Difference between revisions of "Team:Tianjin/Modeling"

Adsorption

We decided to create a model of Janus adsorption for two main reasons:

   Describing the self-assembly process of Janus on the solid substrate or air/water interface

   To support and complement enzyme kinetic modeling as the basic part of heterogeneous kinetics

Model Formation

As literature review, we know that Class I Janus are able to self-assemble at an air/water or water/oil interface, forming a robust, electron-microscopically identifiable monolayer characterized by a rodlet structure. Yu et al. studied the formation of rodlets of the inJanus from Grifola frondosa. They used a Langmuir trough and found that rodlets formed at the air-water interface during compression of a surface film of inJanus. de Vocht et al. repeated the experiment to have an image of rodlet structure after drying an aqueous solution with scanning force microscope. As for Class II hydrophobins, HFBI, HFBII and HFBIII from T. reesei have been shown to form films with a self-assembled hexagonally ordered structure (Paananen et al. 2003; Kisko et al. 2005; Kisko et al. 2007). Multilayer Langmuir-Blodgett films, HFBI and HFBII proteins formed hexagonal crystallites (Kisko et al. 2005.) Self-assembled hexagonally ordered films of HFBIII on an air/water interface and on a silicon substrate were also studied (Kaisa Kisko et al. 2007)

As evidence given above, the pattern of two classes Janus are totally different.

Class I Janus

A key difference between class I and class II Janus is that only class I Janus form amyloid-like rodlets. Ingrid Macindoe et al. compared three types of EAS: wild-type EAS, EAS_Δ15(a truncated version of EAS that lacks 15 residues from the disordered Cys3–Cys4 loop) and F72G EAS_Δ15(F72 mutate to G) by nuclear magnetic resonance(NMR) spectroscopy. They also carried out molecular docking simulations using the data-driven docking program HADDOCK. Different sets of intermolecular hydrogen bond restraints between neighboring monomers over residues S71-I75 in both parallel and anti-parallel arrangements were tested. The width of the rodlet generated in this way is approximately 65 Å, which agrees very well with the measured width of approximately 61 Å for EAS_Δ15 rodlets(Ann H Kwan,2008)(Figure 1)

Figure 1. Ribbon diagram of EAS_Δ15 hexamer in gray showing packing of side chains in the β-spine core and location of charged residues. Side chains of F72, L73, and I74 are shown as purple sticks, N67 as green sticks and T66 and T68 as orange sticks. Red and blue spheres denote positions of Cγ and Cε atoms of Asp an Lys side chains, respectively. Horizontal line illustrates that the majority of charges are located on the “bottom” half of the structure (corresponding to the hydrophilic face).

So, as the data obtained from MD simulation above, the diameter of monomer is 27 Å.

Figure 2. Model of the rodlet unit by overview. Two circles simplify hydrophobins as regular spheres. The connection between dimer is the β-barrel unit.

To figure out the stoichiometric relationship between Janus and surface site, we calculate area of Janus and a unit respectively. We assumed the size of a Janus is far larger than a single surface bound site.

If regarding dimer as a unit (Figure 2), the area of two Janus(S_H)= 1145 Ų, and the area of rectangle unit(S_A) = 1755 Ų.

So, the elementary reaction equation is simplified as,

 Hypothesis：

(1) Each site can hold at most one molecule of Janus(mono-layer coverage only)

(2) The surface containing the adsorbing sites is perfectly flat plane with no corrugations (assume the surface is homogeneous)

(3) The adsorption process is reversible

(4) There is an H-bond interaction in the β-barrel forcing to form rodlets.

When adsorption rate equals to desorption rate,

,

simplify it and solve θ, ,  where 

The adsorption isotherm equation is,

Class II Janus

The high resolution of the AFM images from both the air-facing side and the water-facing side enabled comparison of the repeating structures in the AFM images with the dimensions of an HFBI monomer.

Figure 3. Model of the structure of HFBI film. The film viewed from the hydrophobic side (A)  and from the hydrophilic side (B). (A) and (B) are processed AFM images showing the average repeating structures in a single crystalline area. In the middle panel and expanding to both sides is a model of the monomer arrangement in the film(Géza R. Szilvay,2007)The model in figure suggests that three monomers forming a trimer are arranged to form a hexagonal pattern.

Figure 4. Simplifying model of the structure unit of class II hydrophobin film. Full line in the circle is valid hydrophobin in one unit and the hexagon is a cell of crystal monolayer film.

To figure out the stoichiometric relationship between hydrophobin and surface site ,we regarded hexagonal cell as a unit. (Figure 4)The area of six effective hydrophobins  (S_H)= , and the area of hexagonal cell (S_A) = R.(R is the radius of ideal hydrophobin sphere)

The elementary reaction is as follow,

Hypothesis：

(1) Each site can hold at most one molecule of Janus (mono-layer coverage only)

(2) The surface containing the adsorbing sites is perfectly flat plane with no corrugations (assume the surface is homogeneous)

(3) The adsorption process is reversible

(4) There is an interaction between adjacent Janus forming hexagonal crystalline structure.

When adsorption rate equals to desorption rate,

simplify it and solve θ ,  

The adsorption isotherm equation is,

Parameter Finding

We turned to the literature to find parameters for our model, given in the Table below. In the past few years, M. Linder el at. were doing well in the field of adsorption of Janus. We looked for parameter values that had been measured in the work M. Linder el at. did, but the substrates they used were alkylated gold surface, salinized surface, polystyrene surface, etc. while what we use is PET(polyethylene terephthalate), which has different surface property. Therefore, we estimated parameters according to the data in their assays on fusion protein. Such aggregating parameters is somewhat uncertain endeavor; thereby predicting a range of the parameters and7 preparing it with the practical experiments. An explanation for how we arrived at each parameter is given in the table.

ADSORPTION PARAMETERS

As an attachment, we read almost all the assays about sJanus and inJanus adsorption in the paper published and we found diverse conditions in every assay, such as different substrates: alkylated gold, polystyrene, silanized glass, 1-hexanethiol etc. Hence, it is not easy to estimate the certain parameters when the Janus self-assemble on the PET. NO.1 parameters in the table is in the condition where the fusion protein adsorbs on the silanized quartz surface attained from the paper and we estimate the parameters when the protein is pure Janus by ignoring the conformation change during the protein fusion. Besides, theoretically it only applies to silanized surface but we initially think it applies to all hydrophobic surfaces. Further, we used another assay[8] data to estimate the parameters when inJanus adsorb on PET although in this case they used polystyrene as the substrate.

Initial Model Result

Using these estimated parameters, we simulated our model of the adsorption process. Below are two Janus, sJanus and inJanus, have different adsorbance with different concentration of free Janus. On the left we simulated a red line and a blue line, a range of the adsorption isotherm, which corresponds to pH=4 and pH=10, respectively. On the right is sJanus adsorption isotherm. It is convinced that no significant effect of temperature is noted; hence we do not make any note about temperature on the line graph.

In the initial model, it is indicated that two classes of Janus have similar ability of self-assembly. They both have strong hydrophobic area stuck to hydrophobic substrate.

Result in Lab

We set up this model to predict the quantity of absorption wild Janus and fused Janus. We have done the PET hydrolysis experiment with Janus or fused Janus existing, however, we did not have enough time to accomplish further discussion and parameter fitting which we planned to study with QCM(Quartz crystal microbalance) and SPR(Surface plasmon resonance). Despite that, we are working to make it more clear and specific in the future.

Reference

[1]Wang, X., Graveland Bikker, J., Kruif, C. & Robillard, G. Oligomerization of hydrophobin SC3 in solution: From soluble state to self-assembly. Protein Sci. 13, 810–821 (2004).

[2]Sunde, M., Kwan, A., Templeton, M., Beever, R. & Mackay, J. Structural analysis of hydrophobins. Micron 39, 773–84 (2007).

[3]Géza R. Szilvay. Self-assembly of hydrophobin proteins from the fungus Trichoderma reesei.(2007)

[4]Kisko, K. et al. Self-assembled films of hydrophobin protein HFBIII from Trichoderma reesei. J Appl Crystallogr(2007). doi:10.1107/S0021889807001331

[5]Kwan et al. Structural basis for rodlet assembly in fungal hydrophobins. Proc. Natl. Acad. Sci. U.S.A. 103, 3621–3626 (2006).

[6]Kwan, A. H. et al. The Cys3-Cys4 loop of the hydrophobin EAS is not required for rodlet formation and surface activity. J. Mol. Biol. 382, 708–20 (2008).

[7]Linder, M., Szilvay, G., Nakari Setälä, T.Söderlund, H. & Penttilä, M. Surface adhesion of fusion proteins containing the hydrophobins HFBI and HFBII from Trichoderma reesei. Protein Science 11, 2257–2266 (2002).

[8]Wang, Z. et al. Hydrophilic modification of polystyrene with hydrophobin for time-resolved immunofluorometric assay. Biosens Bioelectron 26, 1074–9 (2010).

[9]Takatsuji, Y. et al. Solid-support immobilization of a ‘swing’ fusion protein for enhanced glucose oxidase catalytic activity. Colloids Surf B Biointerfaces 112, 186–91 (2013).

[10]Takahashi,T.et al.Ionic interaction of positive amino acid residues of fungal hydrophobin RolA with acidic amino acid residues of cutinase CutL1. Molecular Microbiology 96,14-27(2015)