fundamental limits to position determination by concentration gradients基本定位的极限浓度梯度.pdfVIP

Fundamental Limits to Position Determination by Concentration Gradients 1 2 1* Filipe Tostevin , Pieter Rein ten Wolde , Martin Howard 1 Department of Mathematics, Imperial College London, London, United Kingdom, 2 FOM Institute for Atomic and Molecular Physics (AMOLF), Amsterdam, The Netherlands Position determination in biological systems is often achieved through protein concentration gradients. Measuring the local concentration of such a protein with a spatially varying distribution allows the measurement of position within the system. For these systems to work effectively, position determination must be robust to noise. Here, we calculate fundamental limits to the precision of position determination by concentration gradients due to unavoidable biochemical noise perturbing the gradients. We focus on gradient proteins with first-order reaction kinetics. Systems of this type have been experimentally characterised in both developmental and cell biology settings. For a single gradient we show that, through time-averaging, great precision potentially can be achieved even with very low protein copy numbers. As a second example, we investigate the ability of a system with oppositely directed gradients to find its centre. With this mechanism, positional precision close to the centre improves more slowly with increasing averaging time, and so longer averaging times or higher copy numbers are required for high precision. For both single and double gradients, we demonstrate the existence of optimal length scales for the gradients for which precision is maximized, as well as analyze how precision depends on the size of the concentration-measuring apparatus. These results provide fundamental constraints on the positional precision supplied by concentrat