(~40° to 75°C), the same theory predicts^13 e
values of−55 to− 45 ‰( 17 )(tableS5).Nocoal
methoxyl data fit this prediction (Fig. 1A).
Although some data lie on the Rayleigh distil-
lation trend for 300°C pyrolysis, most do not,
and we consider this coincidental. We con-
clude that O-demethylation during coalifica-
tion is not a thermally activated reaction.
Other abiotic mechanisms impart smaller
(less negative) isotope effects. Acid hydrolysis
and permanganate oxidation of methyltert-
butyl ether (MTBE) fractionate methoxyl groups
by^13 e=−16 to− 24 ‰(table S5). However, the
acidic or oxidizing conditions required for
these O-demethylations are incompatible with
the alkaline and reducing conditions in the
Shimokita and Powder River coals (materials
and methods, section S1). Even if these re-
actants were dissolved in coal pore fluids, we
would still expect O-demethylation to conform
to a Rayleigh model. Becaused^13 Cmethoxyl
values in these coals are variable yet uncorre-
lated with methoxyl concentration, no Rayleigh
process with a single^13 ecan explain these data,
and measured^13 efor these mechanisms are still
too large (Fig. 1A). Although each datum could
be fit by a Rayleigh-type model with a distinctive
(^13) e—all between−4 and− 13 ‰(Figs. 1B and
fig. S10)—there is no obvious reason why the
(^13) eof a yet-undiscovered, abiotic process should
systematically vary among similar samples.
Our results are better described by an O-
demethylation mechanism that is isotopically
fractionating at low degrees of reaction prog-
ress and then ceases to discriminate between
(^13) C and (^12) C once methoxyl abundance falls
below a certain threshold (~5% of initial; Fig.
1B). This is consistent with a biologic process
in a transport-limited environment. We first
develop this argument qualitatively and then
with a simple model. Although the specific
organisms and enzymes responsible for
coal methoxyl degradation are unknown,
some distinctions can be made. Aerobic O-
demethylation has a modest intrinsic iso-
tope effect:−2 to− 12 ‰in MTBE (an SN 1
reaction; table S5) and no greater than− 15 ‰
during leaf-litter decomposition (fig. S11).
Rayleigh models with this^13 erange fit our
data (Fig. 1B), but aerobic metabolisms were
not viable beyond the least mature samples.
Rather, Shimokita and Powder River coals
hosted anaerobic communities (materials and
methods, section S1). Anaerobes capable of
O-demethylation (e.g., some acetogens, sul-
fate reducers, fermenters, and methanogens)
employ SN2-type methyltransferases with
large intrinsic isotope effects (−40 to− 80 ‰;
table S5). These would appear incompatible
with our data, but intrinsic isotope effects
are masked when enzymatic reactions are
substrate limited [e.g., ( 18 )]. Considering that
biologic O-demethylation in coal would require
extracellular enzymes to encounter and ac-
tivate parts of the coal matrix, it is conceiv-
able and perhaps expected that microbial
O-demethylation would discriminate less
strongly as this moiety is consumed.
We model this process with the Best equa-
tion ( 19 ), which couples the diffusion of sub-
strate to an enzyme site (or vice versa; so-called
mass transfer) to the Michaelis-Menten equa-
tion for enzymatic rate. Whether a biologic
process operates under a mass transfer or
enzymatic limitation depends on the substrate
delivery rate constant, the specific affinity of
the enzyme, and the concentration of sub-
strate ( 20 ). In a closed system, a biologic
process can transition from enzyme limited
to mass transfer limited as the substrate pool
is depleted. The isotopic fractionation of the
reaction observed at any instant (aobs, where
aobs=Rprod/Rreact) is represented as ( 21 )
aobs¼a 0
1 þA
1 þa 0 A
ð 1 Þ
wherea 0 is the intrinsic enzyme fractiona-
tion factor (a 0 =e 0 + 1) andAis
A¼
1
2
1
Bn
c
Km
1
þ
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1
Bn
þ
1
4
1
Bn
c
Km
1
2
s
ð 2 Þ
Here,cis the methoxyl substrate concentra-
tion,Kmis the Michaelis-Menten constant
for the O-demethylation reaction, andBnis
the bioavailability number (the ratio of the
mass transport rate constant to the specific
affinity of the enzyme). Under conditions of
high bioavailability (largeBn),A→0 and the
enzymatic fractionation factor is expressed
independent ofc. Under low bioavailability,
A→∞, andaobs→1. As the methoxyl pool is
depleted,aobstransitions from ~a 0 to 1.
We apply Eq. 1 to predictd^13 Cmethoxylduring
lignin biodegradation in a closed system (Fig.
1B). The model is underconstrained but con-
sistent with our data (within 2‰) when
reasonable parameters are chosen. Acceptable
(but nonunique) fits have initialc/Km=5×
103 ,^13 e 0 =− 12 ‰, andBnfrom 0.01 to 0.05.
Assuming 1 wt %≈0.01 M methoxyl concentra-
tion, this suggestsKm=0.02mM,consistent
with 0.015 to 0.06 mM for an O 2 -dependent
lignin monomerO-demethylase ( 22 ) and similar
toKmfor an anoxicO-demethylase [0.08 mM
( 23 )]. A more-complex and descriptive model
would transition from a smaller^13 e 0 (− 12 ‰)toa
larger^13 e 0 (~− 70 ‰) as the substrate is depleted,
but this model is nearly indistinguishable from
the simpler one shown. Alternative models
with a fixed^13 e 0 of− 70 ‰andBnof 0.0005 to
0.001 fit the more-mature coals but not the
Belchatow lignites (Fig. 1B).
Our findings suggest that in these samples,
lignin O-demethylation was a microbial reac-
tion. Specifically, the data are best explained by
a model where initial, perhaps aerobic, enzyme
rate–limited O-demethylation was succeeded
896 12 NOVEMBER 2021•VOL 374 ISSUE 6569 science.orgSCIENCE
Fig. 3. Histograms of biogenic methaned^13 C values from conventional hydrocarbon reservoirs and
coal beds.Conventional hydrocarbon reservoirs are shown in green, and coal beds are shown in blue. Data
are compiled in Sherwoodet al.( 33 ). To isolate biogenic methane, only gases with methane/ethane
abundance ratios >10^3 from depths <3 km ( 15 ) are shown. The gray dashed line is the nominal upperd^13 C
limit for primary microbial methane [− 50 ä( 15 )]. Of biogenic CBM samples, 37% exceed this limit.
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