Capacitance and biomass

If permittivity were plotted against log frequency, the plot would be identical to the

curve shown in Figure 2.1. The Apermittivity value (Ac, also known as the

dielectric increment ) is given by the following equation (Schwann 1957):

A c = 9PrCyyi

/ 4

CQ Equation 2.3

where:

Ac

= the dielectric increment, change in permittivity from low to high frequency

P = the volume fraction o f the biomass, i.e. the fraction of the total volume o f the suspension which is enclosed by the plasma membranes o f the cells.

r = the cell radius (m)

Cyyi = membrane capacitance of the cell per unit of membrane area (Fm’^ ) GQ = permittivity o f free space (a constant, 8.854 .10 F m ’^)

As the capacitance measurements described in this work are directly related to the

permittivities, this equation gives a useful means of estimating likely capacitance values for the organisms studied and allows a degree of interpretation o f the results

from the capacitance monitoring. It should be bom in mind that this equation was

derived to describe the dielectric increments of solutions of spherical cells. The

ratio 9/4 changes for different cell morphologies (Kell e / <2/., 1990). Davey (1993) suggests ways of correcting for this effect with suspensions of ellipsoidal and rod­

shaped cells but no method is proposed for filamentous organisms. For a given

cell suspension, the cell radius, r, and the membrane capacitance Cm can be regarded as constants. As c q is also a constant, this means that Ac is linearly

proportional to P, the volume fraction o f the biomass in suspension, which is the biomass. Equation 2.3 is true only for low values o f P. At high volume fractions,

the electrical field effects on an individual cell become distorted by the cells around it, and a plot o f As versus volume fraction (and thus biomass) begins to

plateau out at values of P > 0.15, which corresponds to an approximate wet weight

o f 150 g/L, a dry weight of between 50-75 g/L. A modification to this equation was suggested by Schwann and Morowitz (1962) to allow for this non-linearity:

As

=

9PrCfyi! A

SQ *

P / [1+ (P/2)]^

Equation 2.4

This is Equation 2.3, with an additional term P/ [1+ {PH)Ÿ • This additional factor clearly only depends on the volume fi-action o f the cells present. Some recent work

by Davey et a l (1992) has shown that this additional term does correct the equation for cell suspensions of high volume fi-actions. This allows the dielectric

increment data to correlate with volume fraction and thus biomass measurements, even from high volume fi*action cell suspensions by the application o f a curve-

fitting routine o f non-linear least squares to the data from high-volume fi*action cell

suspensions.

One of the biggest advantages o f using capacitance measurement to estimate biomass is that only viable cells will contribute to the capacitance signal. Viability is a relative term and means different things to different people. In this instance,

viability is taken to mean the possession o f an intact cell membrane, which is a

reasonable definition of viability in general and the most appropriate definition of viability for this work. As discussed above, to contribute to the capacitance attributed to the cells, a cell must possess an intact cell membrane to allow a

polarisation and charge separation to occur. This theory is acceptable for entirely viable cells which have an intact membrane and entirely non-viable cells which are

fully disrupted and their cytoplasmic ions cannot be contained by their cell

membranes. The cells which fall somewhere between these two extremes are still o f interest. The contribution of partially lysed and leaky cells to the capacitance

signal of a cell suspension has not previously been investigated. The normal

turnover o f a cell population and the sometimes harsh environment o f a fermenter,

with the stresses caused by shear forces, will result in a portion o f the fermenter's cell population falling between these two extremes. This is especially true of filamentous organisms which are very shear sensitive, have a tendency to lyse and

also change morphology during typically long antibiotic fermentations such as the

growth of P. chiysogenum to produce penicillin G. Mishima et al. (1991a) demonstrated that, with Aspergillus niger, homogenisation reduced the capacitance o f the cell suspension by around 95%, indicating the viability component of capacitance.

The effect o f non-intact cells on capacitance could be examined using variable,

low-pressure homogenisation to disrupt a portion of the cells and look at the

changes in capacitance, viability measured by conventional means and if possible cell morphology. This technique was employed in this work and will be discussed

in detail in later sections.

Another advantage o f the capacitance method of biomass measurement is that it

should not be interfered with by non-biomass solids, oils, antifoams and gas bubbles in the suspending media. It is relatively common for fermentation media,

especially industrial fermentation, to contain all of these potential interferents.

These all give problems for on-line optical density probes. As they are not significantly polarised by the applied electrical field, they do not contribute to the

capacitance o f the cell suspension. If a large amount of non-polarisable species are present in the fermentation fluid, (e.g. the gas hold-up is high or there is a large solids or immiscible liquids content) then the capacitance will be reduced over the full frequency range as a finite volume of polarisable material (cells and water) has

been replaced with this non-polarisable material. The effect of gas hold-up should be noted. A highly mixed and aerated fermentation vessel, especially a small (<

20L) one can show a significant increase in volume over the liquid volume due to the hold-up time o f the air being input into the vessel. Again, this has the effect of

reducing the overall capacitance o f the fermenter fluid due to the effect described

above. As this effect is more pronounced in small vessels of the type predominately used in this work, a method of correcting for this was determined

(see Section 3.1.6.4). Where possible, the agitation speed and gas flow were kept

constant in small fermenters to avoid exacerbating this problem.

Another potential problem is concerned with the use o f non-biomass solids and

immiscible oils as substrates in some fermentations. If the presence of the non-

polarisable substrates in large concentrations was to reduce the capacitance o f the fermentation fluid at the start o f the fermentation, then the breakdown o f the non-

high biomass estimate as the capacitance o f the fermentation fluid in increasing

due to the increase in cell number and the decrease in the presence o f non-

polarisable substrates.

In document The use of capacitance measurement in fermentation monitoring (Page 41-44)