Homeostasis in Networks with Multiple Input Nodes and Robustness in Bacterial Chemotaxis

Homeostasis in Networks with Multiple Inputs

“…Even though single-input single-output networks are quite popular in many engineering domains [1,4,7,37], the single input (and single input parameter) assumption seems unrealistic in biology, as disturbances that arise are typically very complex and do not have a single well-defined entry point. Maderia and Antoneli [38] extended the classification of [55] to the setting of multiple input nodes affected by a single input parameter. Using this extended theory they were able to completely work out the homeostasis types of a representative model for bacterial chemotaxis [11, 54].…”

“…More precisely, given an input-output network with multiple input parameters we show that one can consider each parameter at a time. Thus, effectively reducing the problem of classification of homeostasis types to the single input parameter case (still with multiple input nodes), that has been completely solved in [38]. Afterwards, we show how to combine these partial classifications for the single input parameter cases into an algorithm that provides the full classification on the multiple input parameter setting (Sec.…”

“…The main discovery of [38, 55] is that, in a given abstract input-output network, there is a finite number of ‘distinct mechanisms’ that may cause homeostasis, i.e., may force the derivative of the input-output function to vanish (at a fixed value of the input parameter). These ‘distinct mechanisms’, called ‘homeostasis types’, bijectively correspond to a specific subnetworks of the abstract input-output network.…”

“…In [38] the single-input single-output theory is generalized, for the first time, to account for multiple input nodes. The main result is that everything from the single-input case generalizes, except that there is a new class of homeostasis subneworks, called input counterweight : every abstract multiple input node network has exactly one input counterweight subnetwork, which can be topologically characterized, as well.…”

“…We end this section by briefly mentioning other aspects of the infinitesimal homeostasis approach that we will not pursue further: general network dynamical systems formalism (network admissible systems) [9, 19, 23], singularity theory networkpreserving changes of coordinates [3, 20–22], biological robustness [29, 31, 33–35, 47, 51–53], numerical discovery and continuation [12, 16, 26], classification of infinitesimal homeostasis in small ‘core networks’ [28], infinitesimal homeostasis for limit cycles [57] and miscellaneous applications to biology [2, 24, 25, 38].…”