Commensalism of methane-producing and motile aerobic bacteria in certain freshwater wetlands

0092-8240/8453.00+0.00

Bulletin of Mathematical Biology Vol. 46, No. 2, pp. 333-336, 1984.

Pergamon Press Ltd. © 1984 Society for Mathematical Biology

Printed in Great Britain

NOTE COMMENSALISM OF METHANE-PRODUCING A N D M O T I L E A E R O B I C B A C T E R I A IN C E R T A I N FRESHWATER WETLANDS •

GERALD

ROSEN

Department of Physics, Drexel University, Philadelphia, PA 19104, U.S.A. It is pointed out that the methane flux measured experimentally for certain ponds and swamps is quantitatively consistent with a commensal dependence of Methanobacteria on O2-chemotacticmotile aerobic bacteria. The Methano species is thereby shielded from oxygen and provided with carbon dioxide for the anaerobic production of methane.

1. Introduction. The three genera of methane-producing bacteria, Methanobacterium, Methanococcus and Methanosarcina, utilize carbon dioxide to produce methane according to anaerobic respiration reactions like (Koyama, 1963; Carpenter, 1967) CO2 + 2C2HsOH

> CH4 + 2CH3COOH,

with carbon dioxide reduced to methane on a mole-for-mole basis. Oxygendepleted organically rich ponds, swamps and other freshwater wetlands provide natural habitats for large steady-state populations of Methanobacteria. Experimental measurements of the methane flux from various wetlands (Koyama, 1963; Baker-Blocker et al., 1977; Harriss and Sebacher, 1981; Sebacher and Harriss, 1982) show that the Methanobacteria can prosper in several qualitatively different types of microbial ecosystems. In particular, for certain ponds and swamps the methane flux is given to an accuracy of about 10% by the simple empirical formula (Baker-Blocker et al., 1977) f = (4.1T -- 42)/lg/cm 2 -day,

( 1)

where T is the temperature in °C through the experimental range 12 °C < T < 26 °C. It is noteworthy that (1) applies to wetlands of various depths and sediment compositions, even though no parametric dependence on the latter variables is evident in (1). For other wetlands the methane flux has been observed experimentally to vary with depth and sediment-composition (Harriss and Sebacher, 1981; Sebacher and Harriss, 1982), and (1) is not applicable in such cases. 333

334

G. ROSEN

The purpose of the present communication is to point out that (1) can arise as a quantitative concomitant of commensalism between methaneproducing and motile aerobic bacteria. Since (1) applies to wetlands of various depths and sediment compositions, the methane production must be rate-controlled by biochemical and biophysical processes which take place near the water-atmosphere interface. It is shown in the following that (1) is quantitatively consistent with a microbial ecosystem in which O2-chemotactic motile aerobic bacteria supply the carbon dioxide for anaerobic respiration of Methano species. Commensal with the O2-shielding and CO2-providing motile aerobic bacteria, the Methano species liberate CH4 at precisely the molal rate that oxygen is consumed and carbon dioxide is generated by aerobic respiration reactions of the former, like 1 0 2 q- 7 C 6 H 1 2 0 6 O

; CO2 + H20.

Thus the methane flux formula (1) can arise as a consequence of commensalism between the aerobic and Methanobacteria species.

2. Steady-state Distribution o f Oz-chemotactic Motile Aerobic Bacteria. Let z denote distance into an oxygen-depleted aqueous medium from the z = 0 surface, n = n(z) denote the n u m b e r per unit volume of motile aerobic O2-chemotactic bacteria cells and s = s(z) denote the oxygen concentration. The coupled ordinary differential equations for the steady-state distributions of the bacteria cells and oxygen take the form (Rosen, 1978, 1983b) d2n /2 dz 2 D

6 d (n ~zz) dz s-1 = 0

d~s dz 2

-- c~ns = 0,

(2) (3)

where the constants g and 6 are the bacteria motility and chemotactic flux coefficient respectively, D = 7.6 X 10 -2 cm2/hr

(4)

is the oxygen diffusivity constant at temperatures of biological interest and = (2.5 X 10 -8 cm3/cell-hr)q~(T)

(5)

is the fractional rate of 02 consumption per unit concentration o f bacteria cells. The dimensionless temperature-dependent factor ¢ ( T ) i n (5) relates the fact that 02 consumption increases with increasing T, while the constant pre-

COMMENSALISM OF METHANE-PRODUCING AND MOTILE AEROBIC BACTERIA

335

factor in (5) derives from experimental data on motile aerobic O2-chemotactic Escherichia coli (see works cited in Rosen, 1983b) for which ~b(20) ~ 1

dq~/dT[T=20 > 0.

(6)

Experiments also reveal the relation 6 = 2/2

(7)

for motile aerobic O2-chemotactic E. coli, and theoretical reasons (Rosen, 1983a) suggest that (7) also holds for other chemotactic bacteria species. Suppose that the bacteria cells and oxygen concentration have the typical surface values n ( 0 ) - - n o = 2.0 × 108 cells/cm 3 z = 0:

(8) s(0) = So = 8.0/2g/cm 3

and decrease to zero far below the surface n(oo) = 0 z = oo:

(9) s(oo) = 0.

Then subject to (7), (8) and (9), the governing steady-state distribution equations (2) and (3) yield the exact solution n = no[1 + (z/z,)1-2

(10)

s = s 0 [ 1 + (z/z,)] -1,

(11)

where 1

z, = (2D/ano) :r _1

(0.174 cm)[$(T)] ~

(12)

in view o f (4), (5) and the first m e m b e r of (8). The total rate of 02 consumption by the motile aerobic congregation is 02 consumption~ rate per unit ] = | surface area ]

/,

a n s d z = - - D ( d s / d z )~ ~0 Jo 1

= Dz-,lso = (3.5/2g/cm2-hr)[~(r)] ~

(13)

by virtue of (3), (4), (11), (12) and the second m e m b e r of (8).

3. Steady-state CH4-flux Produced by Commensal Methanobacteria.

If each mole of 02 produces a mole o f C02 through aerobic bacterial respiration,

336

G. ROSEN

and each mole of CO2 is reduced to a mole of CH4 by commensal Methano anaerobes, then the associated methane flux is given by ½ (= tool. wt of CH4/ mol. wt of 02) of the O2-consumption rate per unit surface area shown in (13), i.e. 1

1

f = ~ D z , l s o = (42 #g/cm2-day)[~b(T)] ~

(14)

where the unit of time is taken as a day in order to facilitate comparison with (1). The theoretical methane flux expression (14) agrees with the experimental formula (1) if ~b(T) ~ [(T/10) -- 1] 2,

(15)

and, indeed, the latter form (15) is in accord with the normalization and montonicity conditions in (6). Thus, for motile aerobic bacteria with an 02 consumption rate given by (5) and (6), the typical parameter values employed in (8) yield the methane flux expression (1) as a precise concomitant of the bacterial commensalism. This work was supported by a NASA grant.

LITERATURE Baker-Blocker, A., T. M. Donahue and K. H. Mancy. 1977. "Methane Flux from Wetland Areas." Tellus 29, 245-250. Carpenter, P. L. 1967. Microbiology, pp. 205-210, 314. Philadelphia, PA: W. B. Saunders. Harriss, R. C. and D. I. Sebacher. 1981. "Methane Flux in Forested Freshwater Swamps of the Southeastern United States." Geophy$. Res. Lett. 8, 1002-1004. Koyama, T. 1963. "Gaseous Metabolism in Lake Sediments and Paddy Soils and the Production of Atmospheric Methane and Hydrogen." J. geophys. Res. 68, 3971-3973. Rosen, G. 1978. "Steady-state Distribution of Bacteria Chemotactic Toward Oxygen." Bull. math. Biol. 40, 671-674. ' 1983a. "Theoretical Significance of the Condition ~ = 2# in Bacterial Chemotaxis." Bull. math. Biol. 45, 151-153. --. 1983b. "Analytical Solutions for Distributions of Chemotactic Bacteria." Bull. math. Biol. 45,837-847. Sebacher, D. I. and R. C. Harriss. 1982. "A System for Measuring Methane Fluxes from Wetland Environments." J. environ. Qual. 11, 34-37. RECEIVED 4-18-83