The mechanism of excitonic stimulation by photo-induced dipoles in a bulk photovoltaic substrate

In general, photo-induced dipoles create extracellular electric fields that can interact directly with the cell’s lipid bilayer (dipole-dipole interaction) or with extracellular ions (dipole-charge interaction). Figs 2(a) and 2(b) show the schematic and energy band diagram of a photo-capacitor, as well as the photo-induced dipoles under light excitation. As demonstrated recently [40], high spatial resolution in organic optobioelectronic devices is critically governed by the properties of photo-induced dipoles formed within nanoscale microdomains of organic semiconductor blends. Recently, in bulk heterojunction solar cells such as PCE12:ITIC-based systems, light absorption generates excitons, bound electron-hole pairs, that dissociate at donor–acceptor interfaces, producing localized photoinduced dipoles within phase-separated microdomains (Fig 2(c)). These dipoles arise from spatially confined charge separation in the organic hybrid matrix, where nanoscale morphology dictates both exciton diffusion and interfacial dynamics. The collective behavior of these synthetic dipoles contributes to the internal electric field, influencing both the open-circuit voltage (V_oc) and photocurrent (I_ph). Significantly, the polarization state of incident laser light can modulate the orientation of dipoles within these microdomains, effectively rotating their alignment and tuning the anisotropy of the generated field (Fig 2(c) inset). Polarized excitation can consequently enhance directional charge separation or, conversely, suppress interfacial charge transfer by orienting dipoles away from donor–acceptor pathways. This optical control enables the system to transition from Faradaic (charge-transferring) to capacitive behavior, reducing current flow while maintaining field-induced stimulation. When interfaced with biological cells, this polarization-driven modulation of synthetic dipole fields enables tunable, non-invasive control of the membrane potential, offering a fundamentally novel and biocompatible approach to neuromodulation through light, without the need for direct ionic or molecular delivery.

Further, the direction and amplitude of photoinduced dipoles are controlled by incident light intensity and polarization. The fundamental equations (equation 1–3) are used to determine the mechanism operating in the hypothesis, establishing a mathematical relation between photovoltaic parameters and light polarization. Equation 1 describes the photo-induced dipoles in which the electrons and holes have different masses of m_n and m_h in different materials in a bulk heterojunction. Equation 2 describes the photo-induced potential as a function of the input light intensity, the intrinsic properties of the semiconductor, and the polarization of the incident light. Equation 3 describes the surface potential drop at the surface due to the double-layer capacitance at the interface with the water. A linear polarization of the light leads to an electrical field displacement in the x and y planes as a Cosine wave, like what has been reported for Si polarizer detectors [15]. At a specific input light intensity, the output photovoltage is saturated and reaches a maximum level. Subsequently, the photo-induced dipole reaches its highest magnitude, as described in the open-circuit voltage in equation 2. A harmonic oscillator can be generated by modulating light polarization between 90° and 270°. In this way, an oscillating electric dipole can be produced to stimulate cells at a neuronal interface.

(1)

where I is the light intensity amplitude, θ the polarization angle, Q the photoinduced charge, d the dipole distance, x and y the coordinates of illumination, and t the time.

(2)

Where the q is the electrical charges, E_C is the conduction energy band, E_HOMO is the HOMO level, and θ is the polarization angle that could be linear.

(3)

In which θ is the polarization angle, r is the radius from the photo-induced dipole, and t is the time.

Open-Loop condition.

In open-loop conditions, a minimal electrochemical reaction, the surface potential can be determined by the open circuit voltage of the photovoltaic device while using an ordinary incident light. However, the alternation of light polarization causes local field potentials, as described in Equation 2. In addition, a uniform illumination to a photovoltaic substrate (bulk model) causes an output photovoltage that can be calculated as equation 3, where the open-circuit voltage is obtained by the photo-induced charges and the energy differences. The photo-induced surface potential can open voltage-gated ion channels by altering the cell membrane potential or through the electrostatic force resulting from the dipolar interaction between the photo-induced dipoles and the lipid bilayer.

Further the change in polarization angle using polarizer can lead to to time-dependent fucntionality of charges. Hence, the polarization can be rewritten as a time-dependent dipole as follows.

(4)

Where, photogenerated charge accumulation with saturation can be represented as photovoltaic internal parameters as follows:

(5)

Where η_q is quantum efficiency, G_ph(t) is photon generation rate (e.g., light intensity × absorption coefficient), τ_life is carrier lifetime, N_max: maximum charge density (saturation limit), d is effective dipole length, and θ(t) is angle between dipole and external field (e.g., light polarization).

Closed-Loop condition.

If there is a short-circuit loop from the substrate and the cell medium, the membrane potential could be displaced by the changes in the photocapacitor’s capacitance because of changing the orientation of the photo-induced dipoles through light polarization modulation as well. Figure S1 in S3 File in supplementary information shows the schematic, and the electrical circuit model of a neuron coupled to a photo-capacitor in a closed-loop condition. Under light excitation, a neuron is electrically stimulated through the electric field displacement at the surface of a bio-interface due to the photo-induced dipoles in the photo-capacitor. At the same time, the intensity controls the amplitude of the photo-induced dipole; the polarization of the incident light can alter the direction of the photo-induced dipole, the internal electric field, the capacitance of the photo-capacitor, and the photocurrent under light excitation. The effective electric field generated by the light excitation in a photocapacitor could be obtained from the following equation:

(6)

Where, the factor, , and photocapacitance, . Therefore,

(7)

Considering we have a linear polarization; k is altered with a cosine function similar to Equation 1. The factor k is affected directly by the photo-induced dipoles in a semiconductor under the light illumination. The change in the capacitance directly alters the potential distribution between the photo-capacitor and the cellular environment. Therefore, the capacitance displacement in the photocapacitor leads to the potential displacement at the interface (ionic charge redistribution across the cell membrane, which leads to cell membrane capacitance displacement) of the neuron with the photocapacitor. If we have an input light pulse U(t) Cos (π/2n), where n is the pulse number and t is the time, the photo-induced dipole rotates between 0 and 90 degrees, and the photocurrent flows in two opposite directions. Like the works that have already been explained before [17,41], we can find the membrane potential related to the input light intensity and polarization [17]:

(8)(9)(10)

We can use V_{m, peak} (I₀) = −1.14 + 6.5 * ln (I_a * cos²(φ)) for PCE12:ITIC after correction based on the α = V_OC-P3HT/V_OC-PCE12 = 0.8/0.6 ≈ 1.33. And finally, the time response could be obtained as follows:

(11)(12)

Dipole-dipole interaction.

Considering that photo-induced dipoles in photocapacitive or nanostructured materials can generate local electric fields [5,42], these fields can induce corresponding dipoles in the nearby cell membrane, which itself behaves as a biological capacitor. This interaction can lead to electrostatic modulation of the membrane potential through the redistribution of ionic charges across the membrane, thereby influencing the cell’s excitability and potentially triggering bioelectrical responses. One example of cellular stimulation through electrostatic force is the use of polyamide 66 embedded with graphene nanoplates for electrostatic polarization of glioblastoma cells [14]. The interaction between photo-induced dipoles (V_dd) in nanostructured materials and the cell membrane can be described through the electrostatic potential generated by a time-varying dipole moment P(t). The resulting potential at a distance r from the dipole is given by:

(13)

Where ε₀ is the vacuum permittivity. This potential induces an electric field at the cell interface leading to polarization of the lipid bilayer, and effectively alters the transmembrane potential through charge redistribution. In addition to membrane potential modulation via local dipole fields, the membrane capacitance itself may evolve over time due to charge accumulation and electrostatic deformation of the bilayer. This dynamic behavior can be modeled as [42]:

(14)

Where C_m is the baseline membrane capacitance, Q(t) is the time-dependent local charge density, Q_ref is a reference charge corresponding to a physiologically relevant scale (e.g., depolarization threshold), and γ is a dimensionless scaling factor reflecting the membrane’s electro-mechanical sensitivity. At nanometer-scale separations, the interaction between a photo-induced dipole in a nanostructured biointerface and an induced dipole on the cell membrane can be described by the dipole–dipole interaction force (F_dd), governed by:

(15)

This force captures both orientation-dependent attraction/repulsion and the dynamic coupling between the dipolar polarization fields. In the context of cellular modulation, this interaction may lead to localized mechanical deformation, redistribution of membrane charges, or even nanoscopic strain fields that influence ion channel gating. The modulation of membrane potential by external fields is a fundamental mechanism in photoelectrical and piezoelectric stimulation.

The change in transmembrane voltage ΔV_m(t) can be approximated as directly proportional to the induced electric field and the local membrane thickness or displacement:

(16)

This relationship reflects how external fields generated by photo-induced surface dipoles, piezoelectric strain, or charge redistribution can penetrate the capacitive membrane structure, altering its potential difference. In soft bioelectronic interfaces, especially those using thin-film semiconductors or quantum dots, spatial field gradients and nanometer-scale dm can amplify this effect, enabling efficient modulation of excitable cells at low stimulation thresholds.

The electrical field induced through the dipole-dipole interaction causes current displacement, and we can find this displacement as follows:

(17)

This formulation highlights the fact that dynamic changes in material polarization, even in the absence of net charge injection, can generate sufficient electrostatic influence to alter the membrane potential of nearby excitable cells.

In capacitive stimulation mechanisms, such as those involving photoactive or piezoelectric biointerfaces, the membrane potential is not altered by charge injection but by displacement currents that charge the cell membrane capacitively. The transmembrane voltage V_m(t) is governed by:

(18)

Here, I_disp(t) originates from the time derivative of polarization in the adjacent material, and C_m is the specific capacitance of the lipid bilayer. This integral relationship shows that the accumulated displacement current, even in the absence of faradaic reactions, can drive significant depolarization of excitable cells, particularly when high-frequency or pulsed stimuli are used.

A more comprehensive description of capacitive stimulation considers both polarization dynamics in the biointerface and ionic currents across the cell membrane. The evolution of the transmembrane potential can be described by:

(19)

Here, dP(t′) represents the time derivative of the polarization vector in the adjacent nanostructured or piezoelectric material, contributing a non-Faradaic displacement current, while J_ion(t′) accounts for ionic leakage or active transport, such as potassium or calcium channel-mediated currents.

This formulation models the membrane potential V_m(t) under complex bioelectronic stimulation, where both the polarization dynamics and membrane capacitance evolve over time in response to the accumulated surface charge:

(20)

The term Q(t′)⋅d⋅cosθ(t′) models the dipole moment aligned between the stimulation interface and the membrane, with θ(t′) denoting the instantaneous angle between the dipole and membrane normal. The denominator models a nonlinear, charge-dependent membrane capacitance, where Cm(t′) increases with surface charge via the scaling term , reflecting electromechanical modulation of the membrane. J_ion (t′) captures ionic leakage or channel currents, acting in opposition to the displacement-induced membrane charging.

Together, this model allows for simulation of light- or force-driven stimulation incorporating field orientation, electrostatic coupling, membrane softening, and active ionic feedback, enabling prediction of neuronal or retinal responses under dynamic stimulation conditions.

Dipole-ion interaction mediated by photofaradaic current.

In the semiconducting NPs-polymeric hybrid system, photo-induced local electrical charges can accumulate in a conductive polymer [43], thereby altering the cell membrane potential [42]. One example of this technology is the hybrid of semiconducting NPs and carbon nanotubes [6]. Additionally, the cell membrane can be altered through Faradaic electrochemical reactions and the accumulation of superoxides [44,45]. Photofaradaic charge transfer initiates local ion redistribution by leveraging Fermi-level alignment and surpassing the ionization thresholds of medium-sized species, such as Cl⁻ and water. These interactions modulate the ionic double layer, leading to capacitive displacement or electrochemical gating of the cell membrane potential. The ionization energies and redox potentials of biologically relevant ions, along with their implications for photofaradaic interactions at the bio interface, are summarized in Table 1. The Faradaic current density J_F(t) describes the charge transfer across the biointerface when electron exchange with the electrolyte or cellular environment becomes energetically favorable. It follows a nonlinear exponential dependence on the interfacial voltage V_s(t), as described by:

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Table 1. Ionization energies and redox potentials of biologically relevant ions in aqueous media, highlighting their role in photo-faradaic interactions at the biointerface. These parameters are critical for understanding how photoelectrode Fermi levels facilitate or restrict ion redistribution, membrane depolarization, and capacitive or electrochemical neural stimulation.

https://doi.org/10.1371/journal.pone.0335978.t001

(21)

This formulation accounts for redox reactions at the semiconductor–electrolyte interface and becomes dominant when the interface potential exceeds the threshold for electron injection into electrochemical states (e.g., reduction of ions, ROS generation).

To describe photofaradaic electron transfer at the interface between nanostructured semiconductors and biological media, the Faradaic current density can be expressed in terms of energy level alignment between the material’s quasi-Fermi level E_F,n and the redox potential E_redox the electrolyte [46]:

(22)

This formulation captures the asymmetric kinetics of forward (reductive) and reverse (oxidative) electron transfer, with the net current driven by the energy difference between E_F,nE and E_redox.

The modulation of the membrane potential ΔVm under photoelectrical stimulation arises from both capacitive and ionic effects. The first term, Q_photo/C_m, represents the capacitive charging of the membrane driven by photo-induced charge accumulation at the interface. This effect dominates in purely capacitive systems where no charge crosses the membrane:

(23)

The second term accounts for ion concentration gradients near the membrane surface, which can emerge due to Faradaic reactions, local electrostatic fields, or ionic redistribution induced by the stimulation. The contribution from each ion species is weighted by its valency z_i and scaled by the local dielectric.

Dipole-ion interaction mediated by photocapacitive current (indicating the electrostatic coupling between an induced dipole and nearby free or bound charges, e.g., on the membrane surface).

Considering that the photo-induced dipoles in a photo-capacitor interact with the extracellular ionic charges (attracting or repelling extracellular ions), and they rearrange the extracellular ionic charges, which alters the membrane capacitance [47]. We can find dipole interactions with ions (e.g., K ⁺ , Na ⁺ , Ca²⁺) as follows:

(24)

This force redistributes ions and induces capacitive currents and cellular stimulation:

(25)

This model is specifically useful when using QDs for cellular stimulation:

(26)

q ⋅ d(t) is the time-dependent photo-induced dipole moment, r is the distance from the QD cluster to the membrane, and δ is the membrane thickness (5 nm).

Transmembrane potential modulation with different photocapacitors.

There are various studies on different photocapacitors embedded with different photovoltaic junctions for controlling neuronal transmembrane potential. To compare different studies from both solar cells and photoelectrodes for neural stimulation, different biointerfaces with various open-voltage circuits and the calculated magnitude of the photo-induced dipoles have been listed with the recorded transmembrane potential experimentally from neurons for different studies (see Tables 2 and 3). In some photovoltaic substrates, plasmonic structures are used to enhance the photo-voltage response to different light polarizations.

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Table 2. The list of different photo-capacitors and calculated photo-induced dipoles for polarization modulation. (See the methodology section supplementary information).

https://doi.org/10.1371/journal.pone.0335978.t002

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Table 3. The list of different photovoltaic substrates and calculated photo-induced dipoles for polarization modulation.

https://doi.org/10.1371/journal.pone.0335978.t003

Experimental validation of light polarization effects in PCE12:ITIC photoelectrode:

The comparison between ITO/ZnO/P3HT:PCBM and ITO/ZnO/PCE12: ITIC device architectures highlights the influence of material selection on open-circuit voltage (V_OC). While P3HT:PCBM devices typically achieve V_OC values of around 0.60–0.65 V, they are limited by strong exciton binding energy and recombination losses due to suboptimal donor–acceptor interfaces. In contrast, PCE12:ITIC blends demonstrate significantly higher V_OC values (~0.75–0.90 V), attributed to improved donor–acceptor phase separation, reduced exciton binding energy, and favorable energy level alignment, particularly due to the deeper LUMO level of ITIC. The chemical structure of PCE12 and ITIC is shown in Fig 3a. UV-Vis absorption spectra of the PCE12:ITIC bulk heterojunction thin film are measured using an Agilent Cary 60 UV-Vis spectrometer and compared with those of the Control (ITO) substrate (Fig 3b). The sample exhibits an appropriate absorption peak for analysis with the red laser of wavelength 635 nm.

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Fig 3. (a) Chemical structure of PEC12:ITIC, (b) Light absorption spectra compared with control.

(c) Potentiostat for photocurrent and photovoltage measurements. (d), and (e) Photocurrent response of a PCE12:ITIC polymer blend under continuous polarized light illumination. The device exhibits polarization-dependent enhancement in both photovoltage and photocurrent, indicating that anisotropic molecular orientation and dipole alignment modulate charge separation efficiency. The results highlight the role of excitonic field alignment and photocarrier dynamics in polarization-sensitive organic photovoltaic systems.

https://doi.org/10.1371/journal.pone.0335978.g003

These features support more efficient charge separation and collection, making PCE12:ITIC blends well-suited for applications requiring enhanced photoresponse and polarization-sensitive stimulation. Fig 3c depicts the potentiostat setup used to record chronoamperometry measurements from our photoelectrodes. The results illustrate the polarization-dependent enhancement in open-circuit photovoltage (V_oc) and photocurrent for a PCE12:ITIC polymer blend under continuous polarized light, highlighting the role of anisotropic molecular orientation in modulating charge separation efficiency (Fig 3d and 3e). To account for near-zero mean currents, in photocurrent measurements, variability was expressed as a normalized relative standard deviation (RSD%), calculated as the ratio of the standard deviation to the mean absolute current (|I|), providing a more robust measure of signal fluctuation for four different samples of ITO/PEC12:ITIC (Supplementary Figure S2 in S3 File).

As shown in Fig 4, the simulated membrane potential V_m(t) of an SHSY-5Y cell follows an RC-like exponential response to the time-varying open-circuit voltage V_OC generated by a polarized-light-driven PEC12:ITIC photovoltaic interface, illustrating how photovoltaic dynamics modulate membrane charging and bioelectrical stimulation in retinal applications. The model employs an RC-like exponential response to simulate the gradual charging of the SHSY-5Y cell membrane, characterized by a resting membrane potential of −30 mV, thereby highlighting the influence of photovoltaic dynamics on bioelectrical stimulation in retinal interfaces.

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Fig 4. (a) Schematic of whole cell patch clamp measurement of an isolated neuron with electrical circuits, (b) Simulated membrane potential V_m(t) in response to a time-varying photovoltage V_OC (t) derived from a polarized-light-driven PEC12:ITIC photovoltaic device.

https://doi.org/10.1371/journal.pone.0335978.g004

A comparison study between charge and excitonic stimulation in PCE12:ITIC hybrid:

We modeled the photo-biointerface as a two-stage linear driver feeding a passive membrane. For the charge model, light pulses produce an interfacial current density J_in(t) = J_max.u(t) (0 ↔ 1 square pulse with 0.2 ms cosine edges), filtered by semiconductor dynamics J_eff = (J_in−J_eff)/ τ_sc with τ_sc = 0.5ms and J_max= 10 A m⁻². The interface potential obeys C_intϕ₀ + ϕ₀/R_leak= J_eff with C_int = 0.30 F m⁻²C and R_leak= 0.02 Ω m² (time constant ∼6.7ms). For the excitonic model, polarization modulation toggles the incident linear polarization 0° ↔ 90°; exciton-domain normal polarization follows Pn_target= P₀Scos (2(θ_pol − θ_dom)) with P₀= 0.01 C m⁻², order S=0.8, θ_dom = 0∘, and first-order kinetics Pn=(Pn_target−P_n) τ_ex = 0.2 ms; the interfacial potential is ϕ₀ = Pn. In both models the extracellular potential at the membrane includes Debye screening and near-field patterning: ϕ_e(t) = ϕ₀(t) γ = exp(−d/λD)cos(kx₀) with λD = 0.8nm, d = 1.2d = 1.2 nm (so exp (−d/λD)≈0.223) and cos (kx₀) =1 (antinodal placement). The membrane is isopotential and passive: V˙_m =−(V_m − E_L)/τm − α_m ϕ˙ e with E_L=−70 mV, τ_m = 10ms, α_m = 1. We simulated at 100 kHz (forward-Euler), initial conditions ϕ₀ = Pn = J_eff = 0, V_m = E_L. Plotted five pulses for each frequency: 1 Hz (20 ms ON/80 ms OFF over 0.5 s) and 100 Hz (2 ms/8 ms over 50 ms). As shown in Figure S3 in S3 File, both charge injection and excitonic polarization produce distinct input waveforms and interface potentials at 1 Hz and 100 Hz, highlighting how carrier dynamics and domain polarization shape the extracellular drive reaching the membrane.

The composite Figure S4 in S3 File shows the simulated membrane potential displacement (ΔV_m) for five light-modulated pulses at 1 Hz and 100 Hz, comparing a charge-injection model (top row) with an excitonic polarization model (bottom row). In the charge case, carrier injection into the electrolyte double layer produces large, sharp transients (≈ 20 mV at 1 Hz) that decay fully between pulses. At 100 Hz, the responses partially overlap, yielding smaller ripple-like displacements (~10 mV). In contrast, the excitonic model, where polarization modulation of microdomains drives bound surface charge, produces more symmetric, Debye-screened responses (≈11 mV), with the 1 Hz traces showing well-separated biphasic spikes and the 100 Hz traces showing compressed but still distinct oscillations. The Debye screening factor (exp(–d/λ_D) ≈ 0.22 for d = 1.2 nm, λ_D = 0.8 nm) strongly attenuates both mechanisms, so the observed ΔVm reflects only the near-surface potential that penetrates to the attached cell membrane.

To assess the compatibility of hippocampal neurons with the organic solar cell substrate, we combined morphological, viability, and functional analyses (Fig 5). Fluorescence microscopy confirmed that cells adhered to and lived on the substrate (Fig 5a), while OD-based viability assays revealed no significant difference between control and substrate conditions, with cell viability maintained above 79% (Fig 5b). Calcium imaging of hippocampal neurons cultured on PCE12:ITIC substrates revealed robust intracellular calcium dynamics in response to optical stimulation. Fig 5c shows the hippocampal cells grown on the PCE12:ITIC, and Figure D shows single cell ΔF/F₀ traces from the PCE12:ITIC sample. The recordings, sampled at 100 ms per frame over a 15 s window, confirm that PCE12:ITIC films effectively mediate optically induced calcium transients at the single-cell level. Individual traces capture cell-to-cell variability, while the population average highlights a consistent increase in intracellular calcium during light stimulation (Fig 5(e)). The recordings demonstrate that PCE12:ITIC films support light-driven modulation of neuronal calcium signaling beyond baseline fluctuations (Fig 5f). While the transparent ITO control occasionally showed artifactual calcium fluctuations due to direct light leakage to the detector, the PCE12:ITIC substrate produced markedly higher and stimulus-locked calcium activity, confirming its photostimulation efficiency.

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Fig 5. Hippocampal cell culture, viability, and calcium dynamics on organic solar cell substrates.

(a) Representative fluorescence micrograph of hippocampal neurons cultured directly on the PCE12: ITIC organic solar cell substrate, showing healthy morphology and network formation. (b) Optical density (OD) measurements across PCE12:ITIC, P3HT:PCBM, and Control groups (bars: mean ± SD), with overlaid relative cell viability normalized to Control. (c) Maximum intensity projection from calcium imaging, highlighting manually selected cell regions of interest (ROIs) with distinct color-coded circles (N = 11). (d) Corresponding ΔF/F₀ calcium transients for the ROIs, demonstrating stimulus-evoked intracellular calcium responses and cell-to-cell variability (N = 11). (e) Calcium fluorescence dynamics recorded from hippocampal neurons cultured on PCE12:ITIC solar cell substrates. Individual cell responses are shown in gray, with the population average highlighted in blue. (f) Average calcium signal difference between a cell grown on top of PCE12:ITIC and on the ITO control substrate.

https://doi.org/10.1371/journal.pone.0335978.g005

The mechanism of excitonic stimulation by photo-induced dipoles in a nanoantenna

Harmonic generation in quantum dots and P3HT/PCBM junctions under polarized light modulation.

Organic junctions are typically non-crystalline, resulting in spatially non-uniform photocurrents and photopotentials across the surface. In contrast, nanocrystals possess a crystalline structure, allowing the generation of a more homogeneous electric field under light excitation. It has been demonstrated that the photo-induced dipole emission patterns in core-shell quantum dots (QDs) can be manipulated by varying the incident light angle, and this effect can also be achieved through polarization modulation of the light. A comparison of photo-induced dipole magnitudes in semiconductor nanocrystals, metallic nanoparticles, and carbon-based particles, measured via Kelvin probe techniques, is provided in Table 4. The Hamiltonian of an electron-photon interaction could be written as follows:

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Table 4. The comparison of the photo-induced dipoles in semiconductor NCs and in metallic and carbon particles measured with the Kelvin probe.

https://doi.org/10.1371/journal.pone.0335978.t004

(27)

For linear light polarization, the electric field could be obtained as follows:

(28)

For circular light polarization, the electric field could be obtained as follows:

(29)

In fact, with the light polarization modulation, we can manipulate the electron-hole wave function of a nanocrystal. Equations 32 and 33 show the sorundinger equations for two linear and circular light polarizations:

(30)(31)

In metal particles such as gold particles, the photovoltages have been shown to be varied by the light polarization and also the electrochemical current (photocatalysis activity) has been shown to be enhanced by the increase of the light polarization angle (it is maximum when the light is prependicular to the particle surface) [18].

To find the effective capacitance displacement due to the photoinduced dipoles in QDs to the cell membrane, we can use the following equation:

(32)

Electric dipole oscillator through light polarization modulation in bulk photocapacitors.

With the polarization modulation of light, an oscillating photo-induced dipole induces a radiation of electric field (gradient of electric field) at the surface of an InP/ Zinc Sulfide (ZnS) Quantum dot or the ITO/Zinc oxide (ZnO)/P3HT: PCBM bio-interface. Equation 35 describes an oscillating photo-induced dipole, while I_a represents the oscillating charges that cause the radiation of an electric field. This facilitates the generation of an extracellular oscillating electric field through a capacitive bio-interface or a core-shell quantum dot. The potential because of the dipole radiation can be represented as follows:

(33)(34)

Where I_a is the amplitude of photo-induced charges’ displacements, is the amplitude of the photo-induced dipole, and r is the distance from any node to the point source.

As illustrated in Fig 6, increasing the frequency of polarization modulation leads to more localized and intensified electric field gradients across the membrane surface, affecting the induced transmembrane potential.

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Fig 6. Polarization modulation for the photo-stimulation of cells with photo-induced electrical dipoles in a photo-capacitive substrate, (a) electrical circuit model for the photoelectrical stimulation of cells through a photocapacitor, (b) Transmission line model for neural stimulation through the radiation of a photo-induced dipole with polarized light effect, (c) Membrane potential induced by a cluster of QDs (nano antennas changing from 5-100 numbers) in contact with a passive cell membrane with the frequency excitation of 5 Hz.

As it is clear, the electric field distribution depends on the frequency of the polarization modulation.

https://doi.org/10.1371/journal.pone.0335978.g006

Spatially patterned stimulation (pixel-wise control)

We also investigated the response of the QD clusters to the left- and right-circularly-polarized (LCP/RCP) for future potential of visual signal processing and selective stimulations based on polarization modulation. Fig 7(a) shows the response of the QD clusters to input LCP and RCP light polarization modulation. In this way, LCP-polarized light would activate excitable retinal areas, thereby mimicking the selectivity of photoreceptors. As illustrated in Fig 7(b), increasing the polarization modulation frequency produces more localized and intensified electric field gradients across the membrane surface, thereby the induced transmembrane potential. The potential applications of polarization-modulated quantum dot interfaces in retinal stimulation and broader neuroprosthetic strategies are summarized in Tables 5 and 6, highlighting both cell-type-specific responses and anisotropic modulation patterns for functional encoding. The biophysical and stimulation parameters used in the simulations, including Hodgkin-Huxley conductance and photo-induced dipole inputs, are summarized in Table 7. In a passive RC membrane model subjected to polarization modulation from 0° to 90°, the membrane potential exhibits a characteristic envelope-shaped waveform. During the 0° phases, where the dipole is aligned with the electric field (cosine projection), the stimulation is strongest, leading to maximal displacement currents and membrane charging. As the polarization shifts toward 90° (sine phase), the dipole orientation becomes orthogonal to the membrane surface, reducing the effective field strength and altering the timing of the capacitive response. This angular modulation results in periodic fluctuations in membrane potential, as the cell integrates varying electrostatic inputs over time (as shown in Fig 7(c)). The observed waveform reflects the dynamic coupling between light polarization, photoinduced dipole alignment, and electrostatic field orientation at the bio-interface.

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Table 5. Potential application of the polarization modulation for retinal application [53].

https://doi.org/10.1371/journal.pone.0335978.t005

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Table 6. Application table for the anisotropic engineered structure [54].

https://doi.org/10.1371/journal.pone.0335978.t006

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Table 7. Parameters used in the simulations [55,56].

https://doi.org/10.1371/journal.pone.0335978.t007

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Fig 7. Photoinduced dipole modulation of membrane potential and effective capacitance based on polarization modulation of the light.

(a) Simulated membrane potential dynamics under left- and right-circularly polarized light (LCP vs. RCP), demonstrating asymmetric stimulation due to dipole orientation. (b) Hodgkin-Huxley membrane potential response under dipole-induced capacitive stimulation across multiple frequencies (1–100 Hz), highlighting frequency-dependent spiking behavior. (c) Gradual membrane depolarization under continuously rotating polarization (0° → 90°), showing cumulative excitatory effects from spatiotemporal dipole alignment. (d) Extracted effective membrane capacitance as a function of photoinduced dipole amplitude, revealing nonlinear charge displacement and field-membrane coupling.

https://doi.org/10.1371/journal.pone.0335978.g007

For a photocapacitor-coupled cell membrane illuminated with 0° and 90° polarized light at adjacent positions, the electric field gradient across the membrane patch is given by:

(35)

(36)

Effective membrane capacitance C_eff can be estimated as a function of the photoinduced dipole amplitude, derived from simulated membrane potential responses. The estimation follows the proportional relationship , which, under photoelectrical stimulation, can be approximated as C_eff∝ Dipole Amplitude. At low dipole amplitudes, the membrane exhibits minimal potential shifts, resulting in apparently lower capacitance values due to limited charge displacement. As the dipole amplitude increases, the membrane potential response becomes more pronounced, reflecting enhanced interaction between the induced electric field and the lipid bilayer. This leads to a greater accumulation of charge across the membrane, effectively increasing the estimated capacitance. The nonlinear rise in C_eff at higher amplitudes indicates that membrane charging is strongly dependent on the strength of the applied dipolar field, highlighting the electrostatic sensitivity of the system under polarized optical excitation.

As shown in Fig 7(d), the amplitude of the photoinduced dipole increases, the resulting electrostatic field at the membrane interface becomes stronger, driving greater displacement of ionic charges in the surrounding electrolyte. This enhanced charge redistribution contributes to an effective increase in membrane capacitance, or more precisely, a greater capacitive displacement. However, this relationship is inherently nonlinear, as the membrane acts as a voltage-dependent filter that modulates the extent of charge displacement. At higher dipole amplitudes, the membrane’s nonlinear dielectric response and ion channel gating effects begin to dominate, introducing saturation or threshold-like behaviors in the capacitive response. In the simulation, we varied the photoinduced dipole amplitude from 2 to 20 arbitrary units to mimic the strength of dipole fields generated by semiconductor materials (e.g., quantum dots or organic solar cells). The effective membrane capacitance was computed as a synthetic, non-monotonic function representing how the lipid bilayer responds electrostatically to increasing dipole strength. This reflects realistic biophysical behavior, where low dipole amplitudes induce weak membrane charging, mid-range amplitudes enhance capacitive coupling, and high amplitudes lead to dielectric saturation or ionic shielding. The simulated capacitance values ranged from −0.03 to –0.70 a.u., consistent with experimental trends in photocapacitive stimulation. The simulations were conducted using experimentally validated biophysical parameters, including membrane capacitance, resistance, and ion channel conductance, as detailed in Table 7.

Preparation of photoactive blend and photoelectrode fabrication

Two photoactive material systems were evaluated to characterize their optoelectronic properties and select the most suitable system for this study. The first combination was poly(3-hexylthiophene-2,5-diyl) (P3HT) and phenyl C61 butyric acid methyl ester (PCBM), a material most studied for the study of photovoltaic devices and photoelectrodes. P3HT:PCBM photoactive blends were prepared by mixing 12.5 mg of P3HT and 12.5 mg of PCBM in 1 mL of o-dichlorobenzene. The second combination consists of poly[(2,6-(4,8-bis(5-(2-ethylhexyl)thiophen-2-yl)-benzo[1,2-b:4,5-b’]dithiophene))-alt-(5,5-(1’,3’-di-2-thienyl-5’,7’-bis(2-ethylhexyl)benzo[1’,2’-c:4’,5’-c’]dithiophene-4,8-dione))] (PCE12) and 3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3-d:2’,3’-d’]-s-indaceno[1,2-b:5,6-b’]dithiophene (ITIC), a high performing photovoltaic material system. PCE12:ITIC photoactive blends were prepared using 10 mg of each in a 1:1 blend ratio with a concentration of 20 mg/mL in o-dichlorobenzene, and an additive named 2-(2-Thienylmethylene)indane-1,3-dione (SA4) was added afterwards 16% by weight. All of these photoactive blends were stirred overnight at 60 °C in a hood under dark conditions before being used for fabrication. All the materials were purchased from Ossila Ltd.

All devices in this study were fabricated in an inverted geometry with the structure ITO/ZnO (70 nm)/photoactive layer (100 nm) [17,57,58]. The protocol for device fabrication is similar to that reported elsewhere. For this, first, precleaned and patterned ITO-coated glass substrates were plasma-treated for 1 min with 70 W power using an air–plasma system. Thereafter, a sol–gel ZnO solution was spin-coated at 2000 rpm for 60 s to obtain a 70 nm film [59]. The substrates were then annealed at 160 °C for 15 min to remove excess solvents. Processing conditions for the different photoactive blends are as follows: 1) P3HT:PCBM photoactive blend was spin-cast at 400 rpm for 100 s in ambient and was allowed to dry for 15 min on a hot plate in air [60], 2) PCE12:ITIC photoactive blend was spin-casted at 2000 rpm for 60 s in the air, and the films were annealed at 100 °C for10 min [61,62].

Electrochemical measurements

Electrochemical impedance spectroscopy (EIS) in frequency response analysis (FRA) potential scan mode was performed on an Autolab Potentiostat Galvanostat PGSTAT (Metrohm, Netherlands). A three-electrode setup consisting of Ag/AgCl as the reference electrode, a platinum wire as the counter electrode, and the photoelectrode as the working electrode was used. The experiment was carried out at room temperature in an aCSF aqueous medium medium as the supporting electrolyte solution. A handheld red laser (635 nm) was directed at the photoelectrode through a linear polarizer. The polarization angle was manually switched between 0° (parallel) and 90° (perpendicular) relative to the device axis. The illumination power density was maintained at 5 mW/cm².

Cell culture

GIBCO Primary Rat Hippocampus Neurons were used for MTT assay and Ca⁺⁺ imaging experiments which are isolated from day-18 rat embryos and cryopreserved in liquid nitrogen. Each vial contains 1 × 10⁶ viable cells⁄mL cells. The photoelectrode and the ITO control were sterilized with deionized water for 2 hours, followed by 70% ethanol, then treated with UV-C for 5 min. The photoelectrodes and control were treated with poly-D-lysine diluted in PBS at a 1:1 ratio for 1 hour, followed by and then rinsing with sterilized deionized water three times. The samples were left uncovered in the culture hood to dry for 2 hours. A 15-mL conical culture tube was rinsed with pre-warmed (37°C) complete Neurobasal Plus Medium and left in the cell culture hood prior to thawing the cells. The frozen vial was rapidly thawed (< 2 minutes) by gently swirling it in a 37°C water bath. The vial was transferred to the cell culture hood and disinfected with 70% isopropanol alcohol. The thawed sample was transferred to the 15 mL tube; and the vial was rinsed with 1 mL of pre-warmed complete Neurobasal™ Plus Medium (37°C) which was then added to the cells in the 15 mL tube extremely slowly, added dropwise (≈1 drop/s). The suspension was mixed by gentle swirling after each addition. Approximately 150 µL of the cell suspension was spread onto the coated sample surface (substrate in the culture dish) and left to stand in the culture hood for 20 minutes. Then, 3 mL of complete Neurobasal Plus Medium was added to the culture dish. The cells were incubated at 37°C in a humidified atmosphere of 5% CO₂ in air. The cells were fed after 4–24 hours, and subsequently, every third day by aspirating half of the medium from each well and replacing it with fresh medium until the sample was used for calcium imaging after 7 days of cell growth.

Biocompatibility test

The cytotoxic effect of photoelectrodes on hippocampal neuron cells was assessed by measuring mitochondrial activity with the MTT assay. Briefly, the photoelectrodes and ITO control were sterilized with 70% ethanol and then treated with UV-C for 5 min. Sterilized samples were placed in a six-well cell culture plate. The MTT assay was performed using the Cell Proliferation Kit I (Sigma-Aldrich, Massachusetts, USA) according to the manufacturer’s instructions. Briefly, primary hippocampus neurons (1 × 10⁵ cells per sample) were seeded on the substrate supplemented with Neurobasal medium and incubated for 48 hours in a 6-well plate. After 48 h incubation, the media were replaced with 1 mL of MTT solution (5 mg/mL in PBS, pH 7.4) and 4 mL of Neurobasal™ Plus Medium mixture per well. The cells were incubated at 37 °C and 5% CO2 for an additional 4 h. The medium was then removed from each well, and the substrates were transferred to an empty six-well plate. In each well, a 1:1 mixture of DMSO and ethanol was added to dissolve the formazan crystals, and the solution was transferred to a 96-well plate for absorbance measurement. The absorbance was measured using a SpectraMax iD3 (Molecular Devices, California, USA) at 570 nm, and the relative cell viability was calculated as follows: Viability = (ODsample/ODcontrol) × 100.

Calcium Imaging

Hippocampal neurons were cultured on conductive substrates (control ITO and experimental PCE12:ITIC photovoltaic films) for calcium imaging experiments. Intracellular calcium dynamics were monitored using a Leica DM IRB epifluorescence microscope equipped with a high-speed digital camera. Cells were loaded with a calcium-sensitive fluorescent dye (Fluo-4 AM, Thermo Fisher Scientific) at 5 μM in culture medium and incubated for 30 min at 37 °C, followed by a 30-min de-esterification period in dye-free medium. Excitation was delivered using a xenon/LED illumination source with appropriate FITC filter sets (excitation 488 nm, emission 510–550 nm).

Time-lapse image sequences were acquired at a frame interval of 100 ms (10 Hz), yielding a total recording window of 15 s (150 frames). For certain analyses, the first six frames (0.6 s) were excluded to minimize motion artifacts prior to light stimulation onset. Fluorescence intensity was quantified from manually or semi-automatically selected regions of interest (ROIs) corresponding to individual neuronal somata. Raw fluorescence traces F(t) were normalized to baseline fluorescence (F0, median of the first 10 frames) to yield relative calcium changes as ΔF/F₀.

Photovoltaic stimulation was applied by polarized light pulses directed onto the cell–substrate interface. Control ITO samples and active PCE12:ITIC solar cell substrates were analyzed under identical conditions. For each recording, single cell ΔF/F₀ traces were extracted and ensemble averages were computed to compare population responses.

Computational modeling and Python simulation

A custom Python framework was developed to simulate the effects of photo-induced electric dipoles on cellular membrane potential and the distribution of transmembrane electric fields. The model combines time-dependent photocurrent injection, capacitive charging dynamics of the membrane, and electrostatic force calculations and is available in Supplementary Python codes.