Our modelling for the use of antimicrobial peptides (AMP) in plaster can be categorized into three main areas:
1. Reaction kinetics on the inhibitory action of bacterial growth (current page)
2. Bioinformatics studies of Antimicrobial Peptides in BSF
3. Phylogenetic analysis by MEGA
To model the impact of antimicrobial peptides (AMPs) on bacterial growth, an Ordinary Differential Equation (ODE) model is used. Ordinary differential equations (ODEs) are mathematical models that illustrate how the state of a system changes over time as a function of its current state and some parameters. It allows for the prediction of bacterial population dynamics over time in response to varying concentrations of antimicrobial substances1.By employing the ODE model and analysing the obtained results, we can approximate the necessary quantity of AMPs to be incorporated into the plaster to effectively hinder bacterial growth to prevent infection. Furthermore, the optimized duration for which the plaster remains efficacious in inhibiting bacterial proliferation can be ascertained. The combination of ODE models with experimental data offers valuable insights into the intricate interactions between AMPs and bacteria. Consequently, these insights can guide the development of disinfectant plasters aimed at preventing bacterial infections.
For simplification, the focus is placed on bacteria capable of forming colonies, while deceased or non-viable ones are disregarded. Additionally, it is assumed that once a bacterium binds to a single antimicrobial peptide molecule, its colony-forming ability is lost. If no peptide bind to the bacteria, then it follows exponential growth. Also, the interaction of antimicrobial peptides and bacteria is regarded as a first-order reaction, indicating that the rate of binding is directly proportional to the concentrations of both reactants, i.e. the bacteria and antimicrobial peptides.
Besides, we have additional assumptions to simplify the situation. The plastic plaster containing antimicrobial peptides is assumed to be securely attached to the skin's surface, thereby suggesting that no additional bacteria are introduced to the wound after its coverage. Furthermore, the temperature of the skin's surface is assumed to remain constant, eliminating the possibility of sudden and significant bacterial growth due to temperature variations. In addition, it is assumed that there is no leakage of antimicrobial peptides from the plaster into the environment. Additionally, the intermediate involved in the reaction is assumed to be short-lived and can be neglected using the steady-state approximation. Also, the antimicrobial peptide is assumed to be evenly distributed on the plaster, ensuring its uniform presence throughout.
Based on these assumptions, the following equations are constructed:
The variables involved in the process are as follows:
The equations above correspond the following rate laws:
In addition, the rate constants involved in the process are as follows:
Due to the lack of wet lab data, the rate constants k1, k-1 and k2 are estimated with reference to a time-kill assay obtained from a literature review2. This was done by measuring the number of viable bacteria present at different time points after being exposed to the antimicrobial peptides. At different time intervals, a certain sample was taken to count the number of colonies on it after a serial dilution. Regarding the time-kill assay, scientists will collect the same mass of the tissues of the experimental subject in every specified time period to investigate the doubling time of the bacteria.
On the other hand, k3 can be estimated by (ln 2) / TD, where the doubling time (TD) is the time required for the bacteria to double in number.
In microbiology, the “105 guideline” is a widely accepted concept that a level of bacterial growth > 105 viable organisms per gram of tissue is necessary to cause wound infection and can be used to diagnose infection8. For wound that shows sign of infection, proper medical treatment from professional should be seek, instead of applying plaster. Hence, the initial number of bacteria used in the model is set to be 1x105 cfu/ml.
There are several limitations in estimating the rate constants by a time-kill assay. According to the time-kill assay, the expected error is that we can’t estimate the exact value of the rate constants k1, k-1 and k2. To determine the exact value of these three rate constants, a different assay must be used, e.g., binding assay between ‘E’ and ‘B’. However, through the time-kill essay, we can determine their values relative to each other and other constants, like the growth rate k3. For k3, which is inversely proportional to the doubling time of the bacteria, the growth rate of bacteria in a wound may differ from the growth rate in a controlled environment due to factors such as temperature, pH, oxygen level, host response, etc. For example, the CA-MRSA (Community-associated MRSA infections) multiplied much faster with a doubling time of 28 minutes while HA-MRSA (Health care-associated MRSA infections) strains take 39 minutes3. Thus, the doubling time of different bacteria is not the same within different conditions. As a result, the recovering time for the injuries after sticking the plaster above is dependent.
The rate of k1, k-1 and k2 is estimated from the time kill array in Figure 1, where the three unknown parameters of the model were fitted to best approximate the time kill array via a python script. The fit result in the rate of k1, k-1 and k2 gives 1.91, 22.0 and 7.36 respectively.
Figure 1 (reproduced from [2])
The rate constant of bacterial growth k3 is estimated using the reference of community-associated MRSA infections (CA-MRSA), i.e. ~28 mins. Hence k3 is considered as 1.49 h-1 5
With the estimated rate constant, the following graphs are constructed by a python program to demonstrate the change in the number of AMP and the bacteria in the plaster:
Initially, the AMP applied in the plaster bind the bacteria.The number of bacteria [B] fall with time as they are killed by the AMP [E] added in the plaster. However, as some of the bacteria survive and keep dividing, the number of bacteria rise again after the 8th hour. That raise our concern as it might cause serious infection even when the plaster is applied.
The focus of our project is to utilize antimicrobial peptides (AMPs) to inhibit bacterial growth in wounds, preventing wound infections. So as to determine the appropriate treatment using the ODE model developed, several criteria must be considered.
Firstly, the number of AMPs used should be sufficient to reduce the bacterial concentration to a standard level, ensuring a safe and acceptable approach for wound healing. While, the number of AMPs should be minimized to avoid excessive costs in healing and the development of resistance in bacteria.
Secondly, the concentration of AMPs within a piece of plaster must be adequate to effectively encounter bacteria for a reasonable period, preventing the need for frequent changes. The fixed inhibition time is recommended to be 20 hours or more, so that people only need to change the plaster once a day.
In short, the minimum number of AMP needed to inhibit the growth of bacteria in wound so that they are kept at an acceptable standard for more than 20 hours should be found.
Then the following graphs are constructed by adjusting the initial value of AMP to test out different situations and interpret them.
Figure 3 (Number of bacteria: 1 x 105 unit/ml, Number of AMP: 1 x 105 unit/ml)
In Figure 3, an extremely low amount of AMP is used. The number of bacteria increased continuously after its slight decrease until the 6th minute. At the same time, the number of AMP has been decreasing sharply since the beginning. This shows that with inadequate amount of AMP present, the bacterial growth cannot be inhibited effectively. The infection will be worsened.
Figure 4 (Number of bacteria: 1 x 105 unit/ml, Number of AMP: 1 x 1050 unit/ml)
In Figure 4, an extremely high amount of AMP is used. The number of bacteria decreased rapidly from 105 to 0 within 0.1 hour, accompanied by a slight decrease in the number of AMP. Subsequently, the number of AMP remained unchanged, indicating that all bacteria in the wound is killed. Although excess AMP is effective in eradicating all bacteria, it is not cost-effective due to the surge in production cost.
Figure 5 (Number of bacteria: 1 x 105 unit/ml, Number of AMP: 1 x 1014.9 unit/ml)
In Figure 5, the initial number of AMPs is 1 x 1014.9 units/mL, which is higher than the number of bacteria at 1 x 105 units/mL. This initial number of AMPs is sufficient to suppress the growth of bacteria for 21 hours, effectively preventing infections. After the 21st hours of encountering the bacteria, the AMPs retain a relatively smaller surplus. This indicates that the number of AMPs are cost-efficient in their effectiveness against the bacteria.
Figure 5
In Figure 5, it shows the minimum required initial number of AMPs (log 10 no./mL) required to suppress the respective initial number of bacteria (log 10 CPU/mL) for 21 hours. When the level of bacterial growth exceeds 105 viable organisms per gram of tissue, there is a high likelihood of causing a wound infection. To prevent infection, it is necessary to suppress the initial number of bacteria below 105 in order to prevent bacterial growth from exceeding this threshold.
According to Figure 5, the minimum required initial number of AMPs to counteract 5 (log 10 CPU/mL) bacteria is 14.88469 (log 10 no./mL). This value is considered the desired condition of AMPs to be coated on the disinfectant plaster. Hence, this model provides a valuable reference for us in the application of AMP in the plaster.
There may be uneven distribution of AMPs on the plaster when applied to the wound. As a result, some areas of the wound may be exposed to the external environment, particularly when the plaster is not applied to a flat surface such as the knee or elbow. In such cases, it is uncertain whether increased bacterial growth may occur, and if it does, the fixed amount of AMPs determined by the model may not be sufficient to encounter the excess bacteria.
Secondly, the ODE model may not capture all the complexities and dynamics of the system, such as whether the bacteria have any counter measure to protect itself from AMP.
Another case is that the AMP might be inhibited by the medicine applied by the user on top of the wound. As the plaster is air permeable, the bacteria and particles in the air will inhibit the binding of the AMP with the bacteria in the wound. It remains uncertain whether bacteria will develop resistance to AMPs, which could reduce the effectiveness of bacterial eradication.
Thirdly, it is unknown whether the undegraded dead bodies of bacteria can form an impermeable barrier to the AMPs, preventing their penetration into the underlying layers of the skin and inhibiting the killing of remaining living bacteria. In the presence of a biofilm, the effectiveness of AMPs in eradicating bacteria is limited, as they are unable to effectively eliminate bacteria residing beneath the biofilm.
Moreover, the impact of environmental factors on the antimicrobial activity of AMPs requires further investigation. Factors such as pH value or the permeability of the plaster to the atmosphere need to be studied to determine their influence on the efficiency of AMPs in killing bacteria.
To sum up, the aim of the investigation of this project is to facilitate human life by extracting the DLP4 from the black soldier fly. Furthermore, the study focuses on the use of an Ordinary Differential Equations (ODE) about the impact of antimicrobial peptides (AMP). As a result, the research concluded that the antimicrobial peptides are natural and synthetic molecules that can kill or inhibit bacteria. On the other hand, the combination of the ODE model and experimental data provides insights into the interaction between AMPs and bacteria, guiding the development of disinfectant plasters for preventing bacterial infections. By applying the ability of antimicrobial peptides (AMPs) to inhibit bacterial growth in wounds, preventing wound infections, thus the recovering time for the users who use the plaster will be hopefully shorter and has a lower risk to experience a bacteria infection of the wound. Nevertheless, it is acceptable to replace a new plaster per day only since the plaster invented will be more long-lasting. Lastly, the new-invented plaster is highly recognized to be more user-friendly.
The non-pest insect Hermetia illucens, also known as the Black Soldier Fly (BSF), is among the most promising sources for AMPs being able to live in hostile environments rich in microbial colonies. Among the 57 identified active antimicrobial peptides in BSF, they can be classified to different classes of AMPs including defensins, cecropins, attacins and lysozyme7 (Fig. 1).
Figure 1. Graphic representation of the identified AMP classes from BSF (reproduced from [1])
Among those AMP, defensins, cecropins and attacins are among the most common and well-studied insect antimicrobial peptides (AMPs) that have broad-spectrum activity against bacteria, fungi, parasites, and viruses8.
In order to define the scope of our investigation, the antimicrobial peptide’s database, CAMP, is employed to analyze the sequence, structure and activity of AMPs with a focus on structural-functional relationships and their potential applications.
With the help of experimentally validated dataset, the entire sequences of AMP can be scanned to predict its antimicrobial activity based on the machine learning algorithms - Random Forests model adopted by CAMP to identify antimicrobial regions9. The required dataset is divided into 2 classes. The positive class which stands for the experimentally validated AMP sequences and the negative class which stands for the proven non AMPs.
With the help of experimentally validated dataset, the entire sequences of AMP can be scanned to predict its antimicrobial activity based on the machine learning algorithms - Random Forests model adopted by CAMP to identify antimicrobial regions3. The required dataset is divided into 2 classes. The positive class which stands for the experimentally validated AMP sequences and the negative class which stands for the proven non AMPs.
Note: Peptide is predicted to be antimicrobial if the probability is ≥0.5
According to the result, all these four classes of peptides have a probability higher than 0.5. It implies that they should possess the ability to kill bacteria. HI-attacin and Stomoxyn ZH1 have relatively lower scores compared to the others. On the other hand, DLP 1-4 and CLP 1-4 are predicted to have the highest antibacterial ability. Hence, the seven of them are chosen for the further investigation of the iGem project.
Among the seven AMPs chosen in the study, DLP4 extracted from BSF is being proved to be antimicrobial10, while other AMPs, e.g. DLP211, DLP3, CLP112 might also have potential antimicrobial capacity. Hence, the relationship between the sequences is analyzed in order to provide insight in terms of their structure and function by phylogenetic analysis in Molecular Evolutionary Genetics Analysis (MEGA).
To carry out the analysis, an amino acid sequence alignment is created. The amino acid sequence of DLP1-4 and CLP1-3 from black soldier fly are located. Then, amino acid sequences are uploaded to MEGA Version 11 and aligned by MUSCLE, which is a computer algorithm for multiple sequence alignment of protein and nucleotide sequences. Finally, the neighbor-joining method, which is a bottom-up (agglomerative) clustering method for the creation of phylogenetic trees13, are used to construct a phylogenetic tree for comparison.
The method of neighbor-joining with 100 bootstrap replications is used to construct the phylogenetic tree for comparison. Neighbor-joining is calculated based on DNA or protein sequence data14. Calculations of the distance from each of the taxa in the pair to the new node and the distance from each of the taxa outside of this pair to the new node are carried out. Then, algorithm is started again with replacing the pair of joined neighbors with the new node and using the distances calculated in the previous step. The phylogenetic tree is finally created.
Figure 1 - The phylogenetic analysis of the seven AMPs
- From the phylogenetic tree constructed, DLP1and 2 shows a small difference with 0.078 amino substitution per site. DLP 1 and 3 also have small differences with a 0.142 amino substitution per site. The difference between DLP1and 4 is also small with 0.142 amino substitution per site . With the evidence that DLP4 displayed potent antimicrobial activity against bacteria.
- CLP1 is proved to be antimicrobial too. CLP1 and 2 has a 0.084 amino substitution per site, CLP1 and 3 has a 0.133 amino substitution per site. Both CLP 2 and 3 have a similar amino acid sequence to CLP 1. Therefore, we hypothesized that CLP 2 and CLP3 are antimicrobial. It is worthwhile to expand the understanding on the antimicrobial activity of DLP1-4 and CLP1-3.
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