The Boolean Kinetics of signal transduction

Abstract

Volume 4(5): 1-8 with electronic circuits [3]. Information is processed in the nervous system by networks of neurons, each of which, at any particular time, is either charged or discharged, without a stable intermediate state.We shall here concentrate on an evolutionarily more primitive form of information processing, the control of gene expression by signalling pathways, and will show that these pathways can be described as Boolean logic circuits.A recurring concept in Boolean logic is that of material implication: The statement A → B (A implies B) means that if A is true, then B is true. In many computer languages this is expressed as IF A THEN B. This is clearly an underlying rule of biochemical systems. In the presence of an enzyme that converts substance A to substance B, if A is present, then B will be present. Unlike chemical kinetics or enzyme kinetics, which are concerned with amounts of substances and rates of their interconversion, here we are only concerned with whether B is present (TRUE) or not (FALSE). The three basic relationships of Boolean algebra are AND, OR, and NOT. To make adenosine 5'-phosphate (AMP) in a cell, in the presence of adenosine kinase, we need its two substrates, adenosine and ATP. If both are present, AMP will be present. If either substrate is absent, AMP will be absent. In fact, in addition to this so-called salvage pathway, some cells, particularly liver cells, can make AMP by the alternative (de novo) pathway, from adenylosuccinate (SAMP), in presence of the enzyme adenylosuccinate lyase [4]. We could express this asThe Boolean Kinetics of signal transduction Robert C Jackson* Pharmacometrics Ltd., UK AbstractHeredity and environment interact at the level of gene expression, controlled by transcription networks, which in turn are driven by signalling pathways. Unlike metabolic pathways, what is transmitted by signalling pathways is information, not matter. Since RNA polymerase II is a limiting resource, only a fraction of the genome can be transcribed at any time. Despite the importance of signalling pathways in the control of gene expression, we know very little about their detailed kinetics. We show here that some transcription networks follow Boolean kinetics: their inputs are a combination of IF→THEN, AND, OR and NOT information and their output is either ON or OFF. A kinetic model of the lac operon in E.coli predicted Boolean kinetics. Such pathways act as monostable systems: their normal, resting state is OFF, and following an input, which may be very weak, and very transient, they amplify and prolong the signal sufficiently to activate the appropriate transcription network, after which (assuming the input signal has now ceased) they revert to the OFF state. A computer model of the MAP kinase pathway of eukaryotic cells also predicted Boolean kinetics. Cross-talk effects between signalling pathways result in the entire signalling network acting as a complex interactive system. Inhibitors of signalling pathways may have all-or-none effects on transcription, making the...