Live Yeast Cells

The fourth particle type included in our library is saccharomyces cerevisiae, more commonly known as yeast cells. Viable yeast cells are widely used in biological research and in the development and testing of technologies dealing biological particles because they are easy to culture in a laboratory and their internal structure and morphology is representative of a large class of cells [47,48]. Figure 3.10 shows a photograph of a typical yeast cell and a diagram of its internal structure. Yeast typically range from 1 to 10μm in diameter and are ellipsoidal in shape. Yeast is an enveloped cell and has many layers to its internal structure. The outer-most layer is a rigid cell wall followed by a periplasmic space. The periplasm separates the wall from a thin cellular membrane that typically measures a few nanometers in thickness. The cell membrane encapsulates the nucleus and many other sub-cellular components.

Figure 3.10 Microphotograph of a yeast cell and diagram of its internal structure [48]

Because of the structural complexity of yeast and many other cells, it is not sufficient to electrically model them using any of the permittivity models presented in this chapter thus far. There are many analyses of the dielectrophoretic forces exerted on biological particles in the published literature [25]. At the heart of these analyses is a concentric shell model for the effective complex permittivity, which in turn determines the Clausius-Mossotti factor [49]. In this model, particles are electrically modeled as concentric spheres of varying thickness, each layer having unique values for electrical conductivity and permittivity. The complex permittivity of a multi-layered particle can be calculated by using the ‘smeared-out’ sphere method [25] illustrated in figure 3.11. Given an inner shell (nth layer) and an outer shell (nth + 1 layer), an effective equivalent complex permittivity for the two layers ( _{) can be calculated using the}

[(r r ) ( )] [(r r ) ( )] (3.5)

which essentially averages the permittivities of the shells according to their relative dimensions. The result is a value for complex permittivity such that a homogenous sphere of that value would be electrically equivalent two the combination of the two shells. In general, this procedure can be used to calculate the effective permittivity for any arbitrary number of shells by successively reapplying equation 3.5 and using the equivalent homogenous sphere calculated in the previous step as the inner layer until the outermost layer has been incorporated into the effective permittivity.

Figure 3.11 Approximating the effective complex permittivity of a two concentric spheres via use of the smearing

Multi-shell models with various numbers of layers have been proposed to model the dielectric properties of viable yeast, and it has been shown that using 5 layers (figure 3.12) yields the most accurate results [50].

Figure 3.12 5-layer multi-shell models used for calculating the effective permittivity of viable yeast cells

In this model, it has been proposed that on average, viable yeast can best be represented by modeling the inner core and all the subcellular components as a sphere with radius of 3μm, conductivity σint = 1.2 S/m and with a dielectric constant of εint = 51. The cellular membrane is approximated to be 3.5 nm thick with a dielectric constant of εmem = 3. The conductivity of this layer depends greatly on the conductivity of the medium it resides in. The value that corresponds with our reference medium was calculated via a linear extrapolation using data points from [50], and results in a conductivity of σmem = 3.63 μS/m for our model. In the model, the membrane layer is followed by 25nm periplasmic space of σper = 4.1 mS/m and εper= 14.4. The multi-shell model better tracks the electrical characteristics of actual viable yeast by dividing

up the cell wall into inner and outer regions of thickness 50nm and 110nm respectively. The inner wall conductivity also depends on the medium (σinn = 4.3 mS/m for our reference medium) and an outer wall conductivity of σout = 20 mS/m. The inner and outer wall dielectric constants were determined to be εint = 60and εint = 5.9. Figure 3.13 shows the Clausius-Mossotti factor spectrum that results from this model in our reference medium and figures 3.14 and 3.15 show the real and imaginary parts of it.

Figure 3.13 Clausius-Mossotti factor spectrum for 5-layer mutli-shell model of viable yeast cells in reference

medium of and

The spectrum for Re{KCM} can be divided into 3 primary regions of operation. At lower frequencies (0 < f < 30kHz) Re{KCM} is negative and slowly increasing, indicating that viable yeast will undergo negative dielectrophoresis at these frequencies. From 30 kHz < f < 200MHz,

Figure 3.14 Real part of Clausius-Mossotti Factor for viable yeast cells

Re{KCM} is always positive, increases to its maximum value of Re{KCM} = 0.754 at f ≈ 1MHz and then decreases towards zero at f ≈ 200MHz. At very high frequencies ( f > 200 MHz), viable yeast behaving according to this model again exhibit negative dielectrophoresis. At these high frequencies, yeast can be made to feel its maximum possible negative dielectrophoresis forces when the Clausius-Mossotti factor saturates to a value of Re{KCM} = -0.174 , almost 3 times smaller in magnitude than the maximum negative forces that can be exerted on polystyrene spheres. The key difference to note here, in comparison to the manufactured particles described earlier, is that viable yeast cells can be made to have either strong positive dielectrophoresis forces exerted on it or relatively weak negative dielectrophoresis forces depending on frequency, whereas polystyrene spheres can only be made to have strong negative forces exerted on them in this medium.

Figure 3.15 shows the imaginary part of the Clausius-Mossotti factor viable yeast cells that results from using the multi-shell model. The primary distinguishing feature here is that the spectrum has two peaks: one that is positive and one that is negative. At low frequencies Im{KCM} = 0 and then gradually increases to a peak of Im{KCM} = 0.43 at f = 88 kHz and then descends back to zero at f = 1.5 MHz. After that zero-crossing, the curve descends to a negative peak of Im{KCM} =- 0.35 at f = 73 MHz. This reveals that viable yeast cells can have TWDEP forces exerted on them that are directed with or against the phase gradient, depending on frequency, as opposed to the polystyrene cases than can feel force vectors in one direction or the other, but not both. It is also of note that the maximum value of Im{KCM} for viable yeast cells can be up to 18 times larger in magnitude than the maximum value calculated for polystyrene beads (PS-COOH), meaning that TWDEP forces will have a much larger impact on their motion.

Based on this model and when introduced into the TWDEP configuration of figure 2.5, the expectation is that yeast cells will have 4 primary regions of operation. At very low frequencies, nDEP forces will cause the particle to levitate, with little to no lateral movement. As frequency increases, the particles will transition into a region where negative forces continue to elevate it, and but strong TWDEP forces will push the particle along the positive phase gradient. In the next band of frequencies where Re{KCM} is positive , strong pDEP forces will pull the particles down towards the electrode edges. If pDEP forces become too strong, the cells will be pinned to the electrodes and will not move laterally, even when Im{KCM} is non-zero. Eventually at high frequencies, when Re{KCM}goes back to being negative, the cells will once again levitate and move laterally due to TWDEP forces. However since the sign of Im{KCM} is negative in this region, the particles will move in a direction opposite the phase gradient.