Modified Generalised Model

The SH-SAW microsensors being used are in the shorted configuration and thus the resonant frequency is only affected by changed in the density and viscosity of the over-layer and can be represented by: ( ) ( ) or, { }

where and are the density and permittivity of the sensing layer (in the present case). As the Sf9 cells were found to be spherical, although variations batch-to-batch size and shape needs to be accounted for

170 Also assuming an absence of a monolayer of Sf9 cells and the cells only cover a fraction ( ) of the surface area which is within the volume of the acoustic wave we can modify to: Eq. 7.1 and 7.2

{ } ( ) { } Eq.7.3 Refining the above equation to accommodate for fractional coverage area the contributions from non-immobilized sensor can be eliminated to give: ( ) { }

It is also know that the central frequencies of the SH-SAW microsensors have an associated penetration depth and that any changes to the viscosity and density that can be related to the acoustic penetration depth by

From Eq.7.5 another parameter can be extracted which is the rate of change of frequency with respect to the rate of change of density and

171 viscosity. Thus by partially differentiating Eq. 7.5 w.r.t to and provides Eq.7.6, 7.7:

( )

( ) ( )

( )

( ) ( )

Eq. 7.6 and 7.7 also provide directional information with regards to the changes in the resonant frequency of the SH-SAW microsensor. The resonant frequency increases due to a decrease in viscosity and an increase in density. Eq. 7.6 and 7.7 can then be substituted into equations Eq. 7.4 to get:

( ) {

( ) ( ) }

( ) {( ) ( ) } Eq. 7.9

( )

172 From Eq. 7.11 it becomes clear that the shift in the resonant frequency (∆F) is primarily affected due to changes in the cell viscosity( ), density ( ) and the volume of the cell or the fractional coverage area( ). The volume fraction depends not only on the number of Sf9 cell immobilized on the surface but also on the morphological and physiological properties of the biological cells e.g. any changes in cell volumes can have an effect on the volume fraction of the sensor area. Any changes to the volume of the cell through external liquid environment, due to ligand receptor activity or internal environment can alter , and . Therefore in order to examine the effects on the Sf9 cells due to the liquid environment it is beneficial if the various properties of the liquid are defined. There are three different types of liquids based on their individual tonicity. They are (when compared to the internal environment of the cell):

 Hypotonic solution – external environment is less concentrated

 Hypertonic solution – external environment is more concentrated

 Isotonic solution – external environment similar to the internal

173 In addition to the environment the condition of the cell membrane can also influence the SH-SAW resonant frequency because it lies within the penetration depth of the microsensor.

The cellular organelles are enclosed within a “biological membrane”. In 1972, Singer and Nicholson proposed the “fluid mosaic model” which is the traditionally accepted model to understand the structure of the cell or plasma membranes[161]. The cell membrane is semi-permeable membrane i.e. the biological cell dimension can change if the concentration of the external environment varying, thereby modifying the density and viscosity of the both the cell as well as the membrane itself. Thus, based on this information one can consider a simplistic model of the Sf9 whole cell considering each layer to be with an associated density, viscosity, conductivity, permittivity parameter. [157]. Based on the different SH-SAW sensor configurations, variables in the model can be narrowed down, as shown in Figure 7.15.

174 Figure 7.15: A simple model demonstrating the different layers of a biological

cell immobilized on a SH-SAW with the colour gradient denoting the penetration depth of the acoustic wave device. (not to scale)

Based on the information with regards to the membrane properties, the external liquid environment, cell density and viscosity different scenarios can be constructed representing the different experimental conditions. Results obtained in Experiments II and IV can then be examined according to the different scenario’s providing information with regards to the direction of the shift in resonant frequency.

Sf9 cell on a FreeSH-SAW device

Sf9 cell on a ShortedSH-SAW device

Piezoelectric Substrate Gold Wave Penetration Depth Piezoelectric Substrate Wave Penetration Depth

Cytoplasm Sf9 cell Sf9 cell Cytoplasm Cytoplasm Cytoplasm Cell Membrane Cell Membrane

External Liquid environment

Cell Membrane

External Liquid environment

Cell Membrane

175 Figure 7.16: Different experimental scenarios with associated changes in cell

properties

Scenario’s 1-3 can be considered as the baseline because that represents the before octopamine interacts with the Sf9 cell’s. It can be seen from Figure 7.16 that two different ligand concentrations have been accounted. We can now apply the different experiment performed to the named scenarios.

7.4.2.2 Octopamine Hydrochloride concentration