Microsystems for Bioelectronics

30% of the wet weight and thus is ~3  10–13 g. Multiplying this number by the percentage of

a given element in the composition yields the total mass, m

at

, of corresponding atoms in the cell (third

column in Table 6.3). The number of atoms of the given element can be calculated based on:

N

at

¼

m

at

ð1 amuÞ,M

(6.29)

Where 1 amu ¼ 1.66  10

–24

g is the atomic mass unit and M is the molar mass of the corresponding

element (see Box 2.2 in Chapter 2). The resulting number of atoms in the cell is given in the fourth

column of Table 6.3.

This estimate results in the total number of atoms in an E. coli cell ~ 3  10

10

.

Next, the the amount of information that needs to be processed to assemble a new cell can be

calculated using (6.28) with K ¼ 3  10

10

, N ¼ 10, and n ¼ 32 bit:

I

cell

w 3,10

10

,ðlog

2

10 þ 3,32Þw3,10

12

bit (6.30)

Expression (6.30) represents an upper bound on the information content that must be processed to

assemble a new cell. This estimate can be refined in a number of ways [4]. For example, since the

atomic composition, i.e. the frequency of occurren ce of different elements, is kn own (Table 6.2), the

Shannon Equation (6.23) can be used for a more accurate estimate of I

1

(left to readers).

Earlier in this chapter, close relations between information and thermodynamic entropy of

a system were briefly discussed. In fact, this relationship has allowed for experimental estimates of

the information content of living cells based on microcalorimetric measur ements. It has been

concluded that the major consumption of energy during a cell’s reproduct ion cycle arises from the

correct placement of molecules within the cell [8]. The experimental information estimates for

bacteria range from 10

11

–10

13

bits per cell [8]. Note that result (6.24) correlates well with exper-

imental estimates. In the following, the conservative edge of the estimated range, i.e. I

cell

~10

11

bits, is used.

6.3 ABSTRACT INFORMATION PROCESSORS

6.3.1 Turing machine

Alan Turing designed a paper model for universal computation which solves a broad spectrum of

mathematical and logical probl ems in a finite number of steps [12]. This model, now called the Turing

machine, is a hypothetical device that manipulates a finite set of symbols (in the simplest case ‘0’s and

‘1’s) according to a finite set of rules. The Turing machine consists of a line of symbols written on an

infinite tape and a monitor or a read/write head wi th a finite number of internal states, i.e. finite

automaton. The monitor reads a symbol from the input tape and consults its rule list. It then performs

two actions: (i) it modifies the internal state of the monitor and (ii) it writes a symbol on the output tape

(in the original design there was one input/output tape, later, machines with two and more tapes were

proposed). A diagram of the Turing machine is shown in Figure 6.2a. Further developments of this

concept led to the Universal Turing Machine that was a prototype of a general-purpose computer –

a machine that could perform all possible numerical computations [13]. All practical computers have

capabilities equivalent to the Universal Turing Machine.

6.3 Abstract information processors 163