1 .pymolrc and colors

In the .pymolrc file, it is possible to redefine colors and other things. I have done this, to ensure that the graphics here look different from any published ones.

2 Trypsin (TRY)

Trypsin (TRY) is a medium-sized globular protein from the small intestine that serves as a proteolytic enzyme, i.e. TRY catalyzes the inverse peptide bond and therefore effectively cuts proteins. The function of TRY is substrate specific, i.e. based on positively charged lysine and arginine side chains [1]. Together with other substrate specific members of the serine protease family, proteins are cut into smaller peptides. These can then be absorbed through the lining of the small intestine.

Fig. shows the carbon trace (the contour of the backbone) of TRY in its folded conformation [2] visualized by pymol [3]. The backbone consists of 245 amino-acids of which 26 are part of an \(\mathrm{\alpha}\)-helix, corresponding to \(10.6 \,\%\) of the total amino acids. There are 2 \(\mathrm{\beta}\)-sheets of a total of 81 monomers that correspond to \(33\,\%\). The rest of the structure is in a random coil formation. These numbers are in poor agreement with measured values in the previous study on CS-TRY NPs [4] which could be due to the autolysis or the different measuring technique. The \(R_G\) of globular TRY is \(\sim1.6\) nm [2].

Carbon trace of TRY"s folded conformation @Transue2004X with $\mathrm{\alpha}$-helixes in red, $\mathrm{\beta}$-sheets in blue and random coil in green. [code](figures/try/try-ss.pml)

Figure 2.1: Carbon trace of TRY"s folded conformation [2] with \(\mathrm{\alpha}\)-helixes in red, \(\mathrm{\beta}\)-sheets in blue and random coil in green. code

An important consideration for the design of biotechnological applications using TRY is the autolysis, namely the process of TRY digesting itself in solution. This process happens at neutral pH within two hours leaving only peptide chains [5] that are still held together by disulfide bridges. The resulting structure is referred to as \(\alpha\)-trypsin. Fig. shows the carbon trace of TRY while highlighting the 6 disulfide bridges and the amino acids lysin and arginin. None of them are in a vital position where cutting them would lead to the molecules falling apart. The pH optimum for tryptic digestion is at pH \(\sim8\) [6] while the pH in the small intestine gradually increases from pH 6. TRY can therefore be assumed to be active over a large pH range. A common recommendation is therefore to store TRY at very low temperatures of \(<40\C\) or at low pH-values of \(\sim3\). It is also possible for many biomechanical applications to allow the autolysis and work with the \(\alpha\)-trypsin.

Trypsin in folded conformation. The line is the carbon trace of the backbone. The width of the line corresponds to the b-factor of the corresponding residues. Disulfide bridges are in yellow. Arginin and lysin are in red.[code](figures/try/trypsin_sslysarg.pml)

Figure 2.2: Trypsin in folded conformation. The line is the carbon trace of the backbone. The width of the line corresponds to the b-factor of the corresponding residues. Disulfide bridges are in yellow. Arginin and lysin are in red.code

The full thermal denaturation of TRY happens around 70 [7], [8].

The temperature induced aggregation behavior or TRY in solution was studied at different pH-values (not considering the autolysis effect) [9]. At pH 4, where the proteins can be assumed to be intact and positively charged, the dominant population appeares to be single proteins over protein aggregates. At neutral and acidic pH, monomers and aggregates coexiste. Heating the dispersions was shown to cause irreversible aggregation related to an unfolding of the protein. The used temperature of 60, is below the denaturation temperature of TRY, meaning that a full denaturation of the protein is not necessary for the formation of hydrophobic bonds between them.

Fig. shows the folded conformation of TRY and an unfolded conformation together with transparent spheres of the corresponding radius (\(R_G = 1.6\) nm for the folded conformation and \(R_G=5.6\) nm for the extended conformation) around their center of mass. The radius of the spheres is the calculated \(R_G\) of the structures (). In conclusion, when a heating protocol is applied to the TRY molecules, the globular structure and also the length-scale of the molecules can be lost.

The pdb2pqr [10], [11] software was used to prepare the crystal structure by reconstructing missing atoms, adding hydrogens and calculating atomic charges and radii for force fields. The so prepared information was further processed by the program APBS [12] that calculates both the overall charge of TRY at different pH-values and creates a surface charge map (surface charge patches). Fig. shows a schematic illustrating the electrostacic properties of globular proteins. The overall charge of the proteins decreases with increasing pH-value from positive values above the IEP of the protein (IEP(TRY)\(\sim10.5\) [13]) to negative values below. surface charge of the proteins folded conformation visualized by pymol. TRYs charge decreases with pH being positive above the calculated IEP of 9.66 (folded) or 9.54 (unfolded) differing from measured values of \(\sim10.5\). Instead of a gradual change of all the monomers, however, TRY is build from amino-acids with different IEP meaning that the charge of the protein is not uniform. In particular for pH-values similar to the IEP, there are positive and negative charge patches on the surface of the protein making electrostatic attraction between TRY molecules possible even when the overall charge is positive or negative.

Electrostatic surface potetial of trypsin at pH 8. The scale is in units of $k_BT/e$.[code](figures/try/1s81_pH8.pml)

Figure 2.3: Electrostatic surface potetial of trypsin at pH 8. The scale is in units of \(k_BT/e\).code

Fig. shows the overall charge of the trypsin as a funcion of pH. The inserts are electrostacic maps as before.

Schematic illustration of the overall protein charge (indicated by the vertical position of the pictures) of TRY as a function of pH (indicated by the horizontal position of the pictures). The pictures illustrate surface charge patches. [code](figures/try/try_charge.py)

Figure 2.4: Schematic illustration of the overall protein charge (indicated by the vertical position of the pictures) of TRY as a function of pH (indicated by the horizontal position of the pictures). The pictures illustrate surface charge patches. code

References

[1] W. E. Brown, F. Wold, Biochemistry 1973, 12, 835.

[2] T. R. Transue, J. M. Krahn, S. A. Gabel, E. F. DeRose, R. E. London, Biochemistry 2004, 43, 2829.

[3] can be found under www.pymol.org.

[4] A. Papagiannopoulos, D. Selianitis, A. Chroni, J. Allwang, Y. Li, C. M. Papadakis, International Journal of Biological Macromolecules 2022, 208, 678.

[5] M. M. Vestling, C. M. Murphy, C. Fenselau, Analytical Chemistry 1990, 62, 2391.

[6] T. Sipos, J. R. Merkel, Biochemistry 1970, 9, 2766.

[7] R. A. Beardslee, J. C. Zahnley, Archives of Biochemistry and Biophysics 1973, 158, 806.

[8] M. H. N. Brumano, E. Rogana, H. E. Swaisgood, Archives of Biochemistry and Biophysics 2000, 382, 57.

[9] S. Trampari, A. Papagiannopoulos, S. Pispas, Biochemical and Biophysical Research Communications 2019, 515, 282.

[10] T. J. Dolinsky, P. Czodrowski, H. Li, J. E. Nielsen, J. H. Jensen, G. Klebe, N. A. Baker, Nucleic Acids Research 2007, 35, W522.

[11] T. J. Dolinsky, J. E. Nielsen, J. A. McCammon, N. A. Baker, Nucleic Acids Research 2004, 32, W665.

[12] N. A. Baker, D. Sept, S. Joseph, M. J. Holst, J. A. McCammon, Proceedings of the National Academy of Sciences 2001, 98, 10037.

[13] K. A. Walsh, in Methods in Enzymology, Elsevier, 1970, pp. 41–63.