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Section 4

Fluorescence Visibility Justification

The human eyes cannot perceive objects that are smaller than a certain size. Also, they cannot recognize light whose intensity is lower than an inherent threshold. We take these limitations into account to determine the number of fluorescent proteins that must accumulate before we can notice any fluorescence, and establish the minimum circular area required for us to perceive any fluorescence. Therefore, the objective of this modeling is following:

   To investigate concentration required for an amount of fluorescent protein in the E.coli that makes light from E.coli be visible for human.

1. Background

Human has the limits in vision. For our objective, we have to know about the limit of recognizing size of objects in human vision. This limit is called the ‘Minimum visible acuity’. The exact definition of minimum visible acuity is the minimum size of object that the human eyes can discern. In Table 1. Types of visual acuity^[1], the value of detection acuity(red box), ~1.0 arc second, is the minimum visible acuity that we take.

Table 1 | Types of visual acuity^[1]

We assume that the E. coli is in a darkroom for discovering the minimum number of fluorescent protein. In this reason, we use 0.1 lx, the minimum intensity of light that cone cells in human can perceive. ^[2] In fig 1 (a), There is a brief picture for minimum visible acuity. We choose that 1 second is the basic time scale, so have to know the number of fluorescent protein per 1 second. By our research, The range of the photon emitted time is wide, from to Although it hasn’t any theoretical reason, we choose the photon emitted time by a fluorescent protein, .^[3]
We will proceed this modeling by using the energy of photons for relating the light and the number of fluorescent protein. One of the unit for light is lm(lumen) and this unit is transformed to J(joule) in 1 lumen.

^[4]

In fig 1 (b), There are two values that we will use.

2. Analysis & Result

For achieving our objective, first we assume that the pictures by E.coli are located at 1 meter from human eyes. From the Background, minimum visible acuity of human is ~1.0 arc second. ~1.0 arc sec, equivalent to the following

Minimum visible acuity of human =
  Since it is a very small quantity, it can be approximated as
Minimum visible acuity of human =
  Hence, the smallest object at a distance 1 meter away discernable to the human eye occupies the minimum visible acuity of human. Additional explanation by illustration will follow in fig 1 (a). Then, we calculate the number of fluorescent protein per second in the discernable area. The cone cells in the human retina recognize green, yellow, red, blue emitted by the GFP, YFP, RYP, and CYP. They detect light with intensity greater than 0.1 lux. Therefore, objects must emit light with the following luminous flux if they are to be discernable at a meter away.

  Because the energy of a photon emitted by a single GFP is the following,

  it takes about for a fluorescent protein to emit a photon, approximately photons are emitted per second. Thus, the energy emitted by a GFP per second is,

  In order to satisfy this value, we need fluorescent proteins per second in minimum visible acuity of human. Unfortunately, it’s not sure that the photon emitted time is . We cannot get any scientific basis for our choice. If we get any theoretical basis for our choice or other reliable value, this result will be more credible.

3. Conclusion

Dividing minimum visible acuity of human by the two dimensional area of E. coli yields E. coli, in conclusion, the human eye can perceive color if each E. coli in minimum visible acuity of human of area produces 0.00257 fluorescent proteins. In other words, 1000 E. coli must make a total of 3 fluorescent proteins. In real life, however, more fluorescent proteins will need to be produced because light emanating from the background may mask the emitted light. This result corroborates the validity of the assumption, used in session 5, that fluorescent proteins produce color instantly upon translation.