Thermal transients excite neurons through universal intramembrane mechano-electrical effects

Modern advances in neurotechnology rely on effectively harnessing physical tools and insights towards remote neural control, thereby creating major new scientific and therapeutic opportunities. Specifically, rapid temperature pulses were shown to increase membrane capacitance, causing capacitive currents that explain neural excitation, but the underlying biophysics is not well understood. Here, we show that an intramembrane thermal-mechanical effect wherein the phospholipid bilayer undergoes axial narrowing and lateral expansion accurately predicts a potentially universal thermal capacitance increase rate of ~0.3%/°C. This capacitance increase and concurrent changes in the surface charge related fields lead to predictable exciting ionic displacement currents. The new theory’s predictions provide an excellent agreement with multiple experimental results and indirect estimates of latent biophysical quantities. Our results further highlight the role of electro-mechanics in neural excitation; they may also help illuminate sub-threshold and novel physical cellular effects, and could potentially lead to advanced new methods for neural control.

Optical neurostimulation modalities have gained considerable attention during the past decade as methods for precision perturbation or control of neural activity, primarily as a result of the co-emergence of optogenetics 1 and of direct infrared neural stimulation (INS) 2 . Both approaches also offer the long-term prospect of remotely affecting aberrant localized neural circuits that underlie many neurological diseases.
A multitude of INS-related studies explored the ability of short wave infrared (IR) pulses to stimulate neural structures including peripheral 3,4 and cranial nerves 5-10 , retinal and cortical neurons [10][11][12] , as well as cardiomyocytes 13,14 . It is stipulated that the INS phenomenon is mediated by temperature transients induced by IRabsorption [15][16][17] ; such transients can alternatively be induced using other forms of photo-absorption [18][19][20] , or potentially by any other physical form of thermal neurostimulation that can be driven rapidly enough 21,22 . Shapiro et al. (2012) 16 showed that these rapid temperature variations are directly accompanied by changes in the cell membrane's capacitance and resulting displacement currents which are unrelated to specific ionic channels. Shapiro et al. 16 also developed a theoretical model where the temperature elevation was seen to give rise to membrane capacitance increase at the membrane's boundary regions (see also Liu et al. 2014 23 and Rabbit et al., 2016 24 ). In these theoretical models, however, the projected capacitance increase in the membrane boundary region as the temperature increases is seemingly paradoxical; from energetic considerations for example, thermal energy input will be offset by correspondingly higher electrical energy and absolute potentials, which corresponds to a capacitance decrease, and this decrease is further compounded by a temperaturerelated decrease in the dielectric constant of water. Indeed, a reanalysis of their model (see below), quantitatively predicts such a net capacitance decrease, which is contrary to the experimental measurements, showing that the seemingly complete theoretical picture resulted from a mathematical convention error.
To address this major apparent gap in the theoretical basis for thermal excitation, we deconstruct and analyze here alternative revised biophysical models (tentative and detailed), where the membrane's physical dimensions themselves also vary in response to the temperature changes, to accurately reflect direct experimental findings [25][26][27] . The new models calculate the effect of temperatures change on the membrane electrical parameters directly and explicitly (rather than implicitly), and are found to both qualitatively and quantitatively predict empirical findings on thermal membrane capacitance increases 16,19,20,28 , unraveling the two underlying sources for thermal membrane currents, and making it possible to indirectly estimate from neural stimulation results a significant new quantity, the membrane surface charge difference.

Dimensional changes are crucial for explaining capacitive thermal response
Capacitive thermal changes were first measured by Shapiro et al. 16 and subsequently by others in artificial membranes 19 , HEK cells 20 and cardiac myocytes 28 . Interestingly, placing these disparate measurements on a uniform capacitance-rate scale, shows that they all approximately share a universal rate of ~0.3 %/ o C (mean: 0.29±0.01 %/ o C), suggesting a potentially universal basis (Fig. 1a).
We next examined how these changes compare to the membrane's capacitance thermal rate-of-change expected purely from temperature-induced dimensional changes, which were recently experimentally estimated using X-ray and neutron small-angle scattering measurements [25][26][27] 29 ), putatively explaining the observed capacitance rates (Fig.1a).

Detailed biophysical model
To further understand the impact of this mechanism on membrane currents and its potential for settling the theoretical conceptual gap, we subsequently studied the effect of temperature changes and transients on detailed Gouy-Chapman-Stern [30][31][32][33][34] multi-compartment realistic biophysical model of the phospholipid membrane electrochemistry. The various model parameters were taken "as is" without re-tuning or posthoc adjustments, and are based on known or previously measured physical and biophysical quantities, wherever attainable (summarized in Supplementary Table 1 with the respective sources). In the model, the membrane geometry and physical

Experimental validation and inference
We next studied the model's response to a temperature transient used extensively by Shapiro et al. in their artificial membranes' experiments and model simulations (Fig.   3a). The resulting membrane currents and potential changes were composed of similar relative contributions from the two underlying mechanisms related to capacitance and surface charge-related potential variations (Fig. 3b,c). Importantly, the membrane capacitance-related current is dependent on the clamped membrane potential, while the surface charge-related current is independent (Fig. 3b).
Can these dynamical responses quantitatively predict the results of INS experiments in artificial bilayer membranes 16

Discussion
This study explored the effects of temperature changes on membrane capacitance and its associated currents in a joint attempt to clarify the experimental results of a key recent study 16 and to pave the way towards predictive modeling of INS 2-15 and other thermal neurostimulation techniques [18][19][20] , which could potentially facilitate the development of more advanced and multimodal methods for neural circuit control.
Another key motivation to pursue this problem came from our noting the very similar temperature-related capacitance rates of change observed in very different model systems (Fig. 1a) suggesting that this value is putatively universal.
Although the pioneering study by Shapiro et al. 16 attempted to unravel their results' underlying biophysical mechanism, their explanation raised a crucial question that had to be theoretically reexamined: how is it possible that a rise in membrane capacitance (1) Thermal membranal dimensional changes inferred from small-angle x-ray and neutron scattering measurements, which lead to an increase in the overall capacitance and to capacitive displacement currents [Im= dCm/dt (Vm-Vs.c.), Fig. 3a,b]. These dimensional changes have been observed in a range of different model membranes, including POPC, SOPC, DPhyPC and more [25][26][27] and are putatively attributed to entropicaly-driven shortening of the phospholipids' tails (Fig. 1b), a process termed trans-gauche isomerization 26 . The predicted associated capacitance rates are relatively insensitive to the specific choice of a membrane (0.33±0.05 %/ o C for SOPC and 0.32±0.06 %/ o C for DPhyPC) and to the baseline temperature 26 .
This dual mechanism, found by separately considering the temperature-dependent behavior in each membrane sub-region, explains the experimental shift of membrane current when multivalent ions (Mg 2+ and Gd 3+ ) that affect the surface charge 36 were added to one side of the membranes' solutions 16 , while almost no effect was observed on membrane capacitance variations (slope in Fig. 3e,g). It also explains the

Constitutive electrostatic laws and equations
The relation between the mobile (Q) and fixed (-s ) membrane charge densities and the potentials ( DF ) that fall on the bulk regions (Fig. 2a)     ( )

Membrane mobile charge notation
Genet et al. 33 (5) made this error 16,23 . In the results section, the fixed geometry model avoids this notational error (Fig. 2c).

Dimensional variations
A major conceptual difference between ours and earlier models is the incorporation here of temperature-dependent variations in the membrane's hydrophobic region dimensions. Estimates of the temperature dependence of the hydrophobic core dimensions were based on published measurements that used X-ray and neutron small-angle scattering experiments 26 , selecting the characteristics of 1-palmitoyl-2oleoyl-snglycero-3-phosphatidylcholine (POPC), because it relatively closely mimics the mammalian phospholipid composition 50 (Fig. 1). The hydrophobic core thermal response also modifies Eqs. (1) and (2) by noting that the charge values correspond to areal charge densities.

Membrane ions absorption
In where S is the maximal charge density of the ions' potential membrane binding sitesequals to 0.2 C/m 2 that corresponds to 0. is the multivalent ions' absorption factor to PE and PC 36,52 ; and h c and h K are the concentration and absorption factor to PS of the Na + ions 53 .

Current and potential calculations
Solving the GCS-based model allowed us to calculate the expected temperatureinduced membrane currents in a voltage clamp mode: is the membrane capacitive current that arises due to changes in the total membrane capacitance and . S C m dV dT C dT dt -× × is the surface charge related current.
The membrane potential in a current clamp mode expressed as:

Estimation of surface charge difference in neurons
To estimate the intracellular and extracellular surface charge difference in neurons, we used our recent discovery that temperature transients excite neurons through formation of membrane currents that proportional to temperature time derivative - , where a is known positive constant 18 . This a constant can be expressed explicitly by the GCS-based model: Although Vm*dCm/dT is dependent on the membrane potential, its maximal variation of several percent (4 -7.5 %) prior the action potential formation negligibly affects the a value; the main weight of the linear temperature dependent parameter - formulas led to (9) simulations of temperature transient-related membrane currents and potentials [Eqs. (7) and (8)].
IR-induced temperature dynamics was extracted indirectly from Shapiro et al.
simulations 16 (laser energy -7.3 mJ; duration -10 ms), wherein currents are proportional to temperature time derivative (Fig. 4c of their study): is the maximal temperature associated with laser energy -7.3 mJ and duration -10 ms.  7)]. The reference artificial membrane capacitance obtained from this analysis is 89±5.5 pF.

Statistical analysis
The reported errors in text and figures are s.e.m., unless it is stated otherwise.  [25][26][27] is thought to result from an increase in the phospholipid molecules' fatty acid chains transgauche rotational isomerization, which shortens the tails' effective length and increases the area per phospholipid molecule. Biophysically, these two phenomena contribute to a predictable increase in both the membrane hydrophobic core's and total capacitance. Error bars for the direct capacitance measurements are ±s.e.m, and for the model predictions are ± chi-squares distribution-related uncertainty 26 .   Table 1). Error bars are ±s.e.m.