Electrophysiologists generally describe cells as electric equivalent circuits,i.e.a combination of resistors and also capacitances. In the following article, we will look at exactly how resistance and capacitance determine the electrical properties that the cabinet to recognize why this is a useful description.

You are watching: How do the resistance and the capacitance of the cell membrane change?


Membrane resistance, RM

The cell membrane is composed of a dual lipid layer the separates ion in the extracellular space from ions and charged protein in the cytoplasm. When pure lipid membranes room excellent electrical insulators, genuine cell membranes consist of a thick mosaic of proteins and lipids. Numerous of these proteins expectancy the membrane and also act as channels that allow charge to pass. These proteins alleviate the otherwise high resistance the the membrane, i beg your pardon has significant consequences for electrophysiology. Assume we want to use a voltage across the cabinet membrane by injecting existing with an electrode. The current required to preserve this voltage is determined by the membrane resistance, according to Ohm"s Law: Voltage = Resistance * present (or V = R * I). We deserve to see the the higher the membrane resistance, the lower the existing required to maintain a offered membrane voltage.


Membrane capacitance, CM

Because the membrane is an electrical insulator separating opposing dues inside and outside the cell, the cell membrane not only has a resistance but likewise a membrane capacitance. Therefore, to readjust the membrane voltage, the is necessary to charge the capacitance. The used charge (Q) split by the membrane capacitance (CM) gives the membrane voltage (Vm): Vm = Q /CM. We have the right to see that for a offered amount of applied charge, the smaller sized the membrane capacitance, the bigger the membrane voltage change.


Combining RM and CM – the RC circuit

As both the membrane resistance (RM) and the membrane capacitance (CM) occur over the cell membrane, they space electrically parallel (see figure 1A). Together a circuit that parallel resistance (R) and capacitance (C) is well-known as one RC circuit. RC circuits are typically used in electronic devices as an easy filters come select particular input frequency ranges. Similarly, the cell membrane acts as a filter on present or voltage injected into the cell.


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Figure 1. Basic schematic that the electrical properties that a plasma membrane. A: A circuit diagram mirroring the membrane capacitance and membrane resistance in parallel to every other. B: Traces reflecting a command voltage action (top) and also the resulting current response (bottom) because that a simple plasma membrane gift voltage clamped.


Basic voltage clamp experiment

To understand how the RC filter nature of the membrane determine a cell’s voltage response, take into consideration how a voltage step applied to the inside of a cell transforms the present injected through an electrode (see number 1B). Initially, a square shaped voltage action leads come an instantaneous run in current (the early peak). This present then decreases exponentially (falling flank) to with a steady state. Contrary, as soon as the voltage action is reversed, us observe a big instantaneous existing of opposing direction that decreases significantly until that reaches stable state again. Regulating the membrane voltage and measuring the resulting existing in this means constitutes a straightforward voltage clamp experiment.

How do the properties of the electrode and cell membrane influence the shape of the present curve (see figure 1B)? Initially, the entire present charges the membrane capacitance through no current flowing throughout the membrane resistance. Thus, the amplitude the the early fast present is entirely identified by the dimension of the voltage step and also the electrode resistance (which is characterized as the amount of the resistance of the electrode and the resistance that the electrode’s link to the cell). As the membrane capacitance becomes much more and much more charged, one increasing fraction of the injected existing flows across the membrane resistance. Once the capacitance is completely charged the device reaches secure state and also the entire current flows across the membrane resistance. In the secure state, the amount of current required to keep the membrane voltage is only determined by the membrane resistance and Ohm"s law applies (steady state existing = voltage step / membrane resistance, or Is = Vs / RM).

The worths of membrane capacitance and also membrane resistance identify how conveniently this stable state is reached: the bigger the capacitance or the resistance, the longer the charging will certainly take. The time consistent describing this charging is known as the membrane time constant t and also is same to the product the membrane resistance and also membrane capacitance (t = centimeter * RM, presume RsM).


Determining the state of a recording

We deserve to use the over relationships come monitor assorted stages that a totality cell recording. To perform so, we apply a little voltage pulse at the electrode, the so-called check pulse. By observing the shape and amplitude that the current response to the test pulse (Figure 2, best column), we acquire lots of valuable information about the record electrode and the cell. Importantly, plenty of of the concepts apply to other creates of electrophysiological recording as well.

To assess the state of our recording we make basic calculations based on rearrangements of Ohm’s regulation (V = R * I). The is feasible to leveling the calculations further by using resistance in devices of MOhm (106 Ohm), voltage in units of mV (10-3 V) and also current in systems of nA (10-9 A), as the unit prefixes, publication each other (10-3 V = 106 Ohm * 10-9 A).


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Figure 2. Schematic explaining the ‘pipette in bath’ configuration. In this configuration, the existing is determinedsolely by the pipette resistance. The pipette is shown on the left. The equivalent electrical circuit isshown in the center with the voltage and current traces depicted on the right.


Recording electrode in the bath

Entering the bathtub is the an initial stage in a recording: the recording electrode, i beg your pardon is inside a pipette to fill with inner solution, is submerged in the perfusion media (Figure 2). By definition, the voltage between the record electrode and also the referral electrode is zero. Accordingly, the amplifier’s counter voltage demands to be adjusted until the measured voltage is undoubtedly 0 mV.

With the pipette in the bath, the current response to the test pulse is determined by the pipette resistance (RP), which have the right to be calculated making use of Ohm’s law: RP = VT / IP, whereby VT is the amplitude of the voltage test pulse and IP is the existing through the pipette. Because that example, a -5 mV check pulse returns a current response of -500 pA. This shows a pipette pointer resistance of 10 MOhm (= -5 mv / 0.5 nA). In whole cell recordings, it is common to usage pipettes with tip resistances that 5-10 MOhm.


Approaching a cell and forming a seal

When approaching a cell v a pipette, one uses positive pressure to the internal solution, to protect against tissue native obstructing the pipette tip. In spite of this precaution, the amplitude the the current an answer to the check pulse will vary throughout the approach: once the pipette guideline touches tissue, the resistance will increase, bring about a fall in the existing amplitude. Slightly retracting the pipette have to return the current an answer (as a an effect of the pipette resistance) earlier to the initial value. However, these transforms are fairly small and transient.

Once the pipette comes an extremely close come a cell, the amplitude of the test pulse reduce which signals a significant increase in electrode resistance. This usually corresponds with the formation of a dimple top top the cell surface, where inner solution expelled from the pipette tip pushes away the cabinet membrane. Remove the push from the pipette at this point enables the cell membrane can contact the pipette yielding a substantial increase in electrode resistance. Applying mild suction to the electrode’s inner solution increases the resistance further. At this stage, a an adverse command voltage (roughly corresponding the supposed intracellular potential of -60 mV to -80 mV, depending on cell type) is applied to the pipette. Analogous come the check pulse, the current response to the holding voltage have the right to be offered to determine the state that the recording, together the hold voltage, and also the required holding current, are connected to the pipette resistance. So, if -200 pA is essential to organize the pipette at -60 mV, the pipette resistance is 300 MOhm (= -60 mV / -0.2 nA).


On-cell configuration

At this point, that is important to think about how the current from the pipette operation to the soil electrode. Together the tiny patch of cabinet membrane in the pipette tip has a very high resistance, any type of current flowing from the pipette will certainly be flowing through the minute void where the membrane seals onto the glass that the pipette. Accordingly, the measured resistance is established by the resistance of this "seal", unsurprisingly described as seal resistance. Trusted patch-clamp experiments frequently require a ‘tight seal’ in the variety of GOhms, a so-called ‘gigaseal’. We have the right to observe that a tight seal has actually been achieved when the current required to organize the pipette in ~ -60 mV is smaller than 60 pA (-60 mV / -0.06 nA = 1 GOhm). This state is recognized as the ‘on-cell configuration’ (Figure 3).

In the on-cell configuration, the current an answer often reflects a an extremely fast spike in ~ the start of voltage steps. This are led to by the pipette capacitance and also can be compensated making use of the ‘fast capacitance compensation’ easily accessible on most amplifiers. Particularly if you are interested in fast ionic currents, that is crucial to carefully compensate the pipette capacitance as much as possible.


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Figure 3. Schematic explaining the ‘on-cell’ configuration. In this configuration, the existing is established by the pipette resistance in series to a parallel circuit of the patch and also seal resistances. The pipette through cellis shown on the left. The equivalent electrical circuit is shown in the middle with the voltage and also current traces illustrated on the right. Keep in mind that together the spot resistance is really high, the current over this resistance is negligible.


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Whole-cell configuration

Once a chop seal has actually formed, us can get electrical and diffusional accessibility to the cell’s cytoplasm by rupturing the membrane under the pipette pointer while maintaining the obtained seal. This process is often referred to together ‘breaking into the cell’, and also the result recording configuration is well-known as ‘whole-cell’. In this configuration, the recording pipette is electrically straight coupled to the cell: the electrode can ‘see’ the electrical activity inside the cell. As a result, the current response to a provided voltage pulse alters dramatically, as does the information that this an answer provides (Figure 4).

On breaking right into the cell, the membrane in the pipette guideline ruptures and current between the recording electrode and the ground have the right to now flow into the cell and throughout the cabinet membrane. In this whole-cell configuration, virtually all existing flows throughout the cell membrane and also charges the membrane capacitance. Only a negligible lot of existing will flow throughout the seal, as the seal resistance is at the very least an bespeak of magnitude bigger than the membrane resistance (now, the membrane resistance is determined by the entire cell’s membrane area, not just the membrane patch in ~ the pipette tip). Due to the fact that the membrane is ruptured and also not removed, membrane materials will obstruct current accessibility from the electrode to the cell and also contribute a so-called "access resistance". The sum of accessibility resistance and initial pipette resistance comprise the total resistance in ~ the pipette tip, described as collection resistance. In practice, just the total collection resistance is known.


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Figure 4. Schematic explaining the ‘whole-cell’ configuration. In this configuration, the present is figured out by the series resistance in series with a parallel circuit the the seal and membrane resistances and also the membrane capacitance. The pipette v cell is indicated on the left. The matching electrical circuit is displayed in the middle with the voltage and also current traces illustrated on the right.


Current an answer in whole-cell configuration

Looking at the current an answer to a voltage step, that is simple to choose apart which electrical properties add to which little of the solution (see figure 4). As before, the quick initial run in existing is established by the flow of charge v the pipette: series resistance (RS) = test voltage (VT) / initial existing (IP). Thus, if in an answer to a -5 mV step, the initial current is measured as -600 pA, the series resistance is 8.3 MOhm (-5 mV / -0.6 nA). The degeneration of the present is figured out by the membrane time constant, which is merely the product that membrane capacitance and membrane resistance (tm = cm * Rm) in the unperturbed cell. Finally, when the existing has reached steady state, the offset current (‘holding current’, IH) is determined by the membrane resistance (Rm = VT / IH). Having measured the membrane resistance, the is in principle possible to recognize the membrane time consistent by installation the exponential decay of the current and calculating the membrane capacitance (Cm = tm / VT).


Theory vs. Practice

In passive and compact cells, a solitary capacitance and resistor are enough to explain the electrical behaviour of the cell, permitting for every the calculations described above. In practice though, neurons are huge extended membrane structures, and also their membranes are not passive however contain voltage-dependent ion channels. Thus, as soon as performing electrophysiological recordings, that is vital to save in mind wherein the truth of neuronal physiology deviates native the concepts presented above.

The great news is the up to and including the development of a chop seal in on-cell mode, every the assumptions described over hold true. The bad news is that much work is excellent in whole-cell mode, at which allude practice deviates from theory and also things become an ext complicated.

One an essential point to think about is that the voltage pulses supplied to assess the state of the recording can activate voltage-dependent conductances. Consequently, the secure state existing can save on computer current components that space not pertained to the membrane resistance however stem from voltage-gated ion channels, such together the hyperpolarization induced existing IH.

Furthermore, in larger cells v a more facility morphology, multiple to adjust of parallel resistors and capacitances are forced for an exact description that the electrical properties of the cell. Together a ascendancy of thumb, the farther from the pipette guideline a cell compartment is, the much more its voltage deviates indigenous the voltage applied through the electrode, the so-called "space clamp" problem.

See more: Which Statement Is Not True Regarding Hierarchical Trust Models?

A full conversation of the fact of solitary cell recordings is beyond the scope of this article, and also we express the leader to the standard literature on the topic.


Recommended reading:

“Foundations of to move Neurophysiology”Daniel Johnston and Samuel Miao-Sin Wu