TY - JOUR
T1 - Circuit Reduction of Heterogeneous Nonequilibrium Systems
AU - Lin, Milo M.
N1 - Funding Information:
The author would like to thank Rama Ranganathan, Elliott Ross, and Kimberly Reynolds for helpful feedback on the manuscript. This work was supported by the Cecil and Ida Green Foundation, the Leland Fikes Foundation, and the Welch Foundation (Grant No. I-1958-20180324).
Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/11/18
Y1 - 2020/11/18
N2 - Predicting the behavior of heterogeneous nonequilibrium systems is currently analytically intractable. Consequently, complex biological systems have resisted unifying principles. Here, I introduce a mapping from dynamical systems to battery-resistor circuits. I show that in these transformed variables (i) arbitrary numbers of heterogeneous dynamical transitions can be reduced to a Thevenin equivalent resistor which is invariant to driving from equilibrium, (ii) resistors (together with the external driving sources) are sufficient to describe system behavior, and (iii) the resistor's directional symmetry leads to universal theorems of nonequilibrium behavior. This mapping is used to derive two general steady-state relations. First, for any cyclic process, the maximum amplification of any state is tightly bounded by the total dissipation of all states; experimental data are used to show that the master signal protein Ras achieves this bound. Second, for any process, the response of any reaction due to driving any other reaction is identical to the reciprocal response rescaled by the ratio of the corresponding Thevenin resistors. This result generalizes Onsager's reciprocal relation to the strongly driven regime and makes a testable prediction about how systems should be designed or evolved to maximize response. These analytic results represent a new perspective applicable to biological complexity and suggest that this mapping provides the natural variables to study heterogeneous nonequilibrium systems.
AB - Predicting the behavior of heterogeneous nonequilibrium systems is currently analytically intractable. Consequently, complex biological systems have resisted unifying principles. Here, I introduce a mapping from dynamical systems to battery-resistor circuits. I show that in these transformed variables (i) arbitrary numbers of heterogeneous dynamical transitions can be reduced to a Thevenin equivalent resistor which is invariant to driving from equilibrium, (ii) resistors (together with the external driving sources) are sufficient to describe system behavior, and (iii) the resistor's directional symmetry leads to universal theorems of nonequilibrium behavior. This mapping is used to derive two general steady-state relations. First, for any cyclic process, the maximum amplification of any state is tightly bounded by the total dissipation of all states; experimental data are used to show that the master signal protein Ras achieves this bound. Second, for any process, the response of any reaction due to driving any other reaction is identical to the reciprocal response rescaled by the ratio of the corresponding Thevenin resistors. This result generalizes Onsager's reciprocal relation to the strongly driven regime and makes a testable prediction about how systems should be designed or evolved to maximize response. These analytic results represent a new perspective applicable to biological complexity and suggest that this mapping provides the natural variables to study heterogeneous nonequilibrium systems.
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U2 - 10.1103/PhysRevLett.125.218101
DO - 10.1103/PhysRevLett.125.218101
M3 - Article
C2 - 33274997
AN - SCOPUS:85097310515
SN - 0031-9007
VL - 125
JO - Physical Review Letters
JF - Physical Review Letters
IS - 21
M1 - 218101
ER -