7.3 Decoding

81

the meteorologist could scarcely have made sense, in his head, of the stream of pixel

densities, but as soon as they were interpreted by writing them down as black and

white squares (which he could have done with a pencil on paper had he been aware

of the structure of the information, especially the order in which the pixels were to

be arranged) it would have been apparent that they code for a picture; that is, there

is a jump in meaning. So it is in biology—the amino acid sequence is structured in

such a way that meaning is accrued, not only as a three-dimensional structure but as

a functional enzyme or structural element, able to interact with other molecules.

Coding—signal transduction—is ubiquitous throughout the cell and between

cells. Typically, a state of a cell is encoded as a particular concentration level of a small

molecule (cf. Tomkins’ (1957) “metabolic code”). For encoding this kind of infor-

mation, a small number of small molecules, such as cyclic adenosine monophosphate

(cAMP) and calcium ions (CaSuperscript 2 plus²⁺), is used. The chemical nature of these molecules

is usually unrelated to the nature of the information they encode (see Chap. 23 for

details).

7.3

Decoding

The main requirement for decoding in a transmission scheme is that the coding

transformation is one-to-one and, hence, each encoded symbol has a unique inverse.

In biological systems, decoding (in the sense of reconstituting the original message)

may be relatively unimportant at the molecular level; the encoded message is typically

used directly, without being decoded back into its original form as envisaged in

Fig. 7.2.

The problem of decoding the simple transformations described in the previous

section is straightforward. Consider now a scheme for encoding that uses a machine

that can be in one of four states StartSet upper A comma upper B comma upper C comma upper D EndSet{A, B, C, D} and that the transformation depends

on an input parameter that can be one of StartSet upper Q comma upper R comma upper S EndSet{Q, R, S}. In tabular form,

StartLayout 1st Row 1st Column down arrow 2nd Column upper A 3rd Column upper B 4th Column upper C 5th Column upper D 2nd Row 1st Column upper Q 2nd Column upper D 3rd Column upper A 4th Column upper B 5th Column upper C 3rd Row 1st Column upper R 2nd Column upper C 3rd Column upper D 4th Column upper A 5th Column upper B 4th Row 1st Column upper S 2nd Column upper B 3rd Column upper C 4th Column upper D 5th Column upper A EndLayout

↓

A

B

C

D

Q

D

A

B

C

R

C

D

A

B

S

B

C

D

A

(7.1)

Given an initial state, an input message in the form of a sequence of parameter values

will result in a particular succession of states adopted by the machine; for example, if

the machine (transducer) starts in stateupper BB, the parameter streamupper Q upper Q upper S upper R upper QQQSRQ will result

in the subsequent output upper A comma upper D comma upper A comma upper C comma upper BA, D, A, C, B. In tabular form,

StartLayout 1st Row 1st Column Input state colon 2nd Column upper Q 3rd Column upper Q 4th Column upper S 5th Column ellipsis 2nd Row 1st Column normal upper T normal r normal a normal n normal s normal d normal u normal c normal e normal r normal s normal t normal a normal t normal e colon 2nd Column upper B 3rd Column upper A 4th Column upper D 5th Column upper A EndLayout

Input state:

Q

Q

S

. . .

Transducer state:

B

A

D

A

(7.2)