Team:NU Kazakhstan/Modeling

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Modeling

Modeling

Fluorescence is the event of emission of the photon after the excitation of fluorophore with the appropriate wavelength. Overall, the fluorescence can be described with the following equation:

Where S1 and S0 are excited and ground states accordingly, and v is the corresponding emission frequency. It is also noticeable that the fluorescence has the wavelength which is higher than those of excitation.
However, upon the excitation of the molecule, different events can occur. While modeling the decay events of our CQDs, we relied on our knowledge of Jablonski diagram.


Figure 1. Jablonski diagram (Dunst and Tomanak, 2019).

As it can be seen, different events can compete with fluorescence, such as Internal conversion, Intersystem crossing and quenching effect. The overall rate of decay can be expressed by the sum of all decay processes occurring after the excitation:
Where [S1] is the concentration of fluorophores present in the excited state, and ki is the rate constant. This differential equation can be solved to obtain the resulting expression:

Where [S1]0 is the initial concentration of the fluorophore in the excited state (at t=0). We also can calculate the lifetime of the fluorophore:

The function of the intensity decay is exponential for many decay processes can be expressed through the equation:

The value of aj shows the fraction of fluorophores with the corresponding lifetime j. To obtain the best fit to the multi-exponential decay, we performed the time-resolved fluorescence measurement of our CQDs and performed analysis with the DecayFit software:

Figure 2. Screen of one of the successful fits of CQDs.
After doing many trials, we detected that our decay has the best fit to the four-exponential decay model (the Chi2 value closest to 1), where the sum of pre-exponential functions a1+a2+a3+a4=1. The excitation wavelength is 500 nm.

Table 1. Lifetimes obtained from the modelling

Name of the strain	Decay process	Value of “a”	Lifetime (s)	Assigned process
58a	1	0.9484	3.7432*10-13	Internal conversion
	2	0.0285	2.2087*10-9	Fluorescence
	3	0.0111	0.8550*10-9	Fluorescence OR excitation energy transfer
	4	0.0129	7.4273*10-9	Fluorescence
62	1	0.0043	0.4706*10-9	Fluorescence OR excitation energy transfer
	2	0.0142	5.7033*10-9	Fluorescence
	3	0.0189	1.6682*10-9	Fluorescence
	4	0.9626	0.0278*10-9	Excitation energy ransfer
53	1	0.0457	3.0600 *10-9	Fluorescence
	2	0.0072	5.8738*10-9	Fluorescence
	3	0.9471	2.2276*10-15	Internal conversion/energy transfer
	4	3.6804e-17	0.1199*10-9	Fluorescence/Excitation energy transfer
Wild type + Ascorbic acid + Chromium VI	1	0.8797	9.4456*10-13	Internal conversion
	2	1.1136e-16	24.1144*10-9	Fluorescence
	3	0.0737	6.7214*10-9	Fluorescence
	4	0.0466	2.4536*10-9	Fluorescence

Thanks to mathematical expressions and the exponential decay model, we were able to predict which decay processes are occurring after the excitation of our CQDs. Based on our knowledge of decay lifetimes, we were able to assign each event to the appropriate type of energy conversion. As it can be seen, most of our events are fluorescence, however we observed competing events such excitation energy transfer, internal conversion and energy transfer. Based on this information, we were able to move towards new improved compositions of our CQDs and improved synthesis. In some cases there is very fast energy transfer which takes the significant fraction among other decays, which can be assigned to quenching due to the high concentration. Such information was very helpful to optimize concentration to avoid quenching but obtain readable intensity data.
One of the meaningful conclusions was made through the analysis of wild type containing ascorbic acid and chromium. Ascorbic acid is able to reduce the Chromium so we can simulate the effect of Chromate Reductase protein in the wild type species. It is noticeable that it contains fluorescence event lasting for 24 ns, which is quite long and stable. This is suitable case for the artificial antennae construction, as it is enough to transfer energy to such systems as Rhodopsin and PSI. Overall, this mathematical modelling significantly changed our perception of CQDs fluorescence events and was very useful in creating new solutions for the advancement of CQDs synthesis.
To understand the structure of HydA several modeling tools were used. First of all hydrophobicity plot of protein was obtained using ProtScale:

Figure 3. Hydrophobicity plot.

From Hydrophobicity it can be predicted that protein is not transmembrane and probably folds into somewhat globular structure. Predicted by SignalP 4.1 server that predicts signal peptides gives following plot:
Figure 4. SignalP4.1 prediction.

Plot predicts no peptide signals in the protein suggesting it is not being transported or attached to the membrane. Lastly we conducted a homology model of our sequence of Hydrogenase A from C. acetobutylicum based on the template of HydA from C. pasterium.

Figure 5. HydA Swiss Model.
The overall score GMQE score is quite good at 0.86 (ideal gets up to 1). The model covers 98% of the sequence and sequence identity is at 71%. From this we can predict that structure of HydA is more or less conserved among Clostridium genus. This can give potential for determining most efficient Hydrogenase from the genus, for better production

Reference:
[1] Waterhouse, A., Bertoni, M., Bienert, S., Studer, G., Tauriello, G., Gumienny, R., Heer, F.T., de Beer, T.A.P., Rempfer, C., Bordoli, L., Lepore, R., Schwede, T. SWISS-MODEL: homology modelling of protein structures and complexes. Nucleic Acids Res. 46(W1), W296-W303 (2018).
[2] Guex, N., Peitsch, M.C., Schwede, T. Automated comparative protein structure modeling with SWISS-MODEL and Swiss-PdbViewer: A historical perspective. Electrophoresis 30, S162-S173 (2009).
[3] Bienert, S., Waterhouse, A., de Beer, T.A.P., Tauriello, G., Studer, G., Bordoli, L., Schwede, T. The SWISS-MODEL Repository - new features and functionality. Nucleic Acids Res. 45, D313-D319 (2017).
[4] Benkert, P., Biasini, M., Schwede, T. Toward the estimation of the absolute quality of individual protein structure models. Bioinformatics 27, 343-350 (2011).
[5] Bertoni, M., Kiefer, F., Biasini, M., Bordoli, L., Schwede, T. Modeling protein quaternary structure of homo- and hetero-oligomers beyond binary interactions by homology. Scientific Reports 7 (2017).
[6] SignalP 4.0: discriminating signal peptides from transmembrane regionsPetersen TN., Brunak S., von Heijne G. & Nielsen H. Nature Methods, 8:785-786, 2011.
[7] Krogh, A., Larsson, B., Von Heijne, G., & Sonnhammer, E. L. (2001). Predicting transmembrane protein topology with a hidden Markov model: application to complete genomes. Journal of molecular biology, 305(3), 567-580.
[8] Gasteiger E., Hoogland C., Gattiker A., Duvaud S., Wilkins M.R., Appel R.D., Bairoch A.;Protein Identification and Analysis Tools on the ExPASy Server;(In) John M. Walker (ed): The Proteomics Protocols Handbook, Humana Press (2005). pp. 571-607.
[9] Dunst, S. and Tomancak, P., 2019. Imaging Flies by Fluorescence Microscopy: Principles, Technologies, and Applications. Genetics, 211(1), pp.15-34.