Chapter 3

Regulation and Control

3.1

The Concept of Machine

“Machine” is used formally to describe the embodiment of a transformation (e.g.,

Eq. (3.1); cf. the automata in Sect. 12.1.1). In this formal sense, it does not have

any particular connotation of animate or inanimate. The essential feature is that the

internal state of the machine, together with the state of its surroundings, uniquely

defines the next state to which it will go. It is, therefore, a suitable abstraction of a

biological entity qua an information processor. A determinate machine is canonically

represented by a closed, single-valued transformation (3.1) and (3.2); a Markovian

machine is indeterminate insofar as the transitions are governed by a stochastic matrix

(e.g., (3.3)); the determinate machine is clearly a special case of the more general

Markovian machine.

If there are several possible transformations and a parameter governs which trans-

formation shall be applied to the internal states of the machine, then we can speak

of a machine with input, the input being the parameter. The machine with input is

therefore a transducer (cf. Sect. 7.3).

A Markovian machine with input would be represented by a set of stochastic

matrices together with a parameter to indicate which matrix is to be applied at any

particular step. If these parameters are themselves controlled by a stochastic matrix,

then we have a so-called hidden Markov model (Sect. 17.5.2).

3.2

Regulation

Regulation may be considered in abstract terms common to any mechanism, whether

living or not. The essential elements of a regulatory system are shown in Fig. 3.1.

The lines connecting the components indicate communication channels. The dotted

lines indicate the paths along which the regulator can receive information about the

disturbance. By way of illustration, consider the operation of a simple thermostatted

© Springer Nature Switzerland AG 2023

J. Ramsden, Bioinformatics, Computational Biology,

https://doi.org/10.1007/978-3-030-45607-8_3

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