Homeostatic Controllers Compensating for Growth and Perturbations

Abstract

authors contributed equally to this work.Abstract 1 Cells and organisms have developed homeostatic mechanisms to maintain internal 2 stabilities which protect them against a changing environment. How cellular growth and 3 homeostasis interact is still not well understood, but of increasing interest to the 4 synthetic and molecular biology community where molecular control circuits are sought 5 and tried to maintain homeostasis that opposes the diluting effects of cell growth. In 6 this paper we describe the performance of four negative feedback (inflow) controllers, 7 which, for different observed growth laws (time-dependent increase in the cellular 8 volume V ) are able to compensate for various time-dependent removals of the controlled 9 variable A. The four implementations of integral control are based on zero-order, 10 first-order autocatalytic, second-order (antithetic), and derepressing inhibition kinetics. 11 All controllers behave ideal in the sense that they for step-wise perturbations in V and 12 A are able to drive the controlled variable precisely back to the controller's theoretical 13 set-point A theor set . The applied increase in cellular volume includes linear, exponential 14 and saturating growth and reflect experimentally observed growth laws of single cell 15 organisms and other cell types. During the increase in V , additional linear or 16 exponentialtime-dependent perturbations which remove A are applied, and controllers 17 are tested with respect to their ability to compensate for both the increase in volume V 18 and the applied perturbations removing A. Our results show that the way how integral 19 control is kinetically implemented and the structure of the negative feedback loop are 20 essential determinants of a controller's performance. The results provide a ranking 21 between the four tested controller types. Considering exponential volume increases 22 together with an exponentially increasing removal rate of A controllers based on 23 derepression kinetics perform best, but break down when the control-inhibitor's 24 concentration gets too low. The first-order autocatalytic controller is able to defend 25 time-dependent exponential growth and removals in A, but generally with a certain 26 PLOS 1/23 offset below its theoretical set-point A theor set . The controllers based on zero-order and 27 second-order (antithetic) integral feedback can only manage linear increases in V and 28 removals in A, in dependence of the controllers' aggressiveness. Our results provide a 29 theoretical basis what controller kinetics are needed in order to compensate for different 30 growth laws. 31 70 because together with the diluting effects of the different growth laws these 71 perturbations represent the most severe conditions for testing the controllers. 72 PLOS 2/23 115 PLOS 3/23 130 Cell internal generated A 131 Compensatory fluxes to counteract diminishing levels of a controlled compound A can 132 be generated by a cell internal compound (assumed here to be homogeneously 133 distributed inside V ) or ...