Physical properties of an RBC membrane



Membrane Elasticity

When an electric pulse of sufficient electric field strength is applied to the RBC cell, the membrane can be stretched to its breaking point due to the electric field and the subsequent osmotic forces.

When electroporation ruptures the cell’s membrane, it’s assumed that:

  1. The total kinetic energy (EKE) can be derived from the critical pulse voltage and duration;
  2. There’s a critical level of cell membrane deformation when cell lysis occurs after electroporation; and
  3. The external electric field intensity (Ec) applied across the electrodes is proportional to the potential difference induced across the cell’s membrane (Em).

The model describing this process assumes that the critical ‘Deformation Energy’ required to stretch the cell membrane and rupture (cell lysis), is produced by a critical pressure (Pc) at a critical volume (Volc). There’s also a proportional relationship between deformation energy DKE to the electrical energy EKE necessary for cell lysis.

Figure 9. A plot of data (based on Figure 3) to compare the relative total electric energy versus sample voltage necessary to cause cell lysis in (a) normal female, (b) normal male, (c) alcoholic hepatitis and (d) blood from donor treated with cyclosporin (Unpublished data by Oliver1).


The total kinetic energy, EKE, of the electric pulse is:

Figure 9. graphs the relative EKE versus sample voltage for the blood of normal male, normal female, alcohol hepatitis and cyclosporin donors. The variation of  EKE for each sample is shown across the voltage range from 300V to 800V (1500 to 4000V/cm electric field strength). 

As expected, the higher voltage and shorter pulse duration for the cell lysis endpoint is around 700V. This infers the elastic limit for alcoholic hepatitis and cyclosporin patients is much less than for normal donors (740V female and 800V male donor).

But, conversely, the blood of a cyclosporin treated patient exhibited maximum membrane elastic strength at 440V (2.2 kV/cm) and 500V (2.5 kV/cm) for the hepatitis patient and female donor. Whereas the male donor maximum elastic strength is 560V (2.8 kV/cm).

The inferred stronger cell membrane of the male donor (as compared to the female donor) and the much higher kinetic energy requirement for cell lysis for the cyclosporin patient’s blood, needs further research to understand the biological complexities causing the variations in cell membrane mechanical strength and elasticity.

Reiterating:

Electric Energy (EKE) ∝ Deformation energy (DKE)

The voltage pulse, expressed as a function of pulse duration causing critical cell lysis, is approximately linear (Figure 7 and 8). 

Unfortunately, the experimental range for these results had insufficient data to support the linear assumption when the pulse width approaches zero. It could be linear or parabolic for pulses < 5µS duration. Nevertheless, the sample’s voltage extrapolated to zero pulse duration is a tempting parameter to use for the existing range investigated.

The results can be used to identify fundamental mechanical properties of the membrane/protein/cytoskeleton structure. Extrapolation of the line-of-best-fit in Figure 8., shows an imaginary voltage for zero pulse duration (EInst). The hypothesis suggests that this could possibly be due to cytoskeleton damage when the pulse duration, EInst, is infinitely small. Normal and abnormal blood samples can be compared using this method.

To investigate the elastic properties of the membrane/protein/cytoskeleton in different blood samples, the slope of the line-of-best-fit (K = volts/microseconds) and EInst are suitable parameters to compare.

For the range of pulse duration measured, these parameters were expressed by the simple relationship:-

Where τ = critical pulse duration for cell lysis and K is the constant of proportionality that describes the physical properties of the membrane/protein/cytoskeleton structure.

The results found wide differences in the average voltage causing cytoskeleton damage:

  • female blood cells:                 = 740V and a K slope of -1.9V/µS
  • cyclosporin treated blood:    = 673V and a  K slope of -1.07 V/µS
  • alcoholic hepatitis blood:      = 703V, -1.73 V/µS), are quite different results. 


Bulk Modulus Properties

Using the electric properties for cell lysis, the slope of the line (K = ∆Ec/∆τc) and EInst in Figure 8, the bulk modulus properties can be investigated.

Figure 10. for (a) normal female versus male donor, (b) normal versus alcoholic hepatitis female donors and (c) normal versus cyclosporin male donors. (Unpublished data by Oliver1).


A comparative study of the characteristic cell lysis line of best fit in these results also provides a convenient method to investigate the elastic properties (such as the mechanical stress and elastic limit) of the erythrocyte’s membrane/protein structure attached to its cytoskeleton.

Using data from Figure 9, the Bulk Modulus ratio for normal and abnormal blood samples are shown in Figure 10. When comparing a normal blood sample to an abnormal sample, the relationship is:

EKE1/EKE2 = β1 K2 / β2 K1

A comparison of normal and abnormal blood for  β⁄K (Figure 10.) shows the blood result of:

(a) normal female versus male donor;

(b) normal versus an alcoholic hepatitis female donor; and

(c) normal versus a cyclosporin male donor.

The cyclosporin blood indicates a much greater β⁄K in the 300 – 500V (1500 – 2500 V/cm field intensity) range but then decreases significantly after 600V (3000 V/cm).

In two tests at different times, the β⁄K ratio for the blood from the two normal donors, was unity. Any variations from this value would indicate a change in the deformation constant, K, and/or a change in the membrane bulk modulus, β.


Return to: The Study of Cells Treated by Electroporation


Lyn Oliver AM PhD June 2021