In order to get lasing, light has to resonance within an optical cavity formed by mirrors or a reflective surface. In bacteria the light has to be reflected in a spherical cavity since the E.coli is rod shaped. The reflective surface produced by E.coli (e.g. silica and tin dioxide layer and PHB granules) are not perfect mirrors and therefore the light can only get reflected by total internal reflection when approaching the edge of the cavity at a large enough angle. When the light gets reflected by total internal reflection in a closed circular path inside a microcavity, this type of optical cavity is called a whispering gallery mode (WGM) micro-resonator (Humar et al., 2015)(figure 2). Whispering gallery modes are the phenomenon that waves are circulating in a spherical object in a closed path as a result of total internal reflection at the surface (Humar et al., 2015, Wilson et al., 2012). A closed path of a an integer number of wavelengths is required so that constructive interference takes place.

For the first method described above E.coli encapsulates itself by a layer of biosilica or tin dioxide. Here we determine what the minimal size of the bacteria should be to fit light inside the E. coli encapsulated with biosilica or tin dioxide using ray optics. We found that a biosilica covered cell should have minimal diameter of \(0.9 \mu m\) and a cell covered with thin dioxide should have a minimal diameter of \(1.3 \mu m\) as can be found here.

The alternative to using the whole cell as an optical cavity we investigated the possibility of using PHB granules inside the cells as an optical cavity. In a similar method as for the encapsulated E.coli the minimal size of the PHB granules is determined by geometrical optics. We found that the minimal diameter of the PHB granules is \(d\approx 1.5\mu m\) which is larger than the small axis of E.coli. Therefore we expected that the granules will not grow to this size and therefore we won’t be able to fit light inside the PHB cavity. Thus lasing won’t be physically possible in PHB granules in E. coli.

The sizes we found for an optical cavity in E.coli encapsulated by a reflective layer are comparable to the natural size of E. coli, however this is the most optimistic model where we computed the absolute minimum size to fit one wavelength of light for hitting the reflective surface two times. Our model thus shows that we can only trap light inside a cell if it functions as a perfect laser cavity.

Because we need enough fluorophores in the gain medium to get lasing we wanted to know how the concentration of fluorophores evolves over time when we use specific promoters. Therefore we made a kinetic model which takes the promoter strength- (P), growth- (\(\mu\)), transcription rate- (\(K_t\)), degradation of mRNA- (\(\gamma_m\)) and maturation (\(K_m\)) of fluorescent protein, and the degradation of non-fluorescent protein (\(\gamma_{GFP}\)) and fluorescent protein (\(\gamma_{GFP}\)) into account as in figure 3. The full description of this model can be found here. To determine the growth rate we were able to fit the measured OD values of the bacteria to a growth equation. The growth rate can then be used in the kinetic model to determine the promoter strength. This model can be used to predict the protein concentration for inducible promoters. It appears that this model cannot be used when using a constitutive promoter which we use in our fluorophore constructs.

To determine the intracellular concentration of the fluorophores we make a calibration curve of EGFP. The fluorophores we are using in the experiments are however GFPmut3b, mVenus and mCerulean. In order to determine their concentration we can use the calibration curve of EGFP and the relative brightness for each fluorophore compared to EGFP (Gambhir et al., 2010). The brightness of a fluorophore is the product of its quantum yield and extinction coefficient and is proportional to the number of photons produced per molecule. Using the relative brightness we are able to determine the concentration of fluorescent molecules in the cells for all the fluorophores. How we exactly determine these concentrations and their results can be found here.

In order to determine the limit concentration of fluorophores required for lasing we made a model that described the kinetics of our biolaser. In this model we included spontaneous emission, stimulated emission and the cavity characteristics, such as mirror reflectivity and absorption by the medium. The complete model can be found here. We compared the results of our model with biolaser experiments from literature (Gather et al., 2011) and derived a threshold for lasing as a function of fluorophore concentration. We found that in a cavity the size of an E.coli cell, (\(1\mu m\) diameter), lasing can occur starting at fluorophore concentrations larger than 0.1 M. However, in our cells the maximum concentration we can achieve is in the nM to µM range and therefore lasing is physically not possible in our cells. To get lasing, we would either need much larger cells or a much higher concentration of fluorophores. The minimal size to get lasing with a concentration of 9.55 mM is around \(10\mu m\).

In order to determine how the light scatters on the bacteria microlenses we created models that simulate the interaction of electromagnetic waves (light) with our structure. The models were created in 3D in the software ‘COMSOL Multiphysics’ and we obtained two results: the focusing of the light after the lens and that there is no back scattering of light after meeting the lenses. Models of the real bacteria shape, rod shaped, and spherical shaped (not orientation related) were made. More details about those models can be found here.