Read more about designing a DARPin library, protein-peptide docking and diffusion modelling.

Designing an optimized DARPin library for ribosome display testing


DARPins (designed ankyrin repeat proteins) are engineered antibody proteins that exhibit high specificity and affinity to different targets of interest due to their repeat protein property, resulting in various biological functions (Stumpp et al., 2008). Thus, modified DARPins are an ideal strategy to potentially address current drug discovery limitations. An example of our first designed DARPin 3D structure predicted by AlphaFold2 (Jumper et al., 2021) and visualised with PyMol (DeLano et al., 2002) is illustrated in Figure 1.

3D structure of a DARPin molecule of three internal repeats (IR) flanked by an N-Cap and C-Cap.
Figure 1. 3D structure of a DARPin molecule of three internal repeats (IR) flanked by an N-Cap and C-Cap.

In addition, due to the amino acid conformation of the internal repeat (IR) sequences, each IR displays similar structural conformation starting by a B-turn due to the motif TPLH highly conserved in such natural ankyrin repeats forming H-bonds leading to the first alpha-helix 1 (the so-called hydrophobic core). Then, the second alpha-helix is formed right after the randomised chosen positions 13 and 14 leading into a loop strand towards the next internal repeat or terminal cap. For more in-depth information please refer to the work of Binz et al., 2003 and Seeger et al., 2013. An illustration of the structure of one (IR) is displayed in Figure 2.

3D structure of each internal repeat module
Figure 2. 3D structure of each IR module (Seeger et al., 2013).


We aim to design and optimise an efficient DNA library of different DARPin molecules by modifying and randomising specific amino acid positions so that biofilm formation in Staphylococcus epidermidis (S. epidermidis) is arrested. The designed library is used in ribosome display to select the DARPin with the highest affinity towards the target AIP1 peptide, which in turn will inhibit the quorum sensing mechanism of S. epidermidis (see Experiments). Our construct was based on three key settings: (1) previous and current state-of-the-art scientific research on designed DARPin molecules, (2) most successful DARPins that bound to their intended targets, and (3) most successful randomised IR modules that resulted in successful outcomes. With this strategy, we expected DARPins with excellent biophysical properties as well as high affinity and stability.


First, we looked at the strategy employed by Seeger et al (2013) focused on the construction of a DARPin library with reduced hydrophobicity in order to generate each DARPin efficiently and more soluble. In our project, we decided for our final design, to still randomise 8 amino acid positions of each IR module and fix both capping repeats (N- and C- caps). To select our DARPin library for ribosome display testing, we developed an algorithm able to randomise the positions of each IR as well as fixed capping repeats and bridge amino acid connections to provide us with several different and optimised DARPin molecules. Finally, our DARPins are 157 amino acids long (471 base pairs) upon which the N-cap comprises 31 amino acids while each IR of 33 amino acids and finally the C-cap with 27 amino acids. A general look of our amino acid sequence strategy can be seen from Figure 3.

Amino acid sequence of single DARPin capping and internal repeats
Figure 3. Amino acid sequence of single DARPin capping and internal repeats. Framework and fixed positions are in black, bridge amino acids in blue, and randomized positions are marked with a specific colour. A. N-terminal capping repeat (or N-cap). B. Three internal repeat modules are chosen (or IRs) which makes our DARPins in the form of N3C. C. C-terminal capping repeat (or C-cap).

Randomization of the internal repeats (IR)

Each internal repeat underwent randomization on positions 1, 2, 3, 5, 10, 13, 14, and 26. Based on the work by Seeger et al. (2013), we still allowed all amino acids except G, P, C, V, L, I, M, and F at positions 2, 3, 5, 13, and 14 while position 1 were only allowed D, N, S, and T due to the excellent chemical properties of the DARPins. In addition, on position 10 we permitted the amino acids A, S, T, V, or L, and position 26 only three: N, H, or Y. Finally, we changed two fixed positions (21 and 25) to E and K, respectively. The choice for both E and K were based on the fact that the majority of previously reported and successful DARPins had these two fixed amino acids such as the novel LoopDARPins allowing for the selection of low picomolar binders with only one round of ribosome display (Schilling et al., 2014) and the reported GFP-binding DARPin (Hansen et al., 2017). Finally, we decided to optimise the bridge amino acids between N-cap and the first IR, the first IR to the second, the second IR to the third, and finally the third IR to the beginning of the C-cap. Finally, we decided to construct our DARPins with amino acids with polar uncharged side chains (for higher solubility) between the N-cap and the first IR as well as the last (third module) to the C-cap for stability purposes of the protein which was Q (Glutamine) and A (Alanine) between IR's.

N- and C-caps

In our final design, we chose not to randomise the N and C- caps (flanking sequences able to shield the hydrophobic core of each IR) but to optimise the amino acids of each so that the stability of our DARPin molecules would increase along with binding chances. Importantly, the main function of said terminal capping repeats is to make the protein more stable and to fold in an efficient manner by protecting and sealing the hydrophobicity of the internal repeats (IR) – the so-called hydrophobic core (Binz et al., 2003). For both the N-cap and C-cap and in contrast to the modifications performed on it with the reduced hydrophobicity DARPin library, we did not randomise the first three amino acids and fixed the whole sequence as proposed by the construct of Schilling et al (2014) and Hansen et al. (2017). A more general illustration of our final DARPin library construct can be seen from the figure down below (Figure 4).

DARPin library construct
Figure 4. Final DARPin library construct. The strategy implies randomization at each internal repeat (IR) with eight amino acid positions that are able to be rearranged for higher chance of efficient binding spots. Both N- and C- caps are fixed sequences that were optimized for higher protein stability.

What do we know now?

Throughout our design we came across several challenges. First, we were too ambitious and desired to test a massive DNA DARPin library (complexity around 1024) which turned out to not be viable due to the lack of finance support and time. Secondly, we now know how challenging it actually is just to hypothesise, design, and construct novel DARPin molecules - a new generation of therapeutics - for validation experiments as well as optimising every single base pair or amino acid sequence.

Protein-Peptide Docking


We will first predict the protein structure of our DARPins of interest to further explore their molecular characteristics and possible binding sites with the AlphaFold2 algorithm. Secondly, we will predict protein-peptide docking in silico with the usage of several available softwares such as the CABS-dock and MDockPeP with the aim to investigate which selected and optimised DARPin sequences best bind to our peptide of interest. Finally, we aim to validate experimentally our computational simulation results with the assist of scientific experiments and couple ribosome display assay with next-generation sequencing (NGS) analysis to find DARPin molecules with high affinity to our target AIP1.


Our aim with the in silico protein-peptide docking simulations with the selected DARPins ought to demonstrate how effective the binding to the AIP1 would be and, more importantly, at which residues the binding actually occurs. Knowing where the binding would most likely happen and its respective best bound DARPin should give an indication where to optimise our DARPin library further. So that the DARPin library can be fully optimised for future studies.

DARPin library construct
Figure 5. Workflow of protein-peptide docking prediction and analysis.


Predicting our DARPin molecules with AlphaFold2

We began by predicting the protein structure of our DARPins with the AlphaFold algorithm developed by DeepMind (Jumper at al., 2021) in order to obtain the most accurate and adequate structures (.PDB) files for protein-peptide docking prediction. For this effect, we used the available Colab notebooks (coding algorithms) for protein prediction and the results highlighted high pLDDT scores above 90 (which represents high accuracy of the model) suitable for our research question (protein-peptide binding prediction). For more information on how the scoring is calculated and interpreted, please refer to (Jumper et al. (2021), Tunyasuvunakool et al. (2021), and Evans et al. (2021)). The used notebooks were the following: AlphaFold Colab and ColabFold

MDockPeP vs CABS-dock

Since protein-peptide docking tools offer a wide variety of opportunities in drug design, we decided to predict protein-peptide docking with two available algorithms and softwares: MDockPep (Xu et al., 2018) and CABS-dock (Kurcinski et al., 2015). Notwithstanding, we were aware of the particular challenges of such simulation predictions including scoring methods, sampling, and modelling. After looking into the literature, we found that the previous docking methods were the most favourable to our research question considering that we required tools for global docking (algorithms that would take the input sequence as it is without previous assumptions such as knowledge regarding the binding site properties of the peptide of interest) (Ciemny et al., 2018).


We used the MDockPep server to predict protein-peptide docking using our predicted DARPin structures by the AlphaFold2 algorithm and the sequence of our AIP (target). Given a protein structure file and the peptide sequence, the algorithm will catch similar previously reported and known sequences as templates for docking calculations and rank or score each model (with ITScorePeP) to output the best predicted model. For more information regarding MDockPeP workflow and rationale, please refer to Xu et al. (2018) and Yan et al. (2016). We tested out 10 DARPins (Figure 6) for validation experiments and with MDockPep we were able to acknowledge that our DARPin #7 had the best probability of binding success to AIP1 (score of -139.4, while the worst predicted docking would be DARPin #9 with a score of -108.6) - the lower the score, the higher chances of affinity (Table 1).

Sequences of 10 selected DARPins
Figure 6. Selected 10 DARPins for wet-lab work and experiments.
Table 1. Top 1 model (best bound to the AIP peptide) for every DARPin after MDockPep protein-peptide in silico prediction.
DARPin molecule for testing
(Top 1 model of the protein-peptide docking prediction)
(Scoring function)
DARPin # 7 -139.4
DARPin # 8 -126.7
DARPin # 4 -125.6
DARPin # 6 -125.5
DARPin # 10 -123.7
DARPin # 5 -122.3
DARPin # 1 -117.8
DARPin # 2 -117.6
DARPin # 3 -112.0
DARPin # 9 -108.6
3D structure of DARPin and AIP
Figure 7. 3D visualisation of the best model of the DARPin #7 with MDockPeP.


The CABS-dock algorithm uses a coarse-grained protein model which simulates proteins assuming its whole amino acid sequence by simplifying the molecular dynamics process (Kmiecik et al., 2016 and 2018). In brief, the CABS-dock workflow begins from the peptide sequence (automated prediction of secondary structure) to then feed the simulation of both binding and docking. In this step, thousands of models are produced for selection of the best one or top 10. This selection process utilises filtering and clustering algorithms for the reconstruction of the final models that would best represent the reality (best predicted binding model). An in-depth explanation is provided on the CABS-dock original paper (Kurcinski et al., 2015).

Again, we tested out our 10 selected DARPins for validation experiments. The results for CABS-dock differed for each DARPin (as expected since different methods usually display non-harmonic outcomes). However, a trend regarding possible theoretical binding positions was detected for both the DARPin and AIP which will be discussed in the conclusions section. CABS-dock results highlight which residues (or amino acids) within the DARPin and AIP sequence the binding would succeed. Table 2 depicts the overall trend and range of binding properties of our both molecules.

Table 2. Residue contact regions of each predicted DARPin-AIP docking for the top model.
DARPin Min(DARPin binding residue) Max(DARPin binding residue) Min(AIP binding residue) Max(AIP binding residue)
DARPin # 1 11 140 1 8
DARPin # 2 11 140 1 8
DARPin # 3 34 110 1 7
DARPin # 4 36 110 1 8
DARPin # 5 34 140 1 8
DARPin # 6 34 140 1 8
DARPin # 7 11 140 1 8
DARPin # 8 11 110 1 6
DARPin # 9 44 110 3 7
DARPin # 10 44 135 1 8

Docking prediction conclusion

Given the simulation outcomes of both global docking methods, it is clear that the probability for the binding differs between each DARPin sequence as well as the contact regions. Our DARPins are able to contact with the AIP signalling molecule at any amino acid position (1 to 8) while the contact for each DARPin can alternate (11 to 140). Additionally, from our predicted results, it was shown that the contact between DARPin-AIP varied from DARPin to DARPin, suggesting and confirming the variability in our library construct. However, a general trend arises from the CABS-dock analysis upon which it was predicted that the AIP will most likely bind between the last amino acids of the N-cap until the first amino acids of the C-cap with highest probability of binding between the first and third internal repeats (i.e., the binding ought to occur at the IR modules). This indicates that our strategy of including a total of three internal repeats (N3C) ought to be an optimal design strategy to find an adequate DARPin-AIP phenomena in the wet-lab experiments.

What do we now know?

During our DARPin-AIP docking prediction analysis, we found out that there are still no concrete answers to practical questions such as: “how accurate MDockPeP and CABS-dock can be” and “to which extent we are confident in our simulation results?”. These are indeed challenging to answer since each method will provide different results and this is where the power of wet-lab validation assays and experimental work come into place (to confirm our simulation results). We expect that this type of global-docking methodology and analysis increases as more powerful computation and methods arise.

Sequence Analysis of DARPin reads


The idea of coupling next-generation sequencing (NGS) analysis to the ribosome display method is to confirm the success of our control molecule (i.e., the GFP DARPin) (Hansen et al., 2017) and to effectively identify our DARPin binding molecules against the AIP peptide. In addition, we aim to analyse such DARPin molecules at the RNA level for the identification of the most prominent amino acids at the randomised positions as well as potential patterns that can lead to the binding effect.


We intend to verify that our control experiment was really successful in preparation for potential future work with a large library of DARPins containing thousands of molecules for ribosome display affinity testing of our target AIP (i.e., proof of concept). With such proof, we would also hypothesise DARPin-binding compounds that reduce the quorum sensing pathway of the bacteria, eradicating the biofilm itself, and suggest a therapeutic molecule for mammalian tissue.


Quality control of NGS paired end read data

Given three main paired end raw sequencing data files (1 - GFP-DARPin and one of the tested wet-lab DARPins; 4 and 6 files containing all DARPins with different selection methods), we decided to preliminary perform quality control. For this, we used the FastQC tool whereupon it was confirmed the duplication of the reads, the quality of the sequence per position (or Phred scores - the higher the value, the more reliable and accurate the reads are), and the overall sequence quality (i.e., the average qualities of all reads). A summary report of our NGS data can be seen from Figures 8, 9, and 10 respectively.

Bar plot for sequence counts
Figure 8. Confirmation of duplicate reads from the NGS data.
curve of mean quality score
Figure 9. Mean quality scores across each base position in the reads.
curve of per sequence quality score
Figure 10. Average quality scores for the reads.

Pre-processing of NGS paired end read data

The workflow of the NGS analysis post quality control was as follows: first, we divided the raw data from the sequencing unit into forward and reverse reads since we got data from both our DARPins and the control GFP DARPin in the form of paired end reads. An illustration of how it looks can be seen from Figure 11.

schematic overview of sequencing
Figure 11. Paired-end sequencing upon which a single DNA strand is read from both ends. This results in higher accuracy compared to single-end sequencing.

Then, it was used for both the forward and reverse reads for downstream analysis and the translation of the DNA content of the reads into RNA (i.e., peptide sequence). The reads were then filtered to detect the starting sequence of the DARPin (the N-cap) and sequence logos were created for the GFP-DARPin and each DARPin molecule tested in the wet-lab using various selection strategies. This analysis was performed with python scripts. Important to note that the results from the filtering highlight loss of reads and the higher the length of the sequencing itself, the steeper the quality of the data ought to decline.

Detection of the GFP-DARPin (control sample)

Given the published peptide sequence of our control with PDB code of 5MA6_B , we were indeed able to detect the molecule, indicating that the ribosome display methodology was carried out correctly. In FASTA format the molecule is as follows:

>pdb|5MA6|B Chain B, 3G124nc




An illustration of the detected GFP-DARPin from the sequencing reads can be seen from Figure 12.

sequence logos
Figure 12. Detected GFP-DARPin (control sample) from file 1.

Confirmation of the selected DARPin molecules with randomised IR positions

Finally, and most importantly, we were able to confirm the presence of both the N-cap and the first randomised internal repeat of our DARPin molecules. This analysis highlights the variation which is needed in our DARPin library construct for the affinity testing to the AIP peptide. However, we did not fully detect the C-cap peptide sequence and it was due to possible contamination within the NGS data. One additional limitation of our analysis was the focus on the forward reads instead of the reversed which might cause loss of data.

sequence logos
Figure 13. Detected N-cap and the first internal repeat (IR) of the novel DARPin molecules that bind to the AIP peptide from the files 4 and 6.

What do we know now?

Post NGS analysis, we now comprehend the workflow of any further bioinformatic analysis of raw sequencing reads, beginning with quality control and preprocessing for any desired analysis. In our case, we wanted to detect possible patterns of DARPin molecules that bound to our AIP in the wet-lab phase. However, we were able to only confirm the presence of the N-cap and the variation in the first internal repeat. As previously mentioned, possible contamination events or the non-processing of unknown adapter sequences might explain such events. The analysis also highlighted the difficulty of obtaining high-quality NGS data and how to recognize it using available tools and sequencing depth (i.e., the longer the sequence, the poorer the quality of the data).

Importantly, our proof of concept was successfully confirmed with the control GFP-DARPin (all its sequence content was confirmed in the NGS analysis stage of the project). The latter indicates that future work focusing on a library of thousands of DARPin molecules and the detection of binding AIP molecules would be feasible.

Diffusion Modelling with Dresden


In the beginning of summer we started a partnership with the iGEM team from TU Dresden. The Dresden team, similar to our project, is working on increasing the healing process of chronic wounds. Dresden's approach lies in using phage display to first remove the bacterial infection in the wounds, before applying growth factors to target tissue rebuilding. These would be applied via hydrogel. Using reaction-diffusion dynamics iGEM TU Dresden is modelling the change of concentration and diffusion of the growth factors VEGF and EGF, that are applied to a wound through a hydrogel.

Reaction-diffusion dynamics can likewise also be used in our project, to model how DARPins and AIP diffuse and react throughout a biofilm. Adding to our proof-of-concept and providing further estimation for the application of DARPins, iGEM Dresden team has modelled the reaction-diffusion dynamics of DARPins and AIPs in the biofilm using COMSOL Multiphysics. The following text provides a detailed description of the model and simulations. It has been written by the TU Dresden team and adapted by Aalto-Helsinki for this page. The original description can also be found on Dresden's wiki page.


The aim is to simulate the propagation of DARPins and AIPs inside the biofilm and thus enable the estimation of the amount of DARPins needed for a successful treatment. Moreover, this simulation will provide deeper insights into the required concentration of DARPins to ensure a sufficient time in which AIP will be inhibited.


Reaction - Diffusion Dynamics

The diffusion of DARPins towards and inside a biofilm together with the DARPin-AIP reaction is a reaction-diffusion system, in which the temporal and spatial change of the concentrations of chemical species originate from chemical reactions and diffusion. Mathematically, such systems are modelled as partial differential equations (PDEs) supplemented by initial and boundary conditions: $$ \frac{\partial c_i}{\partial t} \left(\vec{r}, t\right) = \sum_j R_{ij} (\{c_1, c_2, ...\}) + D_i\nabla^2 c_i \left(\vec{r}, t\right), $$ where \(i \in \{1, 2, 3...\}\) — species number, \( j \in \{1, 2, 3...\}\) — reaction number, \(R_{ij}\) — reaction rate — how concentration of the species i changes in the reaction j, \(D_i\) — diffusion coefficients assumed to be constant. Reaction rates \(R_{ij}\) obey the law of mass action.


Simulations of the reaction-diffusion of DARPin and AIP species were performed using COMSOL Multiphysics. The geometry of the system was constructed based on the following considerations:

  • DARPins are likely to be delivered via a layer of a a hydrogel dressing, which would be around 1 mm in thickness;
  • we target S.epidermidis' biofilms that is aerobic and, hence usually formed on the very top of the exudate of a chronic wound, therefore, we can assume there is nothing between the DARPins layer and the biofilm;
  • biofilms are often tens of micrometres in thickness (Wu et al., 2019; Percival et al., 2015).

The schematic geometry (and boundary conditions) is depicted in Fig. 14. It demonstrates the constituents of the system (sizes and proportions are not kept in the picture): a 10 x 10 x 0.1 mm piece of a biofilm covered by a 10 x 10 x 1 mm layer containing DARPins. Additionally, the biofilm is surrounded by wound content (mostly exudate), the size of which was chosen so that the system with only AIPs has a steady state close to the value found in the literature (discussed later).

Schematic geometry.
Figure 14. Schematic system geometry and boundary conditions(bc) (red — absorbing bc., blue — reflective b.c.). "DARPins container" is a hydrogel that would supposedly be delivering DARPins.

Equations and parameters

The system of biochemical reactions taking place inside the biofilm — AIP-DARPin binding and constant production of AIPs by bacteria (A — AIP, I (inhibitor) — DARPin, AI — AIP-DARPin complex): $$ \begin{cases} \rm A + I \underset{k_d}{\overset{k_a}\rightleftarrows} AI \\ \rm \stackrel{R_{prod}}{\longrightarrow} A \end{cases} $$ can be rewritten into the following PDEs system with uniform initial conditions: $$ \begin{cases} \frac{\partial C_I}{\partial t} = R_I + D_I \nabla^2 C_I \\[10pt] \frac{\partial C_A}{\partial t} = R_A + D_A \nabla^2 C_A \\[10pt] \frac{\partial C_{AI}}{\partial t} = R_{AB} + D_{AI} \nabla^2 C_{AI} \\[10pt] C_A (t = 0) = C_{A0} > 0 \\[10pt] C_I (t = 0) = 0 \\[10pt] C_{AI} (t = 0) = 0 \end{cases} $$ where $$ R_I = -k_a C_I C_A + k_d C_{AI}\\[10pt] $$ $$ R_A = -k_a C_I C_A + k_d C_{AI} + R_{prod} \\[10pt] $$ $$ R_{AI} = k_a C_I C_A - k_d C_{AI} \\[10pt] $$ Inside the cream/hydrogel layer, we have only DARPins diffusing out, therefore, the system there reads as: $$ \frac{\partial C_I}{\partial t} = D_{I_{\text{layer}}} \nabla^2 C_I \\[10pt]$$ $$ C_I (t = 0) = C_{I0} > 0$$ and for the exudate: $$ \begin{cases} \frac{\partial C_I}{\partial t} = D_{I_{\text{ex}}} \nabla^2 C_I \\[10pt] \frac{\partial C_A}{\partial t} = D_{A_{\text{ex}}} \nabla^2 C_A \\[10pt] \frac{\partial C_{AI}}{\partial t} = D_{AI_{\text{ex}}} \nabla^2 C_{AI} \\[10pt] C_A (t = 0) = 0 \\[10pt] C_I (t = 0) = 0 \\[10pt] C_{AI} (t = 0) = 0 \end{cases} $$ Boundary conditions are shown in Fig. 14. All parameters used in the simulations are presented in Fig. 15.

Figure 15. Parameters used in the simulations (\(C_{A0}\) and \(C_{I0}\) are discussed in the text).

Rate constants \(k_a, \; k_d\) of Caspase 7 and DARPin reactions were taken from Seeger et al. (2013) (only the highest affinity was tested), production rate \(R_{\text{prod}}\) (Junio et al., 2013) and diffusion coefficients \(D_I, \; D_A, \; D_{AI}\) (Hornemann et al., 2008) were also found in the literature. All three species (DARPin, AIP, and their complex) were considered as rapidly diffusing molecules according to Hornemann et al. (2008).

With no DARPins, the system of the biofilm and wound is in equilibrium and AIP production and diffusion processes are balanced, i.e. the system is in a steady state. The steady state of the system without DARPins can be found numerically by solving the two PDEs: $$ \begin{cases} \frac{\partial C_A}{\partial t} = 0 = R_{\text{prod}} + D_A \nabla^2 C_A \;\; \text{in the biofilm} \\[10pt] \frac{\partial C_A}{\partial t} = 0 = D_{A_{\text{ex}}} \nabla^2 C_A \;\; \text{in the exudate} \end{cases} $$

Modelling of average AIP concentration inside the biofilm shows a steady state (Fig. 16). However, the plateau value strongly depends on the size of the wound exudate region that has absorbing boundaries. Absorbing boundaries imply infinitely fast diffusion outside of the system because molecules that get in touch with them never come back. In the real wound, no 100% absorbing boundaries and infinite diffusion coefficients exist. However, to compensate for the inability to model the whole wound space available for species diffusion, such highly absorbing boundaries have to be utilised. AIP concentration at a steady state found in the literature, \(C_A0\) = 12.5 µM (Junio et al., 2013), was used to tune the size of the wound in the model such that the calculated steady state is close to

Figure 16. Dynamics of the system without DARPins reaching a steady state at 12.5 uM due to the adjusted size of the wound exudate region.

\(D_I, \; D_A, \; D_{AI}\) in the exudate were estimated via the Stokes-Einstein equation: $$ D = \frac{kT}{6\pi\mu r}, $$

where \( \mu\) — dynamic viscosity of the exudate, \(r\) — radius of a particle, \(T\) — body temperature (310 K). Exudates seem to differ in their properties, e.g. in viscosity (WUWHS, 2019). Assuming thin, watery exudate, \( \mu \) can be taken the same as for water at 310 K — \(7 \cdot 10^{-4}$$\frac{\text{kg}}{\text{m}\cdot\text{s}} \). Sizes of the proteins were calculated from the useful (although approximate) relation of molecular weight and protein radius (Erickson, 2009): $$r = 0.066 \cdot M^{1/3}$$ AIP in a biotinylated state has a molecular weight of 5.3 kDa. DARPins synthesised in the laboratory are usually between 14 and 21 kDa and the average of 17 kDA was taken for the simulations. The molecular weight of the AIP-DARPin complex is 22.3 kDa accordingly, which yields the diffusion coefficients in water (exudate) shown in Fig. 3.

The diffusion coefficient of DARPin inside the layer was taken of the same order of magnitude (~10 \(um^2 \) \(/s \) ) as for growths factors within non-affine PEG/PEG hydrogel (SDF1 \( \alpha\), VEGF165, EGF, VEGF121 — 20-90 \(um^2 \)/\(s\)) (Limasale 2019) which can serve as a future delivery method.


\(C_{I0}\) — initial concentration of DARPins — is a variable and was tested for two types of biofilms: 3.5 and 5.5 days old. Graphs of concentration change show the optimal \(C_{I0}\) — initial concentration of DARPins, which ensures a big enough time span (at least 600 min) until the level of AIP recovers to 50 % of its initial concentration (6.25 µM). For both biofilm ages, the DARPin concentration should be at least 30 µM (Fig. 17, only one type of biofilm, here the 3.5 days old, is presented since the graphs are almost the same). At 10 µM of DARPins AIP concentration drops only by 20 %, while at 30 µM and 50 µM AIP concentration decreases more than by half and slowly recovers. The upper boundary of the optimal concentration depends on the possible side effects and acceptable amount of DARPins inside a body, which requires further research.

Figure 17. Average concentrations of DARPin, AIP, and their complex inside the biofilm over time at different initial concentrations of DARPins \(C_{I0}\): 10 uM (a), 30 uM (b) and 50 uM (c). \(C_I\) curve is not at 0 as it might seem, it is just small compared to the others.

The presence of absorbing boundary conditions can lead to the underestimation of the actual times needed for AIP level to recover as DARPins are simply absorbed faster than in the real system. Yet, such a diffusion model (upon verification with experiments) is a useful tool to predict inhibitor concentration sufficient to prevent the development of biofilms depending on the method of DARPin delivery (e.g. a hydrogel dressing as was assumed in the model) and parameters describing inhibition of quorum sensing.

This also suggests the possibility of combining biofilm formation inhibition through DARPins with Dresden's delivery method. Dresden imagines, medical workers could have a set of three hydrogel patches: the first one would contain DARPins and stop biofilm formation, so that the antimicrobial treatment will become efficient, the second one would deliver bacteriophages to eliminate bacterial infection, and the last patch would bring growth factors to the wound stopping inflammation and increasing general wound healing.

What do we now know?

Thanks to the diffusion-reaction modelling done by the Dresden team we now have more concrete insights into how to implement a possible treatment with DARPins. From the calculations it can be concluded that 30 µM of DARPins administered via a hydrogel would be needed to slow down AIP communication and reduce their amount by 50 % for 10 hours. This gives us some realistic understanding of how the DARPins need to be applied and how often this application needs to be repeated to keep up the inhibition of AIPs. Concretely this indicates applying at least 30 µM of DARPins via a hydrogel directly to the wound and to repeat this step at least every 10 hours to get a sufficient reduction in AIP. Further consideration regarding the implementation can be found here.


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