skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Absolute concentration robustness and multistationarity in reaction networks: Conditions for coexistence
Abstract Many reaction networks arising in applications are multistationary, that is, they have the capacity for more than one steady state, while some networks exhibit absolute concentration robustness (ACR), which means that some species concentration is the same at all steady states. Both multistationarity and ACR are significant in biological settings, but only recently has attention focused on the possibility for these properties to coexist. Our main result states that such coexistence in at-most-bimolecular networks (which encompass most networks arising in biology) requires at least three species, five complexes and three reactions. We prove additional bounds on the number of reactions for general networks based on the number of linear conservation laws. Finally, we prove that, outside of a few exceptional cases, ACR is equivalent to non-multistationarity for bimolecular networks that are small (more precisely, one-dimensional or up to two species). Our proofs involve analyses of systems of sparse polynomials, and we also use classical results from chemical reaction network theory.  more » « less
Award ID(s):
1752672
PAR ID:
10637804
Author(s) / Creator(s):
; ;
Publisher / Repository:
Cambridge University Press
Date Published:
Journal Name:
European Journal of Applied Mathematics
Volume:
35
Issue:
4
ISSN:
0956-7925
Page Range / eLocation ID:
566 to 600
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; (, Journal of The Royal Society Interface)
    null (Ed.)
    In this work, we design a type of controller that consists of adding a specific set of reactions to an existing mass-action chemical reaction network in order to control a target species. This set of reactions is effective for both deterministic and stochastic networks, in the latter case controlling the mean as well as the variance of the target species. We employ a type of network property called absolute concentration robustness (ACR). We provide applications to the control of a multisite phosphorylation model as well as a receptor–ligand signalling system. For this framework, we use the so-called deficiency zero theorem from chemical reaction network theory as well as multiscaling model reduction methods. We show that the target species has approximately Poisson distribution with the desired mean. We further show that ACR controllers can bring robust perfect adaptation to a target species and are complementary to a recently introduced antithetic feedback controller used for stochastic chemical reactions. 
    more » « less
  2. ; ; ; ; ; ; ; ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Meeks, Kitty; Scheideler, Christian (Ed.)
    For general discrete Chemical Reaction Networks (CRNs), the fundamental problem of reachability - the question of whether a target configuration can be produced from a given initial configuration - was recently shown to be Ackermann-complete. However, many open questions remain about which features of the CRN model drive this complexity. We study a restricted class of CRNs with void rules, reactions that only decrease species counts. We further examine this regime in the motivated model of step CRNs, which allow additional species to be introduced in discrete stages. With and without steps, we characterize the complexity of the reachability problem for CRNs with void rules. We show that, without steps, reachability remains polynomial-time solvable for bimolecular systems but becomes NP-complete for larger reactions. Conversely, with just a single step, reachability becomes NP-complete even for bimolecular systems. Beyond what is contained in this brief announcement, we also investigate optimization variants of reachability, provide approximation results for maximizing species deletion, establish ETH-based lower bounds for NP-complete cases, and prove hardness for counting reaction sequences. 
    more » « less
  3. ; ; ; (, Journal of Mathematical Chemistry)
    Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation. 
    more » « less
  4. ; (, Chemical Science)
    Accelerated reactions in microdroplets have been reported for a wide range of reactions with some microdroplet reactions occurring over a million times faster than the same reaction in bulk solution. Unique chemistry at the air–water interface has been implicated as a primary factor for accelerated reaction rates, but the role of analyte concentration in evaporating droplets has not been as well studied. Here, theta-glass electrospray emitters and mass spectrometry are used to rapidly mix two solutions on the low to sub-microsecond time scale and produce aqueous nanodrops with different sizes and lifetimes. We demonstrate that for a simple bimolecular reaction where surface chemistry does not appear to play a role, reaction rate acceleration factors are between 10 2 and 10 7 for different initial solution concentrations, and these values do not depend on nanodrop size. A rate acceleration factor of 10 7 is among the highest reported and can be attributed to concentration of analyte molecules, initially far apart in dilute solution, but brought into close proximity in the nanodrop through evaporation of solvent from the nanodrops prior to ion formation. These data indicate that analyte concentration phenomenon is a significant factor in reaction acceleration where droplet volume throughout the experiment is not carefully controlled. 
    more » « less
  5. ; ; (, Proceedings of the National Academy of Sciences)
    One of the most intriguing features of biological systems is their ability to regulate the steady-state fluxes of the underlying biochemical reactions; however, the regulatory mechanisms and their physicochemical properties are not fully understood. Fundamentally, flux regulation can be explained with a chemical kinetic formalism describing the transitions between discrete states, with the reaction rates defined by an underlying free energy landscape. Which features of the energy landscape affect the flux distribution? Here we prove that the ratios of the steady-state fluxes of quasi–first-order biochemical processes are invariant to energy perturbations of the discrete states and are only affected by the energy barriers. In other words, the nonequilibrium flux distribution is under kinetic and not thermodynamic control. We illustrate the generality of this result for three biological processes. For the network describing protein folding along competing pathways, the probabilities of proceeding via these pathways are shown to be invariant to the stability of the intermediates or to the presence of additional misfolded states. For the network describing protein synthesis, the error rate and the energy expenditure per peptide bond is proven to be independent of the stability of the intermediate states. For molecular motors such as myosin-V, the ratio of forward to backward steps and the number of adenosine 5′-triphosphate (ATP) molecules hydrolyzed per step is demonstrated to be invariant to energy perturbations of the intermediate states. These findings place important constraints on the ability of mutations and drug perturbations to affect the steady-state flux distribution for a wide class of biological processes. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email