction elements in a linear cardiac model through sec-ondary sources: application to defibrillation. Med. Biol. Eng. Comput. 24, 137–144 (1986)

54. R. Plonsey, R. Barr, Effects of microscopic and macroscopic discontinuities on the responseof cardiac tissue to defibrillating (stimulating) currents.Med. Biol. Eng. Comput. 24, 130–136(1986)

55. A. Pumir, V. Nikolski, M. Hörning et al., Wave emission from heterogeneities opens a wayto controlling Chaos in the heart. Phys. Rev. Lett. 99, 208101 (2007)

56. A.E. Lindblom, B.J. Roth, N.A. Trayanova, Role of virtual electrodes in arrhythmogenesis:pinwheel experiment revisited. J. Cardiovasc. Electropys. 11, 274–285 (2000)

57. J.B. White, G.P. Walcott, A.E. Pollard et al., Myocardial discontinuities: a substrate for pro-ducing virtual electrodes that directly excite the myocardium by shocks. Circulation 97,1738–1745 (1998)

58. P. Bittihn, M. Hörning, S. Luther, Negative curvature boundaries as wave emitting sites forthe control of biological excitable media. Phys. Rev. Lett. 109, 118106 (2012)

59. S. Luther, F.H. Fenton, B.G. Kornreich et al., Low-energy control of electrical turbulence inthe heart. Nature 475, 235–239 (2011)

60. M. Hörning, A. Isomura, Z. Jia et al., Utilizing the eikonal relationship in strategies forreentrant wave termination in excitable media. Phys. Rev. E 81, 056202 (2010)

61. A. Pumir, S. Sinha, S. Sridhar et al., Wave-train induced termination of weakly anchoredvortices in excitable media. Phys. Rev. E 81, 010901(R) (2009)

62. P. Bittihn, G. Luther, E. Bodenschatz et al., Far field pacing supersedes anti-tachycardia pacingin a generic model of excitable media. New J. Phys. 10, 103012 (2008)

63. J.P. Keener, K. Bogar, A numerical method for the solution of the bidomain equations incardiac tissue. Chaos 8, 175–187 (1998)

64. B. Roth, J. Wikswo, A bidomain model for the extracellular potential and magnetic-field ofcardiac tissue. IEEE Trans. Biomed. Eng. 33, 467–469 (1986)

65. D. Noble, The relation of Rushton ‘liminal length’ for excitation to the resting and activeconductances of excitable cells. J. Physiol. (London) 226, 573–591 (1972)

66. N.G. Sepulveda, B.J. Roth, J.P. Wikswo, Current injection into a two-dimensional anisotropicbidomain. Biophys. J. 55, 987–999 (1989)

67. S. Takagi, A. Pumir, D. Pazo et al., Unpinning and removal of a rotating wave in cardiacmuscle. Phys. Rev. E. 93, 058101 (2004)

68. E. Entcheva, N.A. Trayanova, F.J. Claydon, Patterns of and mechanisms for shock-inducedpolarization in the heart: a bidomain analysis. IEEE Trans. Biomed. Eng. 46, 260–270 (1999)

69. N.A. Trayanova, K. Skouibine, Modeling defibrillation—effects of fiber curvature. J. Elec-trocardiol. 31, 23–29 (1998)

70. N.A. Trayanova, R.A.Gray, D.W.Bourn et al., Virtual electrode-induced positive and negativegraded responses: new insights into fibrillation induction and defibrillation. J. Cardiovasc.Electrophys. 14, 756–763 (2003)

71. A. Pumir, V. Krinski, Unpinning of a rotating wave in cardiac muscle by an electric field. J.Theor. Biol. 199, 311–319 (1999)

72. X. Feng, X. Gao, D.B. Pan et al., Unpinning of rotating spiral waves in cardiac tissues bycircularly polarized electric fields. Sci. Rep. 4, 4831 (2014)

73. G. Nagel, T. Szellas, W. Huhn et al., Channelrhodopsin-2, a directly light-gated cation-selective membrane channel. Proc. Natl. Acad. Sci. USA 100, 13940–13945 (2003)

74. B.Y. Chow, X. Han, A.S. Dobry et al., High-performance genetically targetable optical neuralsilencing by light-driven proton pumps. Nature 463, 98–102 (2010)

75. O. Yizhar, L.E. Fenno, T.J. Davidson et al., Optogenetics in neural systems. Neuron 71, 9–34(2011)

76. G. Nagel, M. Brauner, J.F. Liewald et al., Light activation of channelrhodopsin-2 in excitablecells of Caenorhabditis elegans triggers rapid behavioral responses. Curr. Biol. 15, 2279–2284(2005)

[email protected]


77. A. Berndt, P. Schoenenberger, J. Mattis et al., High-efficiency channelrhodopsins for fastneuronal stimulation at low light levels. Proc. Natl. Acad. Sci. USA 108, 7595–7600 (2011)

78. S. Kleinlogel, K. Feldbauer, R.E. Dempski et al., Ultra light-sensitive and fast neuronal acti-vation with the Ca(2)+ -permeable channelrhodopsin CatCh. Nat. Neurosci. 14, 513–518(2011)

79. L.A. Gunaydin, O. Yizhar, A. Berndt et al., Ultrafast optogenetic control. Nat. Neurosci. 13,387–392 (2010)

80. J.Y. Lin, P.M. Knutsen, A. Muller et al., ReaChR: a red-shifted variant of channelrhodopsinenables deep transcranial optogenetic excitation. Nat. Neurosci. 16, 1499–1508 (2013)

81. T. Bruegmann, D. Malan, M. Hesse et al., Optogenetic control of heart muscle in vitro and invivo. Nat. Methods 7, 897–900 (2010)

82. O.J. Abilez, J. Wong, R. Prakash et al., Multiscale computational models for optogeneticcontrol of cardiac function. Biophys. J. 101, 1326–1334 (2011)

83. J.C. Williams, J. Xu, Z. Lu et al., Computational optogenetics: empirically-derived voltage-and light-sensitive channelrhodopsin-2 model. PLoS Comput. Biol. 9, e1003220 (2013)

84. Z. Jia, V. Valiunas, Z. Lu et al., Stimulating cardiac muscle by light: cardiac optogenetics bycell delivery. Circ. Arrhythm. Electrophysiol. 4, 753–760 (2011)

85. E. Entcheva, J.C. Williams, Channelrhodopsin2 current during the action potential: “opticalAP clamp” and approximation. Sci. R. 4, 5838 (2014)

86. P.M. Boyle, J.C. Williams, C.M. Ambrosi et al., A comprehensive multiscale framework forsimulating optogenetics in the heart. Nat. Commun. 4, 2370 (2013)

87. J. Wong, O.J. Abilez, E. Kuhl, Computational optogenetics: a novel continuum frameworkfor the photoelectrochemistry of living systems. J. Mech. Phys. solids 60, 1158–1178 (2012)

88. A.B. Arrenberg, D.Y. Stainier, H. Baier et al., Optogenetic control of cardiac function. Science330, 971–974 (2010)

89. E. Papagiakoumou, F. Anselmi, A. Begue et al., Scanless two-photon excitation ofchannelrhodopsin-2. Nat. Methods 7, 848–854 (2010)

90. J. Suzurikawa, M. Nakao, Y. Jimbo et al., Light-addressed stimulation under Ca(2+) imagingof cultured neurons. IEEE Trans. Biomed. Eng. 56, 2660–2665 (2009)

91. N. Wiener, A. Rosenblueth, The mathematical formulation of the problem of conduction ofimpulses in a network of connected excitable elements, specifically in cardiac muscle. Arch.Inst. Cardiol. Mex. 16, 205–265 (1946)

92. D. Frazier, P.Wolf, M.Wharton et al., Stimulus-induced critical point. Mechanism for electri-cal initiation of reentry in normal canine myocardium. J. Clin. Invest. 83, 1039–1052 (1989)

93. M.J. Janse, Functional reentry: leading circle or spiral wave? J. Cardiovasc. Electrophysiol.10, 621–622 (1999)

94. J. Jalife, Deja vu in the theories of atrial fibrillation dynamics. Cardiovasc. Res. 89, 766–775(2010)

95. P.S. Chen, T.J. Wu, C.T. Ting et al., A tale of two fibrillations. Circulation 108, 2298–2303(2003)

96. J. Tonnesen, A.T. Sorensen, K. Deisseroth et al., Optogenetic control of epileptiform activity.Proc. Natl. Acad. Sci. U.S.A. 106, 12162–12167 (2009)

97. A. Klimas, E. Entcheva, Toward microendoscopy-inspired cardiac optogenetics in vivo: tech-nical overview and perspective. J. Biomed. Opt. 19, 80701 (2014)

98. D.J. Dosdall, J. Osorio, R.P. Robichaux et al., Purkinje activation precedes myocardial acti-vation following defibrillation after long-duration ventricular fibrillation. Heart Rhythm 7,405–412 (2010)

99. R.P. Robichaux, D.J. Dosdall, J. Osorio et al., Periods of highly synchronous, non-reentrantendocardial activation cycles occur during long-duration ventricular fibrillation. J. Cardiovasc.Electrophysiol. 21, 1266–1273 (2010)

100. P. Daleau, Effects of antiarrhythmic agents on junctional resistance of guinea pig ventricularcell pairs. J. Pharmacol. Exp. Ther. 284, 1174–1179 (1998)

101. C.F. Starmer, How antiarrhythmic drugs increase the rate of sudden cardiac death. Int. J.Bifurcat. Chaos 12, 1953–1968 (2002)

[email protected]


102. P. Zimetbaum, Antiarrhythmic drug therapy for atrial fibrillation. Circulation 125, 381–389(2012)

103. R. Rezakhaniha, A. Agianniotis, J.T. Schrauwen et al., Experimental investigation of collagenwaviness and orientation in the arterial adventitia using confocal laser scanning microscopy.Biomech. Model Mechanobiol. 11, 461–473 (2012)

104. S.Y. Boateng, T.J. Hartman,N.Ahluwalia et al., Inhibition of fibroblast proliferation in cardiacmyocyte cultures by surface microtopography. Am. J. Cell Physiol. 285, 171–182 (2003)

105. M.L. McCain, K.K. Parker, Mechanotransduction: the role of mechanical stress, myocyteshape, and cytoskeletal architecture on cardiac function. Pflugers Arch. 462, 89–104 (2011)

106. A.J. Engler, S. Sen, H.L. Sweeney et al., Matrix elasticity directs stem cell lineage specifica-tion. Cell 126, 677–689 (2006)

107. H.Y.Yoshikawa, F.R. Rossetti, S. Kaufmann et al., Quantitative evaluation ofmechanosensingof cells on dynamically tunable hydrogels. J. Am. Chem. Soc. 133, 1367–1374 (2011)

108. D.E. Discher, P. Janmey, Y.L. Wang, Tissue cells feel and respond to the stiffness of theirsubstrate. Science 310, 1139–1143 (2005)

109. Y. Orlova, N. Magome, L. Liu et al., Electrospun nanofibers as a tool for architecture controlin engineered cardiac tissue. Biomaterials 32, 5615–5624 (2011)

110. C.Y. Chung, H. Bien, E.A. Sobie et al., Hypertrophic phenotype in cardiac cell assembliessolely by structural cues and ensuing self-organization. FASAB J. 25, 852–864 (2004)

111. M.E. Hubbi, E.H. Ahn, Kshitiz et al., Matrix rigidity controls endothelial differentiation andmorphogenesis of cardiac precursors. Sci. Signal 227, 1–14 (2012)

112. J. Jalife, Ventricular fibrillation: mechanisms of initiation and maintenance. Annu. Rev. Phys-iol. 62, 25–50 (2000)

113. S.W. Moore, P. Roca-Cusachs, M.P. Sheetz, Stretchy proteins on stretchy substrates: theimportant elements of integrin-mediated rigidity sensing. Dev. Cell 19, 194–206 (2010)

114. A. Grosberg, P.-L. Kuo, C.-L. Guo et al., Self-organization of muscle cell structure andfunction. PLoS Comput. Biol. 7, e1001088 (2011)

115. N.B. Hersch, G. Wolters, R. Dreissen et al., The constant beat: cardiomyocytes adapt theirforces by equal contraction upon environmental stiffening. Biol. Open. 2, 351–361 (2013)

116. S.A. Shintani, K. Oyama, F. Kobirumaki-Shimozawa et al., Sarcomere length nanometry inrat neonatal cardiomyocytes expressed with alpha-actinin-AcGFP in Z discs. J. Gen. Physiol.143, 513–524 (2014)

117. J.W. Sanger, S.M. Kang, C.C. Siebrands, N. Freeman, A.P. Du et al., How to build a myofibril.J. Muscle Res. Cell Motil. 26, 343–354 (2005)

118. F. Giesselmann, R. Germer, A. Saipa, Orientational order in smectic liquid-crystalline phasesof amphiphilic diols. J. Chem. Phys. 123, 034906 (2005)

119. A. Zemel, F. Rehfeldt, A.E.X.Brown et al., Optimalmatrix rigidity for stress-fibre polarizationin stem cells. Nat. Phys. 6, 468–473 (2010)

120. C. Fink, S. ErgÜn, D. Kralisch et al., Chronic stretch of engineered heart tissue induceshypertrophy and functional improvement. FASAB J. 14, 669–679 (2000)

121. M. Matsusaki, H. Ajiro, T. Kida et al., Layer-by-layer assembly through weak interactionsand their biomedical applications. Adv. Mater. 24(4), 454–474 (2012)

122. M. Matsusaki, K. Kadowaki, Y. Nakahara et al., Fabrication of cellular multilayers withnanometer-sized extracellular matrix films. Angew. Chem. Int. Ed. 46, 4689–4692 (2007)

123. W.H.Zimmermann, I.Melnychenko,T.Eschenhagen,Engineered heart tissue for regenerationof diseased hearts. Biomaterials 25, 1639–1647 (2004)

124. M. Lovett, K. Lee, Edwards et al., Vascularization strategies for tissue engineering. TissueEng. Part B Rev. 15, 353–370 (2009)

125. K.Kada,K.Yasui,K.Naruse et al., Orientation change of cardiocytes induced by cyclic stretchstimulation: time dependency and involvement of protein kinases. J. Mol. Cell Cardiol. 31,247–259 (1999)

126. L. Liu, Q. Yuan, J. Shi et al., Chemically defined scaffolds created with electrospun syn-thetic nanofibers to maintain mouse embryonic stem cell culture under feeder-free conditions.Biotechnol. Lett. 34, 1951–1957 (2012)

[email protected]


127. A. Salameh, A. Wustmann, S. Karl et al., Cyclic mechanical stretch induces cardiomyocyteorientation and polarization of the gap junction protein connexin 43. Circ. Res. 106, 1592–1602 (2010)

128. E. Tzima, M. Irani-Tehrani, W.B. Kiosses, A mechanosensory complex that mediates theendothelial cell response to fluid shear stress. Nature 437, 426–431 (2005)

129. I.M.Weiss, Species-specific shells: chitin synthases and cellmechanics inmolluscs. Z.Kristal-logr. 227, 723–738 (2012)

130. I.M.Weiss, F. Lücke,N. Eichner et al., On the function of chitin synthase extracellular domainsin biomineralization. J. Struct. Biol. 183, 216–225 (2013)

131. M.L. Lemloh, F. Marin, F. Herbst et al., Genesis of amorphous calcium carbonate containingalveolar plates in the ciliate Coleps hirtus (ciliophora, prostomatea). J. Struct. Biol. 181,155–161 (2013)

132. V. Schönitzer, I.M. Weiss, The structure of mollusc larval shells formed in the presence of thechitin synthase inhibitor Nikkomycin Z. BMC Struct. Biol. 7, 71 (2007)

133. C.M. Ambrosi, E. Entcheva, Optogenetic control of cardiomyocytes via viral delivery. Meth-ods Mol. Biol. 1181, 215–228 (2014)

134. P. Bittihn, A. Squires, G. Luther et al., Phase-resolved analysis of the susceptibility of pinnedspiral waves to far-field pacing in a two-dimensional model of excitable media. New J. Phys.368, 2221–2236 (2010)

135. J.W. Lin, L. Garber, Y.R. Qi et al., Region of slowed conduction acts as core for spiral wavereentry in cardiac cell monolayers. Am. J. Physiol. Heart Circ. Physiol. 294, 1501 (2008)

136. S. Takagi, A. Pumir, D. Pazo, A physical approach to remove anatomical reentries: a bidomainstudy. J. Theor. Biol. 230, 489–497 (2004)

[email protected]

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