Capacitance in Biochemical Networks: Sequential Reaction Delays

Abstract

In an enzymatic reaction network there are four unavoidable, generally neglected, sources of delay: (1) diffusion of substrate S to the enzyme, (2) the rate k1 of binding S to the enzyme E, (3) the retention in the form of the ES complex as S is converted to product P, (4) “volume delay”, the transient delay for concentrations to reach the next steady state after each change in a flux, and (5)flux delay with reversible reactions. Michaelis‐Menten forward flux is the product of the maximal flux, Vmax, times the fractional occupancy of the active site, [S]/(Km +[S]), where Vmax= Etot • k2 , (Etot = enzyme concentration; k2 = rate of product release). This accounts for neither binding/unbinding nor the capacitance of the ES complex. We examine these delays for an unbranched unidirectional reaction sequence A→B→C→D→E, ignoring diffusion delay. The delays are nearly exponential single lags, each with time constant = exchanged mass/flux, e.g. t = ES/(k2 • ES) = 1/k2 . We consider four versions of this reaction set (available at www.physiome.org/Models): #423 forward first order reactions, #424 Michaelis‐Menten forward reaction, #425 M‐M coupled with a correcting time lag of 1/k2 , compensating virtually precisely for the lack of capacitance, and #426, the full enzyme binding and release kinetics. The programs include verification tests, and are open source, human readable differential equations in JSim's MML. Time constants for lags are: for binding substrate, 1/k1; for retention in ES complex 1/k2 ; for the “volume delay”, (Vol ml)/(Clearance in ml/sec) while going from one steady state to the next. A fifth model, #427, “flux reversal”, shows that with simultaneous forward and backward fluxes in an enzyme sequence such as A→B←→C←→D→E, there is increased capacitance or retention in the B←→D block of reactions that is dependent on the relative dissociation constants, Kd's, of the enzyme for binding substrate versus product. Such delays, and resultant flux limitations and increased susceptibility to system instabilities need to be accounted for in characterizing systems especially when branched or feedback‐controlled. Unidirectional M‐M models can be made temporally accurate by adding capacitance‐mimicking lags in series. In the full kinetic models the delays are fully accounted for by equations describing the kinetics directly, including the reversibility delays.Support or Funding Information(Supported by NIH/NHLBI U01‐HL122199)This abstract is from the Experimental Biology 2019 Meeting. There is no full text article associated with this abstract published in The FASEB Journal.