Team:Tunghai TAPG/Model

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Introduction

Eco-Life is through the atomizing way to diffusion, it can help us fix the Health-acquired Infection (HAI) problem to get surrounding clean. We cooperated with dry lab and through small-scale experience to predict how the Eco-Life model works. During the process, we can figure out the optimizing ratio of the JJ01 concentration to reduce the associated cost of expenditure and achieve more results with less effort, and guide consumers to arrive at the best setting/operation mode of our product. In the dry lab team, we have combined the result of the antimicrobial activity in antibacterial agent and three environment factor: time, concentration and diffusion distance and searching for the documents to get the final model.

The models are based on E. coli to discuss.

  1. 1. Concentration-Killing Model (CKM)
  2. 2. Time-Killing Model (TKM)
  3. 3. Concentration Diffusion Model (time & Radius & combinational 3D model)
  4. 4. JJ01 Effect Curve

    Model 1.Concentration-Killing Curve (CKC)

    Concentration-Killing Curve (CKC) is to explore the optimal concentration of antimicrobial effects of the winning peptide (JJ01) at room temperature. Model (Fig.1) is agree with reference1 and set up with calculation.

    Fig.1. The CKC Model of JJ01 .

    N0 = initial concentration (μg/mL)

    r = bactericidal intensity

    BC50 = median bactericidal concentration

    c = peptide concentration

    The maximum bactericidal dynamics of JJ01 at a concentration of 50 μg/mL could be seen in the model, and the peptide at 125 μg/mL reduced the number of bacteria to close to 0.

    Model 2.Time-Killing Curve (TKC)

    The time-killing curve (TKC) is intended to explore the antibacterial effect and optimal duration of action and duration of action of the peptide (JJ01) at room temperature. Time killing curve (Fig.2.) establishment by calculation and reference2.

    Fig.2. The TKC Model of JJ01 .

    Y0 is the decimal logarithm of the bacterial population was observed

    Ym is the decimal logarithm of the minimum observed number of living cells

    α accounts for the intensity of the bactericidal

    It could be seen from the model that JJ01 grew the number of sterilizations over time at room temperature and reduced the amount of bacteria to close to 0 at 100 min.

Model 3.Diffusion Model (DM)

Concentration Diffusion Model is divided into three way to express, including time, radius and combinational 3D Model. Concentration Diffusion model (time) is primarily used to explore the duration and effectiveness of Eco-Life's diffusion in a wide range of spaces, and this experiment can help to understand the spraying intervals to help maintain low-bacteria concentrations. The Concentration Diffusion Model (Radius) is the longest way to understand the space between device installations by analyzing the maximum amount of antibacterial effects to achieve a dead-end environmental purification effect. Finally, a three-phase map is made using the Concentration Combinational 3D model to arrive at the best conditions for the antibacterial agent cast/concentration-time-space-space grid to facilitate the planning of the best setting/operating mode of the product.

The assumptions for the diffusion model are:

  1. a. The concentration at r = L is 0

  1. b. The concentration changes with radius and time.

We want to simulate the diffusion of peptides in space. We turn Fick’s law into a spherical coordinate. After solving the differential equation, we get the following equation:

C=Peptide Concentration (μg/mL)

Co= Initial Peptide Concentration

L= Length of space

Dm= Diffusibility

r= Radius

And the diffusion curves are as follows:

Fig.3. The Concentration Diffusion Model (Time) of JJ01.

Fig.4. The Concentration Diffusion Model (Radius) of JJ01.

Fig.5. The Concentration Diffusion 3D Model of JJ01. This is an animated schematic in the case of continuous release of the product.

Model 4. JJ01 Effect curve

In order to understand the interrelationship between the three factors, our team then publicly deductions and calculations of the conditions of the product (time, concentration, diffusion distance) to arrive at the Effect Curve (Fig.6.). This model can be effective and well-founded on the formulation ratio of antimicrobial agent adjustment and optimization, thereby reducing the associated cost of expenditure, achieving the effect of doing more with less, and for consumers to obtain the best setting/operation mode. From this graph, we can clearly notices the amount of bacteria in space changes over time.

Fig.6. The Effect Curve of JJ01.

Nt=number of bacteria

N0=initial number of bacteria

Kmax=maximum bacteria kill rate

K0=bacteria growth rate constant in the absence of peptide

EC50=peptide concentration necessary to achieve half of maximum effect

C=peptide concentration

As can be seen from the final utility diagram, the recommended concentration of our product should be 150 μg/mL, and the interval time should be 100 min for optimal sterilization results when continuous injection.

Reference

  1. 1. Liu, Y. Q.; Zhang, Y. Z.; Gao, P. J., Novel concentration-killing curve method for estimation of bactericidal potency of antibiotics in an in vitro dynamic model. Antimicrob Agents Chemother 2004, 48 (10), 3884-91.
  2. 2. Guerillot, F.; Carret, G.; Flandrois, J. P., Mathematical model for comparison of time-killing curves. Antimicrob Agents Chemother 1993, 37 (8), 1685-9.