Energy-speed-accuracy relation in complex networks for biological discrimination

Statistical fluctuations limit the precision with which a microorganism can, in a given time T, determine the concentration of a chemoattractant in the surrounding medium. The best a cell can do is to monitor continually the state of occupation of receptors distributed over its surface. For nearly optimum performance only a small fraction of the surface need be specifically adsorbing. The probability that a molecule that has collided with the cell will find a receptor is Ns/(Ns + pi a), if N receptors, each with a binding site of radius s, are evenly distributed over a cell of radius a. There is ample room for many indenpendent systems of specific receptors. The adsorption rate for molecules of moderate size cannot be significantly enhanced by motion of the cell or by stirring of the medium by the cell. The least fractional error attainable in the determination of a concentration c is approximately (TcaD) - 1/2, where D is diffusion constant of the attractant. The number of specific receptors needed to attain such precision is about a/s. Data on bacteriophage absorption, bacterial chemotaxis, and chemotaxis in a cellular slime mold are evaluated. The chemotactic sensitivity of Escherichia coli approaches that of the cell of optimum design.

The specificity with which the genetic code is read in protein synthesis, and with which other highly specific biosynthetic reactions take place, can be increased above the level available from free energy differences in intermediates or kinetic barriers by a process defined here as kinetic proofreading. A simple kinetic pathway is described which results in this proofreading when the reaction is strongly but nonspecifically driven, e.g., by phosphate hydrolysis. Protein synthesis, amino acid recognition, and DNA replication, all exhibit the features of this model. In each case, known reactions which otherwise appear to be useless or deleterious complications are seen to be essential to the proofreading function.

Like other cell-surface receptors with intrinsic or associated protein-tyrosine kinase activity, the T-cell receptor complex undergoes a number of modifications, including tyrosine phosphorylation steps, after ligand binding but before transmitting a signal. The requirement for these modifications introduces a temporal lag between ligand binding and receptor signaling. A model for the T-cell receptor is proposed in which this feature greatly enhances the receptor's ability to discriminate between a foreign antigen and self-antigens with only moderately lower affinity. The proposed scheme is a form of kinetic proofreading, known to be essential for the fidelity of protein and DNA synthesis. A variant of this scheme is also described in which a requirement for formation of large aggregates may lead to a further enhancement of the specificity of T-cell activation. Through these mechanisms, ligands of different affinity potentially may elicit qualitatively different signals.