## 4 Discussion  
Assuming the average phage length of 1 micron and 10 nm thickness, its volume is about 78 \(\times\) 10\({}^{-6}\) um\({}^{3}\) and, being that its density is about 1 g/cm\({}^{3}\), its weight is about 7.8 \(\times\) 10\({}^{-17}\)\(g\) = 0.078 fg. Assuming that, on average, the Au NPs adherent to the phages have a diameter of 40 nm, the volume of the single NP is 3.35 \(\times\) 10\({}^{4}\) nm\({}^{3}\) and, being that the Au density is 19.3 g/cm\({}^{3}\), its mass is about 6.37 \(\times\) 10\({}^{-16}\) g= 0.64 fg, i.e., about a factor ten higher than that of the single phage. Because about 4 Au NPs generally are adherent to a single phage, it means that the phages mobility is strongly influenced by the Au NPs that anchor them in the biological substrate and burden the viruses in their diffusion within a biological solution. At the same time, the Au NPs are aggregated by the phages, reduce their mobility in the solution and can be anchored by the phage filamentation. These aspects find important applications in the field of radiotherapy, hyperthermia and imaging contrast. The high atomic number Z of Au, of 79, is about 5 times higher than that of oxygen and carbon, the main components of biological structures. This higher atomic number determines a high photoelectric cross section \(\mu_{ph}\) when struck by ionizing radiations since it depends on the following relationship:  
\[\sigma_{ph}\propto\frac{Z^{4}}{h\
u^{3}} \tag{2}\]  
where \(h\
u\) is the photon energy. Consequently, the mass absorption coefficient \(\mu_{ph}\) of the medium can be significantly enhanced by the presence of the heavy Au NPs because  
\[\mu_{ph}=\sigma_{ph}\frac{\rho}{A}\ N_{A}\propto\ \left(\frac{Z}{h\
u}\right)^{3} \tag{3}\]  
where \(\rho\) is the medium density, \(A\) the atomic number, and \(N_{A}\) the Avogadro number. Thus, the ionization processes employing Au NPs can be enhanced by a factor of up to 600 times higher than for the carbon and oxygen biological elements. The use of Au NPs, also at concentrations lower than 1% in atomic composition, may increase the absorbance of photons inducing the photoelectric effect mainly in the energy range of about 5-500 keV. The Au NPs embedded in different materials, such as in biological fluids, cells and tissues, permit to absorb high photon energy and to modify the properties of the irradiated medium also at relatively low absorbed doses. Radiotherapy, both using classical X-rays and electron beams and innovative proton and carbon ion beams, represents one important case which reaches the goal to destroy the tumoral cells employing Au NPs transported inside the cells by phages and by diffusive processes. The internalized nanoparticles near the cell nucleus under ionizing irradiation produce high electron emission damaging the DNA of the cell, destroying the cell at absorbed doses lower than the case without Au NPs [26]. To use Au NPs bonded to phages and anchored inside the cell is also advantageous for hyperthermia treatments because the heavy conductive Au element permits to enhance the conduction of heat through the biological fluids. The rate of heat transfer dQ/dt through a material is proportional to the negative gradient in the temperature dT/dx and to the area A through which the heat flows, according to the following heat transport equation:  
\[\frac{dQ}{dt}=-kA\frac{dT}{dx} \tag{4}\]  
where \(k\) is the thermal conductivity of the medium. Thus, although at a low concentration, the insertion of Au NPs having a \(k\) conductivity of about a factor 500 times higher than that of water produces a higher heat transfer to the tissues and cells, permitting to damage the tumoral cells containing Au-NPs during hyperthermia cycles for temperatures of about 38-40 \({}^{\circ}\)C maintained for times of the order of one hour [27].