us apply the theory Shannon's information to calculate how many bits (binary symbols) contains a bacterium. The theory of Shannon information can be summarized in a single formula:
H = - Σp (x) log p (x) / log 2
where:
H = amount of information measured in bits.
p (x) = frequency of each of the elements of a message.
This algorithm determines the minimum number of units or bits of information needed to send a message. The universality of this theory is that one can speak of messages in a broad sense and applies whenever there is a flow of information between two systems. There is a parallel between this equation and the formula of Boltzmann entropy that measures the level of disorder of a system. The theory of information, on the contrary, we quantified the degree of order of the systems between which there is information flow, and thus we can measure the degree of complexity of that system.
Tindallia californiensis
To quantify the degree of ordering to bacteria has been made since the beginning of the evolution we consider it as a volume divided into M atoms. A bacterium is more or less complex depending on their size and chemical composition (not the same bacteria-rich proteins that confer multiple functions that the lipid-rich bacteria.) So for the same volume and for the same chemical composition, different configurations are available to swap the position of atoms in the volume. For a given configuration, the chemical bonds between neighboring atoms can be distributed in space in different ways. If we call N 'the number of atomic configurations of the bacteria and B' the number of bound states for each configuration, then we get that N = N 'x B' where N is all possible states for the above bacteria. Of all these states only L of them correspond to the living state of the bacteria, so that the probability of being in a living state is L / N. As you can guess L is a very small number so that we can consider that the probability is 1 / N. Although the N states are not equiprobable then follow the distribution law Maxwell Boltzman we will consider them as such. Thus we conclude that H = log N / log 2 for the living state of the cell, ie for a particular cell.
The set of atoms M is composed of chemical elements that make a living (n) so that M = Σ n The number of atomic configurations is then N '= M! / Πn!. The number of bound states for an atomic configuration is B '≈ B = Π an elevated Bi, where Bi are independent ways in which an atom can distribute their links with their neighbors.
Thus N = N 'x B'
log N / log 2 = log N '/ log 2 + log B / log 2
H = log N / log 2
H = log N' / log 2 + log B / log 2
Using Stirling's approximation which states that x! High x ≈ x we \u200b\u200bobtain H = M log M / log 2 - Σ n log n / log 2 + Σ n log Bi/log2.
Simplifying the different n of a living are the following chemical elements: C, H, N, O, P, and S constituting 99% of the biomass of the bacteria. The watery part of the bacteria is neglected, it is not relevant to their structure, so that the weight of the dried bacteria is 10 raised to -13 g. According to data values \u200b\u200bfor different elements (n) are:
C: 2.4 x 10 to 9.
H: 4.2 x 10 to 9.
N: 6.1 x 10 to 8.
O: 4.7 x 10 to 8.
P: 2.3 x 10 to 7.
S: 1.3 x 10 to 7.
To calculate the various Bi assume that each atom is in the center of a cube that can be bound to atoms located in the 6 adjacent cubes. If the number of valences of each element is r, the number of distributions of r bonds between the 6 cubes is determined by the formula:
Bi = (m + r -1)! / R! (M -1)!
Thus:
H: Bi = 6
O: Bi = 21
N: Bi = 56
C: Bi = 226
etc.
Substituting all the values \u200b\u200bwe obtain H ≈ 46.000.000.000 bits. To get an idea of \u200b\u200bwhat this value, the amount of information of all the interconnections of the telephone network in the United States has a value of 2,300,000,000 bits. Thus we conclude that the amount of information from the simplest of living is 20 times greater than that of one of the most complex ever human talents created.
Bibliography: "Artificial Life: from chaos to order" José Gabriel Segarra
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