Depolymerization pattern as a major driver of organic matter accessibility to uptake by microbe

We ran a first scenario of cellulose decomposition to investigate if enzyme depolymerization, reported in an original manner by the α_enz parameter in C-STABILITY, is a crucial regulator of substrate decomposition kinetics compared to other well-known drivers such as carbon use efficiency or enzyme action rate (also called catalytic rate). A cellulose polymer was subjected to the cellulolytic action of a set of enzymes and split into smaller fragments, which corresponded to a gradual decrease in the cellulose polymer size distribution toward short oligomers in the microbial uptake domain, $$ {\mathcal{D}}_u$$ (Fig. 3a). Cellulose oligomers small enough to be assimilated were continuously produced and almost fully taken up with the chosen parameters (Table 1). They were used either to produce microbial biomass or to generate energy trough the respiration process (Fig. 3b). Ninety-five percent of the cellulose-C was consumed after 123 days, with a mean residence time of 97 days, which was consistent with results of laboratory incubation studies³⁵. Note that during the first 25 days the enzyme action mostly generated oligomers that were too large to be accessible to microbe uptake, inducing a decrease in the living microbe biomass (Fig. 3a, b).

Fig. 3

Dynamics of cellulose degradation by one decomposer community (scenario 1).

a Changes in the distribution of cellulose polymer length over time, reported in g_C. p⁻¹ with p standing for the substrate polymerization. Cellulose is progressively depolymerized by enzymes. The $$ {\mathcal{D}}_{\mathrm{cellulolytic}}$$ domain (blue) is indicative of cellulose accessible to cellulolytic enzymes, the $$ {\mathcal{D}}_u$$ domain (red) is indicative of cellulose oligomers accessible to microbe uptake; $$ p_{\mathrm{cell}}^{\min }$$ and $$ p_{\mathrm{cell}}^{\max }$$ are the minimum and maximum levels of cellulose polymerization. The distribution shift toward $$ {\mathcal{D}}_u$$ over time illustrates the depolymerization of cellulose. Microbial uptake induces a substrate depletion in $$ {\mathcal{D}}_u$$ and causes a distribution discontinuity. b Amount of residual cellulose-C, C available for microbial uptake, cumulated CO₂, living biomass-C, and dead microbial residues-C. There is no microbial recycling in this simulation. Note that the sum of cellulose-C and living microbes-C at the beginning is equal to the sum of cumulated CO₂ and microbial residues-C at the end. c Sensitivity analysis on the amount of residual cellulose-C (±5% uniform variability of the parameters) at different times. Relative importance of model parameters changes over time depending on their role in the substrate degradation process. Tested parameters are the carbon use efficiency $$ e_{\mathrm{mic}}^0$$, mortality rate $$ m_{\mathrm{mic}}^0$$, substrate cleavage factor α_enz, enzyme activity rate τ₀, and initial microbial-C to total-C ratio. For instance α_enz has no influence at the beginning while it explains more than 40% of the total model variance at 100 days.

Table 1

Synthesis of C-STABILITY parameters and scenarios setups with values for initial conditions, microbes traits, and enzymes families. Scenario 1 corresponds to cellulose degradation, scenario 2 to lignocellulose degradation, scenario 3 to succession of two different microbial communities on lignocellulose, considering microbial recycling, and scenario 4 to soil organic matter at steady state considering a continuous plant input and microbial recycling, with only one microbial community. Initial amounts of microbes and substrate are respectively noted $$ {\left(C_{\mathrm{mic}}\right)}_{t=0}$$ and $$ {\left(C_{\mathrm{sub}}\right)}_{t=0}$$, mic. stands for microbe and sub. for substrate. For scenario 3, two $$ u_{\mathrm{mic}}^0$$ values were tested to compare non-cheating and cheating behavior of decomposers. For scenario 4, the values of $$ {\tau }_{\mathrm{enz}}^0$$ were divided by 5 to account for in situ conditions, while other scenarios are based on laboratory case studies (Supplementary Table 1).

Parameter	Description							Unit
$$ u_{\mathrm{mic}}^0$$	Microbial uptake rate per microbial carbon mass							g$$ {}_C^{-1}$$.d−1
$$ e_{\mathrm{mic}}^0$$	Microbial carbon use efficiency							−
$$ m_{\mathrm{mic}}^0$$	Microbial mortality rate							g$$ {}_C^{-1}$$.d−1
$$ {\tau }_{\mathrm{enz}}^0$$	Enzymatic action rate per microbial carbon mass							g$$ {}_C^{-1}$$.d−1
αenz	Enzymatic substrate cleavage factor							−
Initial setup for each scenario
Scenario	Microbes	Initial conditions (gC)		Microbial signature			Plant biochemistry
		$$ {\left(C_{\mathrm{mic}}\right)}_{t=0}$$	$$ {\left(C_{\mathrm{sub}}\right)}_{t=0}$$	Lipid	Protein	Mic. sugar	Plant sugar	Lignin
1	Plant decomposer	5	95	–	–	–	100%	–
2	Plant decomposer	5	125	–	–	–	76%	24%
3	Plant/mic. decomposer	5/5	125	30%	20%	50%	76%	24%
4	General decomposer	–	–	30%	20%	50%	76%	24%
Microbes parameters for each scenario
Scenario	Microbes	$$ e_{\mathrm{mic}}^0$$	$$ m_{\mathrm{mic}}^0$$	$$ u_{\mathrm{mic}}^0$$
				Lipid	Protein	Mic. sugar	Plant sugar	Lignin
1	Plant decomposer	0.4	0.02	−	−	−	5	−
2	Plant decomposer	0.4	0.02	−	−	−	5	5
3	Plant decomposer	0.4	0.02	0/3	0/3	0/3	5	5
3	Mic. decomposer	0.5	0.01	5	5	5	0/3	0/3
4	General decomposer	0.4	0.02	5	5	5	5	5
Enzymes parameters for each scenario
Scenario	Enzymes action						$$ {\tau }_{\mathrm{enz}}^0$$	αenz
1-2-3/4	Cellulolysis						1.8/0.36	5
2-3/4	Lignolysis						1/0.2	7
3/4	Lipidolysis						0.8/0.16	1.5
3/4	Proteolysis						1.8/0.36	5.5
3/4	Microbial sugar lysis						1.8/0.36	5

The sensitivity analysis of parameters shows that their relative influence on the amount of residual cellulose varied over time (Fig. 3c). As the decomposition dynamics was driven by microbes, any modification affecting the size of their biomass had a marked impact on the residual cellulose amount. Thus, the mortality rate $$ m_{\mathrm{mic}}^0$$ and the initial C_mic/C_tot ratio had a strong influence at the beginning of the simulation, while the microbial carbon use efficiency $$ e_{\mathrm{mic}}^0$$ was a sensitive parameter at the end of the simulation. The enzymatic substrate cleavage factor α_enz and enzyme action rate $$ {\tau }_{\mathrm{enz}}^0$$, which controlled the amount of substrate accessible to microbe uptake, became crucial parameters once the microbe community started growing. The decrease in the α_enz value induced a faster depolymerization pattern and made the substrate accessible to decomposer uptake more rapidly (Fig. 2). α_enz indeed indicated whether the enzyme preferentially attacked substrate end-members (exo-cleaving enzyme – high α_enz values) or randomly disrupted any substrate linkage (endo-cleaving enzyme – low α_enz values). Exo-cleaving enzymes released monomers or dimers, which caused a gradual decrease in the polymer length (Fig. 2). Endo-cleaving enzymes efficiently shifted the polymer size distribution toward short lengths. Variations in the microbe uptake rate $$ u_{\mathrm{mic}}^0$$ had a negligible impact on the model sensitivity. Due to the other parameters values, the available C in $$ {\mathcal{D}}_u$$ is almost instantaneously taken up, whatever the $$ u_{\mathrm{mic}}^0$$ value within a range of ±5% variability around the default value.

This simulation illustrates that C-STABILITY differentiates substrate transformation by enzyme and substrate uptake by decomposers, contrary to other models, which do not represent substrate polymerization and consider implicitly that depolymerization and uptake are simultaneous. This innovation enables us to demonstrate that depolymerization, whose action is reported by the enzyme cleavage factor, is a major limiting step controlling microbe uptake and decomposition of SOM. It has been largely overlooked until now and would deserve more attention in future experimental and modeling works. In addition, reporting the depolymerization process in the model frame permits to describe how the decaying substrate is transformed over time through a distribution of polymer sizes.

Coordinated action of enzymes regulates substrate accessibility

We ran a simulation of lignocellulose decomposition to examine the regulation of substrate accessibility to enzyme. In this study case, the activity of one enzyme family provides a gateway to the substrate for another one. Indeed in wood the spatial arrangement and the interactions of cellulose with lignin makes it inaccessible to cellulases. Cellulose depolymerization and utilization can only start once the lignin barrier has been altered. This typically occurs during wood attack by wood-rotting fungi producing lignolytic factors and cellulases, sometimes in a temporal sequence^16,17,36. In this second scenario, lignocellulose was made of 76% cellulose, 24% lignin. A specific design of the initial cellulose distribution was made to represent its embedment with lignin, which made it inaccessible to cellulolytic enzymes (Fig. 4a and Supplementary Movie). Parameters were chosen to model a decomposition pattern, in general agreement with the findings of lignocellulose decomposition studies performed in microcosms³⁷.

Fig. 4

Degradation of lignocellulose by a microbe community producing cellulolytic and lignolytic enzymes (scenario 2).

Cellulose is initially embedded in lignin and not accessible to its enzymes. a Distribution of polymerization, noted p, in the pools of inaccessible cellulose (left), cellulose accessible to cellulolytic enzymes (center), lignin accessible to lignolytic enzymes (right). Domains of substrate accessibility to enzymes are in blue, domains of substrate accessibility to microbial uptake are in red. The black arrow between inaccessible and accessible cellulose highlights the transfer of C between the two cellulose pools. Inaccessible cellulose is progressively transferred in the accessible pool without alteration of its polymerization. The transfer is directly related to lignin depolymerization and the associated degradation of the physical barrier. b Residual amount of C in the different pools over time. The lignolytic activity induces a quick disentanglement of the cellulose from the lignocellulosic complex (from orange to green), which makes polymerized cellulose accessible to its enzymes. Depolymerized cellulose and lignin are taken up by microbes. A Supplementary Movie illustrates this scenario.

Lignin deconstruction was initiated from the beginning of the simulation but the amount of lignin-C did not decrease prior to 120 days (Fig. 4 and Supplementary Movie). Lignin depolymerization was very slow because of the combined effects of the low lignolytic rate $$ {\tau }_{\mathrm{enz}}^0$$ and a high substrate cleavage factor α_enz (Table 1). Nevertheless the simulation revealed that the alteration of the lignin framework rapidly opened the wood cell wall structure³⁸ and cellulose, which was initially inaccessible to cellulolytic enzymes, became completely accessible after 25 days (Fig. 4a). This required step for lignolysis delayed cellulose decomposition compared to the previous simulation (Fig. 3) with a pure cellulose substrate (95% of the cellulose-C is consumed after 140 days versus 123 days in the previous case) (Fig. 4 and Supplementary Movie). Formally, mechanisms regulating cellulose accessibility to cellulases were modeled in C-STABILITY with a translation of the cellulose polymerization distribution from a pool where it was not accessible to another pool where it became accessible to its enzymes. This was assumed to be a linear function of the lignolytic enzymes activity. The substrate remained unaltered as long as it was inaccessible to enzymes, as also implemented in³⁹. This approach conceptually differs from that adopted in many compartment models where inaccessibility is reported by diminishing the substrate turnover rate compared to its free form^20,26,40,41.

This simulation illustrates how the action of one enzymes family on a complex substrate may be a prerequisite to the action of another enzymes family. It demonstrates the capacity of C-STABILITY to report the joint action of specific enzymes and to provide quantitative information about it, which may be hard to capture experimentally. This scenario could be further utilized to theoretically explore different depolymerization strategies implemented by decomposers to degrade complex substrate. For example, tuning the α_enz parameter for lignolytic activity would enable to compare brown rot and white rot fungi degradative strategies and evaluate their impact on fungal growth and wood degradation kinetics. Random bond disruption mediated by hydroxyl radical produced by brow rot fungi would be reported by a lower α_enz value than enzyme-mediated disruption of bonds by white rot fungi.

Interactions between successive decomposer communities regulate the persistence of decomposing substrate and its chemistry

The C-STABILITY framework is tailored specifically to reflect the succession of microbial players during litter decomposition and their biogeochemical functions. In a third scenario we implemented the model with two microbial functional communities succeeding each other on a lignocellulose substrate. We examined how microbes dynamics is regulated by the chemistry of the decaying substrate and conversely how residual substrate chemistry is affected by the interaction between the microbial communities. The two microbial communities had the same biochemistry, consisting of lipids, proteins, and sugars (Table 1), but differed in their catabolic abilities. Recent studies showed that saprophytic fungi are the first to take action in wood decomposition. They are the main producers of enzymes involved in lignocellulose degradation. Bacteria or mycorrhizal fungi peak thereafter, breaking down and utilizing dead fungal biomass rather than plant polymers^42–45. We referred to them as plant decomposers and microbial residue decomposers, respectively. In our simulation, the two communities also differed in their fitness. Microbial residue decomposers were more competitive than plant decomposers because of their higher carbon use efficiency and lower mortality rate (Table 1). This succession is illustrated in Fig. 5a. Plant decomposers dominated the microbial biomass during the first 260 days. They fed on the plant small polymers released through the action of the cellulolytic and lignolytic enzymes they produced, until their exhaustion. The microbial residue decomposer community slightly declined during this first stage because of the lack of resources—it had no access to the small plant oligomers. It started growing once the microbial residues were released upon the death of plant decomposers, after around 200 days (Supplementary Fig. 1). At the end of the simulation, there was almost no plant or microbial substrate left.

Fig. 5

Effect of the succession of two decomposer communities on the residual substrate amount and biochemistry (scenario 3).

The two communities have the same biochemical signature (50% sugar, 30% lipid, and 20% protein). Plant decomposers (red) produce cellulolytic and lignolytic enzymes. Microbial residues decomposers (Mic. decomposer = blue) produce enzymes that depolymerize lipids, proteins and microbial sugars. The two communities differ in their fitness. Microbial residue decomposers are more competitive than plant decomposers because of their higher carbon use efficiency and lower mortality rate (Table 1). The effect of cheating behavior was tested as follows: a substrate uptake is only possible for the enzyme producer or b uptake is also possible for the cheater but at a lower rate than that of the enzyme producer (dashed uptake arrows). Cheating has a strong effect on communities dynamics and the resulting biochemical composition of substrate. When cheating occurs, plant decomposers are outcompeted by microbes decomposers, what results in the persistence of lignin.

Despite the strategies implemented by decomposers to achieve privileged access to the substrate they depolymerize, e.g., antibiotics or secondary metabolites secretion⁴⁶, bacteria can also proliferate on simple carbohydrates released by fungal enzymes⁴³. This has been referred to as cheating behavior. We simulated this behavior by changing the substrate uptake rate of the community that was not producing enzymes from zero to a positive value (Table 1). This change had direct impacts on decomposer communities dynamics and substrate residue chemistry at the end of the simulation. Indeed, when microbial residue decomposers had an opportunity to opt for cheating behavior and benefit from the plant compounds fragmented by plant decomposers, they developed faster than the plant decomposers and rapidly dominated them (Fig. 5b and Supplementary Fig. 1). The decline in fungal communities involved in plant depolymerization downregulated cellulose and lignin depolymerization and disappearance rates. Lignin-C therefore persisted at the end of the simulation (Fig. 5b).

This set of simulations provides novel insights on the processes governing SOM cycling and persistence. C-STABILITY elucidates the dependence of decomposers succession on the availability of accessible substrate, generates the kinetics of decomposer communities succession, and highlights their drivers. It also reveals that a substrate may persist in soil as a partly depolymerized form due to decomposers competition.

Contributions of plant and microbe residues to SOM at steady state

Prediction of the contribution of microbial materials to the total carbon stock is of great interest for assessing the C sequestration potential of a system. Indeed microbial residues are currently considered as being the main precursors of stable SOM⁸. For this purpose, we resolved the analytic formulation of the C stock and chemistry at steady state (Eqs. (25), (27), and (28)) while considering one microbial community, microbial residue recycling, continuous plant input and the substrate accessibility to enzymes (scenario 4).

A steady-state C stock of 1.553 g_C.cm⁻² was computed with the parameters given in Table 1. The living microbial biomass accounted for 0.6% of the total carbon stock (Eq. (25)), which was at the lower limit but within the range observed in soil across biomes⁴⁷. Cellulose and lignin were the most abundant biochemical substances, each representing 33% of the C stock at steady state (Fig. 6a). Microbial residues contributed to the remaining 33% as follows: 16% microbial sugar, 10% lipids, and 7% proteins. Within each biochemical class, the substrate was a continuum of forms at different decomposition stages. In Fig. 6a, the short peak on the right of the polymerization distribution of SOM corresponded to large polymers initially entering the system as plant litter or microbial residues. Organic matter altered by enzyme action was the main contributor of steady-state SOM, as shown by the dominance of polymers with a lower degree of polymerization. There was no or almost no substrate in the $$ {\mathcal{D}}_u$$ domains due to active microbial uptake of the smallest substrate fragments. The simulation closely reflected the SOM chemistry observed in situ in boreal soils^48,49. To predict the SOM chemistry in mineral soil horizons, C-STABILITY should account for the reduction in substrate accessibility due to interactions with the mineral phases, particularly for microbial products that are frequently involved in aggregates or bind on mineral surfaces^8,50–53.

Fig. 6

Soil organic matter at steady state (scenario 4).

a Biochemistry and level of polymerization (noted p) of microbe necromass signature (left), plant material input flux (center), and the resulting soil organic matter at steady state (right) with reference parameter values given in Table 1. Different biochemical substrates are separated by vertical solid lines. They are all accessible to enzymes. Microbial uptake domains are positioned at the left of biochemical classes and are delimited by vertical dashed lines. This simulation leading to a C stock of 1.553 g_C.cm⁻² at steady state is considered as reference in the sensitivity analysis. b Sensitivity analysis showing the relative changes in total C stock and its distribution among biochemical classes with ±50% changes in the parameters (variations in uptake rate $$ u_{\mathrm{mic}}^0$$, carbon use efficiency $$ e_{\mathrm{mic}}^0$$, and mortality rate $$ m_{\mathrm{mic}}^0$$ at row 1; variations in enzyme action rate $$ {\tau }_{\mathrm{enz}}^0$$ and cleavage factor α_enz illustrated for lipid depolymerases, cellulolytic and lignolytic enzymes at rows 2 and 3, respectively). For instance, a reduction of 50% of the value of $$ m_{\mathrm{mic}}^0$$ leads to a decrease of 50% of the steady-state C stock in comparison to reference simulation. In this case, the biochemical relative composition remains stable. Note that the scale of the y-axis varies.

The sensitivity analysis we carried out for the default parameters (Fig. 6b), in a system where substrates were accessible to their enzymes, confirmed the importance of microbial processes in controlling the amount and chemistry of SOM at steady state. As widely reported⁹, the carbon use efficiency parameter, $$ e_{\mathrm{mic}}^0$$, which was set to the same value for all biochemical classes (Table 1), was a major driver of C amount. C stock varied in the opposite direction to that of $$ e_{\mathrm{mic}}^0$$: total C declined by 37% with a 50% raise in $$ e_{\mathrm{mic}}^0$$, while it increased by 111% with a 50% decrease in $$ e_{\mathrm{mic}}^0$$. The increase in $$ e_{\mathrm{mic}}^0$$ raised the microbial biomass at the expense of CO₂ production, which accelerated the C turnover rate through increased substrate depolymerization and uptake (Eqs. (5) and (18)). The steady-state amount of C resulting from the increased value of $$ e_{\mathrm{mic}}^0$$ was lower and exhibited a larger relative contribution of microbe-derived metabolites. When looking at the individual biochemical classes sensitivity to $$ e_{\mathrm{mic}}^0$$ we noticed that the microbe-derived compounds were not impacted by variation in $$ e_{\mathrm{mic}}^0$$. The accelerated SOM cycling induced by raising $$ e_{\mathrm{mic}}^0$$ was indeed exactly counterbalanced by a higher rate of microbial necromass input into the SOM pool with the mathematical formulation and parameters currently implemented in C-STABILITY (Eqs. (27) and (28)). The C stock was also sensitive to the mortality rate $$ m_{\mathrm{mic}}^0$$ and exhibited a strong positive linear dependence on it, without any distinction among the various substrate biochemistries. In contrast, the C stock and biochemistry were quite insensitive to changes in the $$ u_{\mathrm{mic}}^0$$ uptake rate for the range of tested values (Fig. 6): C uptake was indeed limited here by the amount of accessible C. Consequently, the enzyme parameters controlling the amount of accessible substrate for microbe uptake had a marked impact on the C stock and biochemistry (Fig. 6b). An increase in the action rate of any enzyme, $$ {\tau }_{\mathrm{enz}}^0$$, decreased the quantity of its substrate at steady state, and vice versa. All biochemical substrates exhibited the same sensitivity to their own enzyme action rate (Eqs. (27) and (28)). An increase of 50% in any given $$ {\tau }_{\mathrm{enz}}^0$$ caused a 33% decrease in the C amount of the biochemical class impacted by the enzyme, while a 50% decrease doubled the C amount of the considered biochemical class. A variation in the cleavage factor of any enzyme, α_enz, caused a linear variation in the amount of its substrate at the steady state. In term of mechanisms, an increase in α_enz corresponded to an enhanced substrate exo-cleavage, which promoted the release of small fragments and preserved large polymers. The sensitivity to α_enz differed amongst biochemical classes (Eqs. (27) and (28)). For example a 50% variation in α_cellulose caused a 37% in the cellulose-C amount, and a 50% variation in α_lipid caused a 22% in the lipid-C amount.

The sensitivity analyses realized on C-STABILITY steady-state simulations question our current perception of SOM cycling drivers. Carbon use efficiency is widely recognized as critical regulator of SOM and microbe dynamics^54,55 and is integrated in many microbial-explicit models. But C-STABILITY predicts that carbon use efficiency variation differently affects plant and necromass residues. This theoretical output requires experimental investigations to verify its accuracy, because of potential significant implications on soil properties related to SOM nature. In addition, the sensitivity analyses contradicted the general belief that enzyme traits have a limited effect on SOM chemistry and quantity^6,9. It calls for closer consideration of the impact of catabolic processes on SOM cycling.

C-STABILITY description

Organic matter representation

The description of SOM in C-STABILITY consists of several subdivisions. First, organic matter is separated in two main pools, one for living microbes (noted C_mic) and one for the substrate (noted C_sub) (Fig. 1a). Several groups of living microbes can be considered simultaneously (e.g., bacteria, fungi, etc.) and C-STABILITY classes them into functional communities. Second, SOM is also separated between several biochemical classes, e.g., cellulose (or plant sugar), lignin, lipid, protein, and microbial sugar in this study (Fig. 1a). Third for each biochemical class, substrate accessible to its enzymes (noted ac) is separated from substrate which is inaccessible (noted in) due to specific physicochemical conditions, e.g., interaction between different molecules, inclusion in aggregates, sorption on mineral surfaces, etc.

Polymerization is a driver of interactions between substrate and living microbes and a continuous description of the degree of organic matter polymerization (noted p) is provided for each of these pools, as a distribution (Fig. 1b). The polymerization axis is oriented from the lowest to the highest degree of polymerization. A right-sided distribution corresponds to a highly polymerized substrate whereas a left-sided distribution corresponds to monomer or small oligomer forms. For each biochemical class ∗ (∗ = cellulose, lignin, lipid, etc.), the polymerization range is identical for both accessible and inaccessible pools. The total amount of C (in g_C) in the accessible and the inaccessible pools of any biochemical class is as follows:

where $$ p_{*}^{\min }$$ and $$ p_{*}^{\max }$$ are the minimum and maximum degrees of polymerization of the biochemical class ∗ and $$ {\chi }_{*}^{\mathrm{ac}}$$, $$ {\chi }_{*}^{\mathrm{in}}$$ (g_C.p⁻¹) are the polymerization distributions. Finally, the total substrate C pool is defined as the sum of all biochemical pools,

Accessibility to microbe uptake is described by the interval (also called domain) $$ {\mathcal{D}}_u$$, which corresponds to small substrate compounds, monomers, dimers or trimers smaller than 600 Daltons¹, that microbes are able to take up (in red in Fig. 1b). Besides, accessibility to enzymes occurs in the $$ {\mathcal{D}}_{\mathrm{enz}}$$ domain (in blue in Fig. 1b). Over time the substrate accessible to enzymes is depolymerized and its distribution shifts toward $$ {\mathcal{D}}_u$$ where it eventually becomes accessible to microbe uptake.

The numerical rules chosen to represent polymerization are as simple as possible in the context of theoretical simulations. Each pool is associated with a polymerization interval $$ \left[p_{*}^{\min },p_{*}^{\max }\right]$$ of length two. Initial substrate distributions are represented by Gaussian distributions centered at a relative distance of 25% from $$ p_{*}^{\max }$$ (here 0.5), with the standard deviation set at 5% of polymerization interval length (here 0.1). In the accessible pool, the microbial uptake domains $$ {\mathcal{D}}_u$$ are positioned at the left of the interval with a relative length of 20% (here 0.4), and enzymatic domains $$ {\mathcal{D}}_{\mathrm{enz}}$$ overlap the entire polymerization intervals.

Organic matter dynamics

As described in Fig. 1, three processes drive OM dynamics: (i) enzymatic activity, (ii) microbial uptake, biotransformation, and mortality, and (iii) changes in local physicochemical conditions. First, enzymes have a depolymerization role, which enables the transformation of highly polymerized substrate into fragments accessible to microbes. Second, microbial uptake of substrate is only possible for molecules having a very small degree of polymerization. When C is taken up, a fraction is respired and the remaining is metabolized, and biotransformed into microbial molecules that return to the substrate upon microbe death. Each microbial group has a specific signature that describes its composition in terms of biochemistry and polymerization. Third, changes in local substrate conditions drive exchanges between substrate accessible and inaccessible to enzymes (e.g., aggregate formation and break). All of these processes are considered with a daily time step (noted d).

Enzymatic activity Enzymes are specific to biochemical classes. They are not individually reported, but rather as a family of enzymes contributing to the depolymerization of a biochemical substrate (e.g., combined action of endoglucanase, exoglucanase, betaglucosidase, etc., on cellulose will be reported as cellulolytic action). Figure 2 describes how substrate polymerization distributions are impacted by enzymes. The overall functioning of each enzyme family (noted enz) is described by two parameters: a depolymerization rate $$ {\tau }_{\mathrm{enz}}^0$$ providing the number of broken bonds per time unit and a factor accounting for the type of substrate cleavage α_enz. The term $$ F_{\mathrm{enz}}^{\mathrm{act}}$$ (g_C.p⁻¹.d⁻¹) represents the change in polymerization of $$ {\chi }_{*}^{\mathrm{ac}}$$ due to enzyme activity for all $$ p\in {\mathcal{D}}_{\mathrm{enz}}$$,

The depolymerization rate, τ_enz (d⁻¹), is expressed as a linear function of microbial C biomass C_mic (g_C),

where $$ {\tau }_{\mathrm{enz}}^0$$ (g$$ {}_C^{-1}$$.d⁻¹) is the action rate of a given enzyme per amount of microbial C. If several microbial communities are associated with the same enzyme family, we replace the C_mic term by a weighted sum of the C mass of all communities involved in Eq. (5). The $$ {\mathcal{K}}_{\mathrm{enz}}$$ (p⁻¹) kernel provides the polymerization change from $$ p^{\prime }$$ to p,

where $$ {\mathbb{1}}_{p\le p^{\prime }}$$ equals 1 if $$ p\le p^{\prime }$$ and 0 otherwise. The α_enz cleavage factor denotes the enzyme efficiency to generate a large amount of small fragments and to shift the substrate polymerization distribution toward the microbe uptake domain $$ {\mathcal{D}}_u$$ (Fig. 2). α_enz = 1 is typical of the action of endo-cleaving enzymes, which randomly disrupts any bond of its polymeric substrate and generates oligomers. The shift toward $$ {\mathcal{D}}_u$$ is slower if α_enz increases. This is characteristic of exo-cleaving enzymes, which attack the end-members of their polymeric substrate, generate small fragments, and preserve highly polymerized compounds. To satisfy the mass balance, the kernel verifies $$ \int {\mathcal{K}}_{\mathrm{enz}}\left(p,p^{\prime }\right)dp=1$$. Then $$ F_{\mathrm{enz}}^{\mathrm{act}}$$ does not change the total C mass but only the polymerization distribution (i.e., $$ \int F_{\mathrm{enz}}^{\mathrm{act}}\left(\chi ,p,t\right)dp=0$$).

Microbial biotransformation Each microbial group (denoted mic) produces new organic compounds from the assimilated C. After death, the composition of the necromass returning to each biochemical pool ∗ of SOM is assumed to be constant, accessible and is depicted with a set of distributions s_mic,∗, named signature. Each distribution s_mic,* (p^–1) describes the polymerization of the dead microbial compounds returning to the pool ∗. The signature is normalized and unitless to ensure mass conservation, i.e., if we note that,

then we have ∑_*S_mic,* = 1.

For each accessible pool of substrate, the term $$ F_{\mathrm{mic},*}^{\mathrm{upt}}$$ describes how the microbes utilize the substrate available in the microbial uptake $$ {\mathcal{D}}_u$$ domain (Fig. 1b). For all $$ p\in {\mathcal{D}}_u$$,

where $$ u_{\mathrm{mic},*}^0$$ (g$$ {}_C^{-1}$$.d⁻¹) is the uptake rate per amount of microbe C. The substrate uptake rate linearly depends on the microbial C quantity.

Depending on a carbon use efficiency parameter $$ e_{\mathrm{mic},*}^0$$ (ratio between microbe assimilated C and taken up C), taken up C is respired or assimilated and biotransformed into microbial metabolites. This induces a change in the biochemistry and polymerization (Fig. 1a).

Finally, microbial necromass returns to the substrate pools with a specific mortality, which linearly depends on the microbial C quantity,

where $$ m_{\mathrm{mic}}^0$$ (d⁻¹) is the mortality rate of the microbe (Fig. 1a).

Change in local physicochemical conditions The polymerization of a substrate inaccessible to its enzymes remains unchanged over time. A specific event changing the accessibility to enzymes (e.g., aggregate disruption or desorption from mineral surfaces) is modeled with a flux from the inaccessible to the accessible pool. Transfer between these pools is described by the $$ F_{\mathrm{ac},*}^{\mathrm{loc}}$$ term for each biochemistry ∗,

where $$ {\tau }_{\mathrm{tr},*}^{\mathrm{ac}}$$ (d⁻¹) is rate of local condition change toward accessibility.

Transfer in the opposite way (e.g., aggregate formation, association with mineral surfaces) is described by the $$ F_{\mathrm{in},*}^{\mathrm{loc}}$$ term,

where $$ {\tau }_{\mathrm{tr},*}^{\mathrm{in}}$$ (d⁻¹) is rate of local condition change toward inaccessibility.

Organic matter input We defined time dependent distributions for carbon input fluxes. There are denoted $$ i_{*}^{\mathrm{ac}}$$ and $$ i_{*}^{\mathrm{in}}$$ (g_C.p⁻¹.d⁻¹) for both accessible and inaccessible pools of biochemical classes ∗. The total carbon input flux, expressed in g_C.d⁻¹, is:

General dynamics equations The distribution dynamics for each biochemical class * is obtained from Eqs. (4)–(6) and (8)–(11),

Then, the expended equations are,

where $$ {\mathbb{1}}_{{\mathcal{D}}_u}\left(p\right)$$ equals 1 if $$ p\in {\mathcal{D}}_u$$ and 0 otherwise.

The dynamics of the total substrate is ruled by,

The dynamics of microbial C_mic is obtained by,

and the CO₂ flux (g_C.d⁻¹) produced by the microbes is given by,

Scenarios

Scenario 1: cellulose decomposition kinetics and model sensitivity

A first simulation was run to depict cellulose depolymerization and uptake by a decomposer community over one year (see parameters in Table 1). A global sensitivity analysis focusing on the residual cellulose variable was made to determine (i) the relative influence of parameters, and (ii) how parameters influence varies over time (Fig. 3c). A specific attention was given on enzymatic parameters (especially α) to verify the pertinence of their introduction in the model.

We considered a specific method defined by Sobol for calculating sensitivity indices⁶⁵. It provides the relative contribution of the model parameters to the total model variance, here at different times of the simulation. The method relies on the same principle as the analysis of variance. It was designed to decompose the variance of a model output according to the various degrees of interaction between the n uncertain parameters $$ {\left(x_i\right)}_{i\in \left\{1,n\right\}}$$. Formally, by assuming that the parameter uncertainties are independent, the model output, denoted y, could be expressed as a sum of functions that take parameter interactions into account,

Under independence assumptions between models parameters variability, model variance is:

This variance decomposition leads to the definition of several sensitivity indices. The first-order Sobol’s index of each parameter is,

and higher order indices are defined by:

and so on. These indices are unique, with a value of 0–1 and their sum equals 1. Here we focused on Sobol’s first-order indices as they are usually sufficient to give a straightforward interpretation of the actual influence of different parameters^66,67. We computed the sensitivity of the model outputs at several times of the simulation to highlight the role of model’s parameters at different phases. Figure 3c shows the normalized Sobol’s first-order indices to illustrate the relative influence of the model parameters on residual cellulose-C amount. Sobol’s indices were estimated using a Monte Carlo estimator of the variance⁶⁸. This was performed for a small variation in parameter values (±5% uniform variability), by running 12,000 model simulations for the Monte Carlo sampling.

Scenario 2: effect of substrate inaccessibility to enzyme on litter decomposition kinetics

A simulation of lignocellulose (76% cellulose, 24% lignin) degradation was performed by taking into account peroxidases, which deconstruct the lignin polymer, and cellulases, which hydrolyze cellulose. The cellulose was initially embedded in lignin and inaccessible to cellulase. The lignolytic activity (peroxidases) induces a disentanglement of the cellulose from the lignocellulosic complex. Therefore, the action of peroxidases was seen as a change of cellulose physicochemical local conditions resulting in a progressive transfer to the accessible pool. This transfer was assumed to be linearly related to the activity of lignolytic enzymes in Eq. (10),

where $$ {\mathcal{D}}_{\mathrm{lig.}}$$ is the domain of lignolytic activity and where the $$ {\tau }_{\mathrm{tr,cell.}}^{ac,0}$$ coefficient is set at 13 g$$ {}_C^{-1}$$ for the current illustration.

The simulation was performed over one year. Enzymatic and microbial parameters given in Table 1 were chosen to be closely in line with the litter decomposition and enzyme action observation^16,37,69.

Scenario 4: soil organic matter composition at steady state

We resolved the analytic formulation of the C stock and chemistry at steady state under several assumptions. We only considered one microbial community, a continuous constant plant input I at a rate of 2.74.10⁻⁴ g_C.cm⁻².d⁻¹ and microbial recycling⁴⁷. To be able to explicitly calculate the steady state, we only considered accessible pools, then cellulose substrate was not embedded in lignin but directly accessible to cellulolytic enzymes (Fig. 6). Finally, we considered that C use efficiency ($$ e_{\mathrm{mic}}^0$$) and uptake ($$ u_{\mathrm{mic}}^0$$) parameters were identical for all biochemical classes. A full mathematical proof is given in Supplementary Note 3.

At steady state, the amount of microbial carbon is,

For each biochemical class ∗, we define $$ p_{*}^u$$ which verifies $$ p_{*}^{\min }<p_{*}^u<p_{*}^{\max }$$ and $$ {\mathcal{D}}_u=\left[p_{*}^{\min },p_{*}^u\right]$$, and

By considering the scenario setup (Table 1) and Eq. (26), if ∗ = plant sugar and lignin, $$ {\theta }_{*}\left(p\right)=m_{\mathrm{mic}}^0\frac{\left(1-e_{\mathrm{mic}}^0\right)i_{*}\left(p\right)}{e_{\mathrm{mic}}^{0}I}$$ and if ∗ = lipid, protein and microbial sugar, $$ {\theta }_{*}\left(p\right)=m_{\mathrm{mic}}^0{s}_{*}\left(p\right)$$. The steady-state distribution of C is obtained for $$ p\in \left[p_{*}^u,p_{*}^{\max }\right]$$,

and for $$ p\in \left[\right)p_{*}^{\min },p_{*}^u\left[\right)$$,

where $$ \beta =\frac{{\tau }_{\mathrm{enz}}^0-{\alpha }_{\mathrm{enz}}{u}_{\mathrm{mic}}^0}{{\tau }_{\mathrm{enz}}^0+u_{\mathrm{mic}}^0}$$.

Compared to previous scenarios related to laboratory experiments, enzymatic activities were divided by five to account for the impact of in situ climatic conditions. Other enzymatic and microbial parameters are given in Table 1. To explore how the catabolic traits of enzymes and anabolic traits of microbes affect the SOM composition, we modified individual parameters by 50% and documented their effects on the steady-state amount of C and its biochemistry.