Static capacitive pressure sensing using a single graphene drum

To realize nanomechanical graphene-based pressure and gas sensors, it is beneficial to have a method to electrically readout the static displacement of a suspended graphene membrane. Capacitive readout, typical in micro-electro-mechanical systems (MEMS), gets increasingly challenging as one starts shrinking the dimensions of these devices, since the expected responsivity of such devices is below 0.1 aF/Pa. To overcome the challenges of detecting small capacitance changes, we design an electrical readout device fabricated on top of an insulating quartz substrate, maximizing the contribution of the suspended membrane to the total capacitance of the device. The capacitance of the drum is further increased by reducing the gap size to 110 nm. Using external pressure load, we demonstrate successful detection of capacitance changes of a single graphene drum down to 50 aF, and pressure differences down to 25 mbar

The capacitance and electromechanical coupling of lipid membranes close to transitions. The effect of electrostriction

Biomembranes are thin capacitors with the unique feature of displaying phase transitions in a physiologically relevant regime. We investigate the voltage and lateral pressure dependence of their capacitance close to their chain melting transition. Since the gel and the fluid membrane have different area and thickness, the capacitance of the two membrane phases is different. In the presence of external fields, charges exert forces that can influence the state of the membrane, thereby influencing the transition temperature. This phenomenon is called electrostriction. We show that this effect allows us to introduce a capacitive susceptibility that assumes a maximum in the melting transition with an associated excess charge. As a consequence, there exist voltage regimes where a small change in voltage can lead to a large uptake of charge and a large capacitive current. Furthermore, we consider electromechanical behavior such as pressure-induced changes in capacitance, and the application of such concepts in biology.Comment: 5 figure

Ion-liquid based super-capacitors with inner gate diode-like separators

We demonstrate that the capacitance of ionic-liquid filled supercapacitors is substantially increased by placing a diode-like structure on the separator membrane. We call the structured separator: gate, and demonstrate that the order of a p-n layout with respect to the auxiliary electrode affects the overall cell's capacitance. The smallest ESR and the largest capacitance values are noted when the p-side is facing the auxiliary electrode.Comment: 11 pages, 8 figure

Stochastic Dynamics of Electrical Membrane with Voltage-Dependent Ion Channel Fluctuations

Brownian ratchet like stochastic theory for the electrochemical membrane system of Hodgkin-Huxley (HH) is developed. The system is characterized by a continuous variable $Q_m(t)$, representing mobile membrane charge density, and a discrete variable $K_t$ representing ion channel conformational dynamics. A Nernst-Planck-Nyquist-Johnson type equilibrium is obtained when multiple conducting ions have a common reversal potential. Detailed balance yields a previously unknown relation between the channel switching rates and membrane capacitance, bypassing Eyring-type explicit treatment of gating charge kinetics. From a molecular structural standpoint, membrane charge $Q_m$ is a more natural dynamic variable than potential $V_m$; our formalism treats $Q_m$-dependent conformational transition rates $\lambda_{ij}$ as intrinsic parameters. Therefore in principle, $\lambda_{ij}$ vs. $V_m$ is experimental protocol dependent,e.g., different from voltage or charge clamping measurements. For constant membrane capacitance per unit area $C_m$ and neglecting membrane potential induced by gating charges, $V_m=Q_m/C_m$, and HH's formalism is recovered. The presence of two types of ions, with different channels and reversal potentials, gives rise to a nonequilibrium steady state with positive entropy production $e_p$. For rapidly fluctuating channels, an expression for $e_p$ is obtained.Comment: 8 pages, two figure

SOLUTION OF THE CROSS-TALK PROBLEM IN CELL IMPEDANCE ANALYSIS OF CARDIAC MYOCYTES

Membrane capacitance is a fundamental electrical characteristic of the surface membrane of living cells. The membrane capacitance is quantitatively related to the surface area, thickness and dielectric properties of the cell membrane and thus provides valuable information about the state of the cell. A generally accepted method for measuring membrane capacitance is based on stimulation of the cell with rectangular voltage pulses and approximation of the recorded membrane current by a mono-exponential decay function. We found that in cardiac muscle cells this method provides high variability of the measured capacitance and large cross-correlation among parameters of the measured circuit. In this study we focused on the elimination of cross-correlation error between the membrane capacitance, the membrane resistance, and the access resistance of the recording set-up. We showed how the use of the standard approximation model affects the level of crosstalk between estimates of these parameters. We proposed a modified model and tested its applicability on simulated and experimental data. The results revealed that the crosstalk error can be reduced by three orders of magnitude, well below the natural variability of membrane capacitance arising from biological reasons in cardiac myocytes

Capacitance fluctuations causing channel noise reduction in stochastic Hodgkin-Huxley systems

Voltage-dependent ion channels determine the electric properties of axonal cell membranes. They not only allow the passage of ions through the cell membrane but also contribute to an additional charging of the cell membrane resulting in the so-called capacitance loading. The switching of the channel gates between an open and a closed configuration is intrinsically related to the movement of gating charge within the cell membrane. At the beginning of an action potential the transient gating current is opposite to the direction of the current of sodium ions through the membrane. Therefore, the excitability is expected to become reduced due to the influence of a gating current. Our stochastic Hodgkin-Huxley like modeling takes into account both the channel noise -- i.e. the fluctuations of the number of open ion channels -- and the capacitance fluctuations that result from the dynamics of the gating charge. We investigate the spiking dynamics of membrane patches of variable size and analyze the statistics of the spontaneous spiking. As a main result, we find that the gating currents yield a drastic reduction of the spontaneous spiking rate for sufficiently large ion channel clusters. Consequently, this demonstrates a prominent mechanism for channel noise reduction.Comment: 18 page

Measurement of the cell membrane capacitance and conductance of colonic crypt cells of the rat using the patch clamp technique

Using the patch clamp technique the membrane capacitance and membrane conductance of colonic crypt cells of the rat was measured. The influence of the intracellular agonists Ca++, cAMP and of osmotic changes on the membrane capacitance and conductance was studied.Comment: Diploma thesis, University of Freiburg, Germany (in German