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Governing equations
Variations of this multiplicative function were used to determine metabolic relationships of the physicochemical state variables used in this model:
F = Vmax * f(O2) * f(H2S) * f(PAR) * f(NIR)*f(H)

where F is the microbial reaction rate, Vmax is the maximum reaction rate , and f(x) = one of three types of functional relationship (see below)

Ks = the ½ saturation constant; Ki = inhibition constant; Kmax= the lowest inhibitory value of x; K1/2 = the value at which y=0.5.
  • Growth of each bacterial guild occurs as a function of initial biomass multiplied by the metabolism and a yield factor (see table below).
  • DIC, sulfide, and O2 move between mat layers (and from the mat surface to the diffusive boundary layer) based on a diffusion gradient.
  • PAR was primarily attenuated by the mat, whereas NIR was primarily attenuated by the water overlying the mat
  • A three day MBGC simulation using field-measured temperature and light data from June 4-5, 2001 and October 10-11, 2001 generated DIC, sulfide, and O2 results that were compared to June 4-7, 2001, and October 10-11,2001 field-collected mat data.
    Organism Metabolism Mode1 O2 H2S [H] PAR(%) NIR(%) PAR µmol
    NIR µmol
    Yield factors Vmax
    Cyanobacterium (CYA) Oxygenic photosynthesis Cn I I - O - S - +8.55g per mol
    O2 consumed
    0.0323 h-1
      Aerobic respiration Cn S - - - - - - -8.55g per mol
    O2 produced
    -0.0017 h-1
      Anoxygenic photosynthesis Ind - O - O - S - +8.55g per mol
    H2S consumed
    0.0043 h-1
    Purple Sulfur
    Bacterium (PSB)
    Anoxygenic photosynthesis Ind - O - - O - S +17.1g per mol
    H2S consumed
    0.072 h-1
      Aerobic chemosynthesis Cn S O - - - - - +5.28g per mol
    H2S consumed
    0.067 h-1
    +3.94g per mol
    O2 consumed
    Colorless Sulfur
    Bacterium (CSB)
    Aerobic chemosynthesis Cn S S - - - - - +3.0g per mol
    H2S consumed
    0.54 h-1
    +1.67g per mol
    O2 consumed
    Sulfate Reducing
    Bacteria (SRB)
    Aerobic(?) chemosynthesis Cn - - S - - - - +1.8g per mol
    [H] consumed
    0.004 h-1
    1 The metabolism can be constitutive (Cn = always present) or Inductive (Ind = induced by mechanisms built into the model).
    Table 1. Types of metabolism by the different microbes in the model. The effect of each physicochemical state variable upon metabolism is modeled using either an inhibition (I), saturation (S), or optimum curve (O). CYA, PSB, and CSB is from de Wit et al.1995; SRB values are from Widdle 1988; and from a combination of published values (Invorsen & Jørgensen 1984; Widdel et al. 1983) and sensitivity testing.

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