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, 60 (6), 1158-1178

Computational Optogenetics: A Novel Continuum Framework for the Photoelectrochemistry of Living Systems

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Computational Optogenetics: A Novel Continuum Framework for the Photoelectrochemistry of Living Systems

Jonathan Wong et al. J Mech Phys Solids.

Abstract

Electrical stimulation is currently the gold standard treatment for heart rhythm disorders. However, electrical pacing is associated with technical limitations and unavoidable potential complications. Recent developments now enable the stimulation of mammalian cells with light using a novel technology known as optogenetics. The optical stimulation of genetically engineered cells has significantly changed our understanding of electrically excitable tissues, paving the way towards controlling heart rhythm disorders by means of photostimulation. Controlling these disorders, in turn, restores coordinated force generation to avoid sudden cardiac death. Here, we report a novel continuum framework for the photoelectrochemistry of living systems that allows us to decipher the mechanisms by which this technology regulates the electrical and mechanical function of the heart. Using a modular multiscale approach, we introduce a non-selective cation channel, channelrhodopsin-2, into a conventional cardiac muscle cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, this channel opens and allows sodium ions to enter the cell, inducing electrical activation. In side-by-side comparisons with conventional heart muscle cells, we show that photostimulation directly increases the sodium concentration, which indirectly decreases the potassium concentration in the cell, while all other characteristics of the cell remain virtually unchanged. We integrate our model cells into a continuum model for excitable tissue using a nonlinear parabolic second order partial differential equation, which we discretize in time using finite differences and in space using finite elements. To illustrate the potential of this computational model, we virtually inject our photosensitive cells into different locations of a human heart, and explore its activation sequences upon photostimulation. Our computational optogenetics tool box allows us to virtually probe landscapes of process parameters, and to identify optimal photostimulation sequences with the goal to pace human hearts with light and, ultimately, to restore mechanical function.

Figures

Figure 1
Figure 1
Channelrhodopsin-2 is a light-gated cation channel native to the green alga Chlamydomonas reinhardtii. It consists of seven transmembrane proteins and absorbs blue light through its interaction with retinal. Photoisomerization of retinal opens the channel to sodium ions, which have a higher concentration outside than inside the cell. To make our cells responsive to light, and allow sodium concentrations to equilibrate, we induce channelrhodopsin into a conventional cardiac muscle cell model.
Figure 2
Figure 2
Channelrhodopsin-2 is activated by photoisomerization of all-trans retinal to 13-cis retinal at wavelengths of 470 nm. After photoisomerization, the covalently bound retinal spontaneously relaxes to all-trans in the dark, providing closure of the ion channel and regeneration of the chromophore.
Figure 3
Figure 3
Multiscale model for the photoelectrochemistry of living systems. Optical stimulation opens the cation channel channelrhodopsin gChR2. This initiates a photocurrent IChR2 increasing the chemical concentration of sodium ions cNa inside the cell. Concentration changes evoke changes in the electrical potential ϕ, which propagates across the tissue system in the form of smooth excitation waves.
Figure 4
Figure 4
Three-state model for the channelrhodopsin photocycle. Upon photo absorption, molecules in the closed state gclosed undergo a fast transition into the open state gChR2. The molecules spontaneously turn into the refractory state grefrac where the ion channels are closed, but the molecules are not yet ready to photoswitch again. After the refractory period, the molecules return to the closed state gclosed, ready to undergo a new photocycle when subjected to light [32, 33].
Figure 5
Figure 5
Genetically engineered light sensitive cardiac cell. The electrophysiology of the cell is characterized in terms of nion = 4 ion concentrations, the intracellular sodium, potassium, and calcium concentrations and the calcium concentration in the sarcoplastic reticulum. Ion concentrations are controlled through ncrt = 16 ionic currents, where we have enhanced the conventional cell model [43, 47] with the channelrhodopsin photocurrent IChR2, here shown in blue [1]. The channels are governed by ngate = 14 gating variables, where we have added the channelrhodopsin gating variable gChR2 to characterize the cell’s response to photostimulation.
Figure 6
Figure 6
Genetically engineered light sensitive cardiac cell stimulated conventionally with an electric field, dashed lines, and optically with light, solid lines. Temporal evolution of sodium activation gate gm, fast sodium inactivation gate gh, slow sodium inactivation gate gj, L-type calcium activation gate gd, L-type calcium inactivation gate gf, intracellular calcium dependent calcium inactivation gate gfCa transient outward activation gate gr, transient outward inactivation gate gs, slow delayed rectifier gate gxs, rapid delayed rectifier activation gate gxr1, rapid delayed rectifier inactivation gate gxr2, inward recrification factor gK1, calcium-dependent inactivation gate gg, and channelrhodospin activation gate gChR2. The gating dynamics for the electrically stimulated cell have been delayed by 34 ms for the purposes of comparison against the optically stimulated cell.
Figure 7
Figure 7
Genetically engineered light sensitive cardiac cell stimulated conventionally with an electric field, dashed lines, and optically with light, solid lines. Temporal evolution of fast sodium current INa, background sodium current IbNa, sodium potassium pump current INaK, sodium calcium exchanger current INaCa, inward rectifier current IK1, rapid delayed rectifier current IKr, slow delayed rectifier current IKs, plateau potassium current IpK, transient outward current It0, L-type calcium current ICaL, background calcium current IbCa, plateau calcium current IpCa, leakage current Ileak, sarcoplastic reticulum uptake current Iup, sarcoplastic reticulum release current Irel, and channelrhodopsin current IChR2. The current dynamics for the electrically stimulated cell have been delayed by 34 ms for the purposes of comparison against the optically stimulated cell.
Figure 8
Figure 8
Genetically engineered light sensitive cardiac cell stimulated conventionally with an electric field, dashed lines, and optically with light, solid lines. Temporal evolution of intracellular sodium cNa, potassium cK, calcium cCa concentrations, and calcium concentration cCasr in the sarcomplastic reticulum. The chemical concentration dynamics for the electrically stimulated cell have been delayed by 34 ms for the purposes of comparison against the optically stimulated cell.
Figure 9
Figure 9
Genetically engineered light sensitive cardiac cell stimulated conventionally with an electric field, dashed lines, and optically with light, solid lines. Temporal evolution of transmembrane potential ϕ. The characteristic action potential consists of five phases. Phase 0: The rapid upstroke is generated through an influx of positively charged sodium ions. Phase 1: Early, partial repolarization is initiated through the efflux of positively charged potassium ions. Phase 2: During the plateau, the net influx of positively charged calcium ions is balanced by the efflux of positively charged potassium ions. Phase 3: Final repolarization begins when the efflux of potassium ions exceeds the influx of calcium ions. Phase 4: Throughout the interval between end of repolarization and the beginning of the next cycle the cell is at rest. The transmembrane potential for the electrically stimulated cell has been delayed by 34 ms for the purposes of comparison against the optically stimulated cell. This delay agrees nicely with the time delay of activation of 19.7±3.4 ms reported in the literature [6].
Figure 10
Figure 10
Virtual injection of genetically engineered light sensitive cardiac cells into a human heart. Magnetic resonance imaging generates a sequence of two-dimensional images at different depths (top, left). We segment cardiac muscle tissue semi-manually using standard image processing techniques (bottom, left). Thresholding and binary masking convert the raw grayscale images to monochrome images with sharply defined boundaries (top, right). From these slices, we create a preliminary triangular surface mesh and converted it into the final tetrahedral volume mesh consisting of 3,129 nodes and 11,347 tetrahedral elements (bottom, right). Last, we virtually inject photosensitive cells into different regions of the heart and stimulated with light (middle).
Figure 11
Figure 11
Photostimulation of a human heart. Spatio-temporal evolution of transmembrane potential ϕ, intracellular sodium cNa, potassium cK, and calcium cCa concentrations for atrioventricular node paced heart. Photosensitive cells are virtually injected into the basal region of the septum, while all other regions are modeled as conventional cardiac muscle cells. A depolarization wave forms at the atrioventricular node, travels down the septum, and activates the left and right ventricles.
Figure 12
Figure 12
Photostimulation of a human heart. Spatio-temporal evolution of transmembrane potential ϕ, intracellular sodium cNa, potassium cK, and calcium cCa concentrations for apically paced heart. Photosensitive cells are virtually injected into the apex, while all other regions are modeled as conventional cardiac muscle cells. A depolarization wave forms at the apex, travels up, and activates the septum and both ventricles simultaneously.
Figure 13
Figure 13
Photostimulation of a human heart. Spatio-temporal evolution of transmembrane potential ϕ, intracellular sodium cNa, potassium cK, and calcium cCa concentrations for bi-vnetricularly paced heart. Photosensitive cells are virtually injected into the lateral walls of the left and right ventricles, while all other regions are modeled as conventional cardiac muscle cells. Two depolarization waves form in the lateral left and right ventricular walls to travel along the ventricles and activate the apex and the septum.

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