Survival of the fewest: Microbial dormancy and maintenance in marine sediments through deep time

Abstract Microorganisms buried in marine sediments are known to endure starvation over geologic timescales. However, the mechanisms of how these microorganisms cope with prolonged energy limitation is unknown and therefore yet to be captured in a quantitative framework. Here, we present a novel mathematical model that considers (a) the physiological transitions between the active and dormant states of microorganisms, (b) the varying requirement for maintenance power between these phases, and (c) flexibility in the provenance (i.e., source) of energy from exogenous and endogenous catabolism. The model is applied to sediments underlying the oligotrophic South Pacific Gyre where microorganisms endure ultra‐low fluxes of energy for tens of millions of years. Good fits between model simulations and measurements of cellular carbon and organic carbon concentrations are obtained and are interpreted as follows: (a) the unfavourable microbial habitat in South Pacific Gyre sediments triggers rapid mortality and a transition to dormancy; (b) there is minimal biomass growth, and organic carbon consumption is dominated by catabolism to support maintenance activities rather than new biomass synthesis; (c) the amount of organic carbon that microorganisms consume for maintenance activities is equivalent to approximately 2% of their carbon biomass per year; and (d) microorganisms must rely solely on exogenous rather than endogenous catabolism to persist in South Pacific Gyre sediments over long timescales. This leads us to the conclusion that under oligotrophic conditions, the fitness of an organism is determined by its ability to simply stay alive, rather than to grow. This modelling framework is designed to be flexible for application to other sites and habitats, and thus serves as a new quantitative tool for determining the habitability of and an ultimate limit for life in any environment.


| INTRODUC TI ON
Microorganisms in marine sediments are characterized by extreme energy limitation and slow metabolisms (Hoehler & Jørgensen, 2013;Lever et al., 2015). Marine sediments can thus be used to better understand constraints on the origin, proliferation and longterm survival of life on Earth, while also serving as an analogue for extra-terrestrial environments. Dormancy, a reversible state of low metabolic activity, is one strategy utilized by microorganisms to cope with perpetual energy limitation. Dormancy can contribute towards maintaining diversity in unpredictable and sub-optimal habitats (Lennon & Jones, 2011), and is thought to be widespread among the subsurface biosphere (Jørgensen & Marshall, 2016).
Once dormancy is initiated by starvation or resource limitation (Lennon & Jones, 2011), a cell's metabolism is reserved mostly to essential functions such as biomolecular repair and replacement, rather than to support growth (Kempes et al., 2017;Orcutt et al., 2013;Tijhuis, Van Loosdrecht, & Heijnen, 1993). "Maintenance" energy refers to the sum of the energetic costs of the activities that do not produce growth, but that are required to sustain life.
These costs are poorly quantified in many environments (Hoehler & Jørgensen, 2013). Nevertheless, since most microorganisms in marine sediments appear to be merely surviving rather than growing, maintenance is thought to comprise a substantial component of the total power (the rate of energy utilization) that is consumed in these habitats (Bradley, Amend, & LaRowe, 2018a;LaRowe & Amend, 2015b;Orcutt et al., 2013).
The power that is available to microorganisms in an environment is dependent on the Gibbs energy harvested from the catalysis of redox reactions and the rate at which those reactions proceed. Catabolic reactions can generally be classified as endogenous, where cellular biomass is utilized as a reactant to serve as a source of energy (Dawes & Ribbons, 1962;Herbert, 1958), or exogenous, where the energy is supplied by the consumption of external substrates (Morita, 1988;Pirt, 1965). The operation of one strategy or the other by microorganisms is thought to be determined by environmental and thermodynamic factors (Wang & Post, 2012), and is enormously important in rates of carbon cycling and associated reactions in marine sediments (Arndt et al., 2013).
Presently, the extent of dormancy in the deep biosphere, as well as the role of endogenous and exogenous catabolism to support cellular maintenance, is virtually unknown. Numerous challenges to investigating life in the deep biosphere, including accessibility, measurement of extremely low biomass and rates of energy processing, and designing laboratory incubations whose conditions resemble the natural environment, have hindered progress in understanding these factors. Alternatively, mathematical models, which have long been used to describe microbial processes (reviewed in Bradley et al. 2018a;, have proven useful in providing a mechanistic framework with which to interpret observations (e.g., Dale, Bruchert, Alperin, and Regnier 2009). However, dormancy and maintenance processes in marine sediments have not been modelled, and there are presently no suitable numerical models that capture the details necessary to simulate these processes pertaining to sediments or the deep biosphere in a single framework (Bradley et al., 2018a).
Here, we present a new model "MicroLow 1.0" (Microbial Ecophysiology in Low Energy Environments 1.0) that includes novel mathematical constructs for microbial growth, yield, maintenance and physiological state, including a single active and multiple dormant phases. This model was designed with the marine sediment biosphere in mind, but it is also transferable to other transitory or low-energy environments. The microbial model presented and implemented here is novel not only in its components and the processes that it simulates, but also in the multi-million-year timescales over which it is implemented. After describing the modelling framework, we simulate the biogeochemical dynamics of a deeply buried microbial community in oxic sediments underlying the South Pacific Gyre (SPG) and their role in particulate organic carbon (POC) degradation. The newly developed model is used to provide insight into the ecophysiology of these microorganisms and to suggest the means by which they may persist over extraordinarily long timescales, enduring prolonged energy limitation for upwards of millions of years.

| Microbial model
The microbial model implemented in this study divides microbial biomass, B, into four pools (B 1-4 ), which are distinguished by their state of activity, and a single pool of organic matter representing POC (Table 1).
A system of coupled ordinary differential equations (

| Microbial dynamics
We consider a single pool of active biomass (B 1 ) and three pools of dormant biomass, from recently active (B 2 ) to long since dormant (B 4 ). It is intended that this framework represents a gradient (or depth) of dormancy across the microbial community (Lennon & Jones, 2011;Locey, 2010;Stolpovsky, Martinez-Lavanchy, Heipieper, Van Cappellen, & Thullner, 2011). Note that we distinguish discreet pools for sake of a numerical description of this gradient and do not suggest the existence of three distinct dormancy states in natural settings. Active biomass is the only pool that is capable of growth (i.e., cellular division). It is assumed that aerobic heterotrophy is the dominant metabolism in oxic SPG sediments , and thus, the growth rate of B 1 is dependent on POC concentration, via Michaelis-Menten kinetics ( Figure 2a) (Michaelis & Menten, 1913). Dormant cells are viable but must undergo activation before they are capable of growth. Dormancy requires that an organism (a) is not growing or dividing (i.e., has a reproductive rate equal to zero) and (b) has a lower metabolic demand than when it is active (Lennon & Jones, 2011;Stolpovsky et al., 2011). Furthermore, a dormant microorganism may better endure inhospitable conditions and thus have a lower mortality rate than its active counterpart (Johnson et al., 2007;Lennon & Jones, 2011;Price & Sowers, 2004). Organisms transition to a "deeper" state of dormancy the longer they have been dormant, decreasing their metabolic and mortality rates (Lennon & Jones, 2011;Stolpovsky et al., 2011). Stolpovsky et al. (2011) use a continuous function "S" to describe "depth of dormancy," as a means to modify the mortality rate of dormant microorganisms based on the duration of unfavourable conditions. This necessitates the use of multiple additional parameters. Our approach, which is based instead on transitions between discreet pools, eliminates the need for such a function and requires fewer parameters. Biomass from all pools can die, utilize POC and biomass to fulfil maintenance power requirements, and transition to active and dormant phases.
The overall rate of change in active biomass (B 1 ) is given by: where t is time, V B1 represents the rate of new biomass growth, D B1 denotes the death rate of B 1 , ξ B1 corresponds to the deactivation rate of B 1 into B 2 , M En,B1 represents the consumption of biomass due (1) Microbial growth and death Deactivation and activation Deactivation of biomass (B n ) The overall change in all other biomass pools (B n ) is given by: where D Bn represents the death rate of B n , ξ Bn corresponds to the rate deactivation of B n to B (n+1) , ξ B(n−1) corresponds to the rate of deactivation of B (n−1) to B n , ϵ Bn is the activation of B n to B 1 , and M En,Bn represents the consumption of biomass due to endogenous catabo- Biomass growth is given by: where B 1 is the concentration of active biomass in units of μg C/ cm 3 sediment, v max is the maximum growth rate of active biomass, POC is the concentration of particulate organic carbon, and K v is the half-saturation constant for microbial growth according to standard Michaelis-Menten kinetics (Michaelis & Menten, 1913) (see Figure 2).
The microbial death rate is given by: where α Bn is the mortality rate of biomass B n .

| Activation and deactivation
The model is based on the principle that microorganisms in marine sediments can take on various physiological states, from active and growing (B 1 ) to dormant (B 2 -B 4 ) (Stolpovsky et al., 2011). The deactivation and reactivation of biomass (i.e., the transitioning of states between B 1 and B 4 ) depends on the potential supply of catabolic energy to the cells in relation to a threshold concentration of a limiting factor (K S ), which is, in this case, POC concentration.
The deactivation (ξ) of biomass B n to B (n+1) is given by: where R S,D is the specific rate of deactivation. Similarly, the activation (ϵ) of biomass B n to B 1 is given by: where R S,A is the specific rate of activation.
θ S is a function that accounts for the direction and rate of state change depending on POC as a limiting resource. It is based on the principle that if conditions in the environment are better than a certain threshold, there will be net activation of biomass and vice versa.
The function, from Stolpovsky et al. (2011), is adapted from Fermi-Dirac statistics: where K S is a threshold POC concentration for net activation-deactivation, and st S is a non-dimensional parameter controlling the steepness of the sigmoidal function as shown in Figure 2b. There is a net deactivation of biomass (i.e., B n to B (n+1) ) under unfavourable conditions when the concentration of POC falls below K S and thus θ S < 0.5. Similarly, there is a net activation of biomass (i.e., B n to B 1 ) when the concentration of POC rises above K S and thus θ S > 0.5.
Unlike deactivation, where cells must first transition through the first stages of dormancy to enter into a deeper state of dormancy (Lennon & Jones, 2011;Stolpovsky et al., 2011), dormant microorganisms from any state transition directly to the active state (B 1 ) upon the onset of favourable conditions at a rate determined by θ S and R S,A (Morono et al., 2011;Takano et al., 2010). where m Bn is the specific maintenance power requirement of B n .

| Maintenance
Maintenance power requirements (m Bn ) are described as a proportional carbon cost per unit of biomass per thousand years (i.e., similar

| Particulate organic carbon dynamics
The rate of POC degradation is given by: where Y G represents the true growth yield (i.e., the yield in absence of maintenance (Bradley et al., 2018a;Heijnen & Van Dijken, 1992;Pirt, 1965;Van Bodegom, 2007)), M Ex,Bn represents the rate of exogenous consumption of substrate for maintenance by B n , and D Bn represents the rate at which dead cells contribute POC from B n (i.e., necromass).

| Model application
We selected sediments underlying the SPG for a detailed case study site to model microbial ecophysiology over multi-million- year timescales (D'Hondt et al., 2009. Ocean primary productivity in the SPG is so low that organic carbon concen-

| Initial values and test data
Cell abundance and POC concentrations are taken from published analyses of extracted drill cores (D'Hondt et al., 2011. To convert sediment depth (z) to sediment age (age(z)), we use the following equation (Berner, 1980): where Φ 0 represents the porosity at the sediment-water interface (SWI), c 0 corresponds to the compaction length scale, and ω 0 refers to the sedimentation rate, which is assumed to be constant. The porosity at depth z, Φz, is calculated by (Athy, 1930): We use a SWI porosity (Φ 0 ) equal to 0.87, a uniform sedimentation rate (ω 0 = 10 −6 m/year) and grain density ( We assume a cell mass of 14 fg C/cell, consistent with recent estimates for microbial cells in marine sediments (Braun et al., 2016; Kallmeyer, Pockalny, Adhikari, Smith, & D'Hondt, 2012) and a bioenergetic analysis of SPG sediments (Bradley et al., 2018b). POC provided in weight % is converted into μg C org per cm 3 for every depth accounting for changes in porosity using the physical model described above. We used regression models from a previous study (Bradley et al., 2018b) to provide initial values (i.e., t 0 ) for microbial abundance and POC (R 2 > 0.97) ( Table 1).

| Implementation and numerical solution
The mathematical expressions described above and in Table 2 are implemented in the open-source computing environment and programming language R, which is freely available (http://www.r-project.org/). Model code is available for free online via the Supporting Information Appendix S1.
The model is run with nominal parameters for a period representing 75 million years. Parameter values are constrained from results published in other studies (Table 3). A sensitivity study of 16 model parameters is carried out to assess the stability of model output and the dependency of output on individual parameters. Every parameter is sequentially adjusted by +5% of the nominal value and tested, and then returned to its nominal value before testing the next one.
Results of the sensitivity tests are compared to the baseline simulation in which the model parameters are equal to those shown in Table 3.   Model results show that nearly all of the carbon processed by microorganisms is dedicated to maintenance activities (<886,000 fg C degraded cm −3 year −1 ) rather than growth (<140 fg C degraded cm −3 year −1 ) (Figure 5e). Endogenous catabolism is negligible, at a magnitude that is too small to appear in Figure 5. Additionally, the autochthonous (i.e., formed in situ) necromass-derived POC is negligible (<156 fg C cm −3 year −1 ).

| Endogenous catabolism
Two additional simulations are performed in which parameters were manipulated to simulate an environment where microorganisms are more likely to utilize their own biomass as a source of energy in SPG sediments (i.e., a preference of endogenous catabolism over exogenous catabolism). In the first simulation, illustrated in Figure

| Sensitivity of model parameters
The sensitivity of (a) total biomass and (

| Model results
Microorganisms are found to inhabit remote and oligotrophic marine sediments at very low abundances (~10 3 to 10 4 cells/cm 3 ) for extraordinarily long timescales (> 20 million years) . Just the fact that intact microbial cells are found in this ancient habitat has remarkable implications concerning the resilience of these organisms, yet almost nothing is known about the physiological mechanisms concerning their growth, death and activity.
The new model presented and implemented here, which is the first model to explicitly represent microbial dormancy in the deep biosphere, is an attempt to reconcile these unknowns, using a quantitative and mechanistic approach. Thus, we provide a process-based account of the mechanisms that might enable microorganisms to persevere in these settings and endure extreme energy limitation over prolonged timescales.
First, model results suggest that marine sediments at SPG constitute an unfavourable habitat for the growth and proliferation Nevertheless, at this locale, mortality rates are highest and new biomass growth is insignificant ( Figure 5). Thus, we infer that the vast majority of microorganisms that are entombed in sediments at SPG are poorly suited to this environment. This is supported by empirical measurements of cell abundance at SPG (Figure 3).
Moreover, the rapid decline in biomass in recently deposited nearsurface sediment is a global phenomenon (Jørgensen & Marshall, 2016), suggesting that the low-energy environment typical of sediments is not favourable to the organisms found inhabiting them.
Second, model results are suggestive that dormancy is prevalent in the SPG subsurface and that the vast majority of these microorganisms exist in a state of reduced metabolic activity.
Microorganisms are initially prescribed to a metabolically "active" state (B 1 ), that is they are capable of growth. However, in response to unfavourable environmental conditions, the vast majority of F I G U R E 5 Flux of carbon in and out of (a-d) each biomass pool (B 1 to B 4 ) resulting from growth, maintenance, death and the deactivation of microbial groups into various stages of dormancy (shaded regions). Flux of carbon in the (e) POC pool results from exogenous maintenance (turquoise), growth and necromass contributions. Fluxes due to growth and necromass are extremely small in magnitude (<160 fg C cm −3 year −1 ) and thus are not visible on this scale. The net change in carbon is represented by the dashed black line (a-e). Increases in biomass are due to growth (dark green) and the deactivation of less dormant biomass pools (light green). The loss of biomass arises from transitions to a more dormant state (blue) and death (pink). There is no activation of biomass (e.g., transition from B n to B 1 ) or consumption of biomass for maintenance (endogenous catabolism).  Konopka, 1999;Lennon & Jones, 2011;Stenström, Svensson, & Johansson, 2001;Stolpovsky et al., 2011). The near-zero growth of deeply buried microorganisms, as well as the prevalence of dormancy among the community, leads to the premise that these cells are ancient "relic organisms," comprised of a few rare members of the surface microbial community that survived burial. This interpretation is corroborated by evidence from comparative DNA amplicon, single-cell and metagenomic sequencing in marine sediments from Aarhus Bay, Denmark, showing that deep sub-seafloor sediments (>5,000 years old) are populated by a select few descendants and survivors of microbial communities from surface sediments .
In many habitats, microorganisms experiencing favourable changes in their environment may exit the dormant state and become active once again (Lennon & Jones, 2011;Morono et al., 2011;Takano et al., 2010;Trembath-Reichert et al., 2017). subsurface being likened to a "dead-end strategy" (Jørgensen, 2012). The estimated generation times for the deep biosphere, up to several thousands of years (Braun et al., 2017;Trembath-Reichert et al., 2017;Biddle et al., 2006;Jorgensen, D'Hondt, & Miller, 2006;Jørgensen, 2011;Lomstein et al., 2012;Whitman, Coleman, & Wiebe, 1998;Xie, Lipp, Wegener, Ferdelman, & Hinrichs, 2013), necessitate very low mutation rates, and therefore, selection is likely dominated by the presence of pre-adapted sub-seafloor taxa (Orsi, 2018;Petro, Starnawski, Schramm, & Kjeldsen, 2017). Further, whether these generation times reflect actual growth (i.e., new biomass generation from cellular division) or replacement (i.e., turnover of biomolecules without division, akin to maintenance activities) is not known. Accordingly, organisms in the deep biosphere may effectively be precluded from the evolutionary emergence of advantageous traits since this requires cellular growth and division. In accordance with previous findings (Lennon & Jones, 2011;Stolpovsky et al., 2011), our results suggest that cells that are able to successfully transition to dormancy may outcompete organisms exhibiting a "fast growth" strategy in ultra-oligotrophic settings such as SPG, thereby enabling their persistence over extremely long timescales.
Third, model results lead us to believe that POC consumption is dominated by catabolism to support maintenance activities rather than new biomass synthesis (i.e., growth). The decline in cell abundance is accompanied by a decline in POC concentration, which, in both modelled and experimental data, is most rapid near the SWI (Figure 3). Modelling studies LaRowe & Amend, 2015b) and measurements (D'Hondt et al., 2009(D'Hondt et al., , 2011 suggest that microorganisms at SPG utilize this POC as an electron donor coupled to the reduction in oxygen as a primary source of energy. The main source of POC to microorganisms at SPG is allochthonous material that was deposited and buried along with the inoculum of microbial cells, rather than POC supplied autochthonously in the form of necromass ( Figure 5). This is corroborated by a previous finding that despite relatively high mortality, the autochthonous recycling of microbial necromass is a negligible source of power at SPG (Bradley et al., 2018b). The rate of POC degradation, which is initially rapid, noticeably decreases between 2 and 10 million years. In both model predictions and measurements, a minor fraction of POC (0.01-0.1 weight %) is preserved over extended timescales (~75 million years). Observed growth yield at SPG declines from ~0.00015 in shallow sediment to effectively zero in sediments older than 4 million years (Figure 5e).
These values are remarkably low compared to other environments such as other marine sediments (0.08-0.20 Whitman et al., 1998)) and soils (0.06-0.84 ). Thus, we interpret a near no-growth scenario in shallow SPG sediments, and a no-growth scenario in sediments older than 4 million years (Bradley et al., 2018a). Our deduction of maintenance-dominated catabolism is consistent with a number of substrate-or energy-limited environments where cells do not grow despite being known to consume POC (Blagodatsky et al., 2000;del Giorgio & Cole, 1998).
Our interpretation of these results also aligns with the findings of theoretical studies in which the maintenance activity of increasingly small and starving prokaryotes converges on total activity, since energy expenditure is dominated by biomolecule repair and replacement rather than new biomass synthesis (Kempes, Dutkiewicz, & Follows, 2012;Kempes et al., 2017;Maitra & Dill, 2015).
Furthermore, we believe that it is possible that the low rates of microbial activity prescribed to the model are in fact too high. There is generally good agreement between modelled POC concentration and measured POC from SPG sediment cores; however, a notable mismatch occurs between ~2 and 8 million years following burial, where the model predicts POC concentrations lower than those measured. It is likely, therefore, that simulated POC degradation rates exceed the actual POC degradation rates over this interval, and thus, by extension, simulated microbial maintenance activity is too high. This idea challenges our understanding of the minimum power requirement of microbial life under extreme energy limitation, which has been suggested to be as low as 10 −21 J s −1 cell −1 (LaRowe & Amend, 2015b). Furthermore, it has been shown that the distribution of activity among a population of starving microorganisms may be highly negatively skewed (i.e., a small number of cells utilizing a large proportion of total energy) (Shoemaker & Lennon, 2017). This possibility is not accounted for in our estimation of power per cell and may have ecological consequences on the POC profile and the interpretation of results. By focusing on implementing various versions of eco-physiological models for microorganisms in extremely energy-limited settings, and also capturing the variability and distribution of activity within a community, we may improve the understanding of the minimum power that is required to support microbial life.
Finally, modelling results presented here clearly reveal that POC in SPG sediments plays a critical role in the supply of catabolic power for an organism to undertake maintenance activities, thus enabling its survival. We deduce that microorganisms must rely solely on exogenous catabolism rather than endogenous catabolism to be able to persist in SPG sediments over millions of years. In two additional simulations designed to test a strategy whereby microorganisms partially rely on endogenous catabolism (i.e., biomass used in place of POC as an electron donor in oxygenic respiration), the community rapidly declines to extinction (at suggestions that dormant microorganisms that deplete their internal reserves will die without replenishment of those resources (Lennon & Jones, 2011).

| Model framework and parameter values
Parameter values are taken from the literature and constrained by measurements at SPG as well as calculations based on these data.
No single value for maintenance powers (m B1-4 ) and death rates (α B1-4 ) can account for the observed biomass and POC concentrations over 75 million years of burial, thus justifying our selection of multiple pools representing biomass at different depths of dormancy (Lennon & Jones, 2011;Stolpovsky et al., 2011). Mortality rates (α Bn ) are some of the most sensitive parameters. However, they are suitably constrained based on previous bioenergetic and non-linear regression models (Bradley et al., 2018b), providing values from ~4 × 10 −6 per year at the SWI to ~2 × 10 −8 per year at 75 m sediment depth. Obtaining a measurement of microbial growth rates in marine sediments, on the other hand, has proved to be challenging, and the subject of whether microorganisms undergo growth at all in oligotrophic sediments is highly debated (Jørgensen & Marshall, 2016;Lever et al., 2015). A nominal value for v max of 0.17 per thousand years is based on an estimate of biomass turnover time from ancient sediments on the Peruvian continental shelf , which is at the upper end of published estimations of turnover times from ancient marine sediments, spanning 1,000 to 73,000 years (Biddle et al., 2006;Jørgensen, 2011;Jorgensen et al., 2006;Lomstein et al., 2012;Whitman et al., 1998;Xie et al., 2013).
Turnover times derived from amino acid racemization modelling are highly uncertain and have recently been revised (Braun et al., 2017).
Despite a high degree of uncertainty associated with v max , cells at SPG are generally precluded from growth in any meaningful way due to the lack of available POC (POC << K v ), and thus growth (V B1 ) is minimal. The half-saturation constant for growth (K v ) is a relatively poorly constrained parameter with a moderate influence on model results and must account not only for the concentration but also reactivity of POC, given the quasi-1G approach implemented here.
To derive more meaningful values for v max and K v , future research should investigate the extent to which absolute (rather than net) microbial growth occurs in the marine subsurface, and how growth depends on substrate (and thus power) availability, POC reactivity and other factors.
In a natural environment, the bacterial growth yield, representing the proportion of organic carbon taken up that is incorporated into new biomass, is subject to trade-offs based on a variety of selective pressures (Heijnen & Van Dijken, 1992;Lele & Watve, 2014;Sinsabaugh, Manzoni, Moorhead, & Richter, 2013). Distinguishing between true growth yield (Y G , Lipson, 2015) and maintenance activities is important in low or no-growth environments, especially since maintenance activities potentially constitute a much greater fraction of total power utilization in these habitats (Bradley et al., 2018a;Kempes et al., 2017). A standalone maintenance requirement is used to mechanistically account for the utilization of large amounts of power by bacteria to serve functions that are not directly related to growth (Bradley et al., 2018a). The majority of estimates for bacterial growth efficiency for marine sediment microorganisms are within the range of 0.08 < Y G <0.20 (Biddle et al., 2006;D'Hondt, Wang, & Spivack, 2014;Heijnen & Van Dijken, 1992;Jørgensen & Marshall, 2016;Langerhuus et al., 2012;Lomstein et al., 2012;Starnawski et al., 2017;Whitman et al., 1998). We select the highest estimate (Y G = 0.20) since the published values typically do not distinguish growth yield from maintenance power requirement and thus are negatively skewed, accounting for the additional energy expended on maintenance activities (Jørgensen & Marshall, 2016;Whitman et al., 1998). Nevertheless, the model results are insensitive to variation in Y G so the absolute value of Y G is not important so long as maintenance activity is accounted for separately.
It is rare that studies simultaneously quantify respiration rates and cell numbers in deep marine sediments and thus estimates of per-cell respiration (resulting from total growth and maintenance activities) are lacking (Hoehler & Jørgensen, 2013;Holmkvist et al., 2011;Leloup et al., 2007;Sahm, MacGregor, Jørgensen, & Stahl, 1999). We obtain estimates of maintenance power demand (m Bn ) from a previous bioenergetic investigation of SPG sediments (Bradley et al., 2018b). A reactive continuum model was fit to measured POC data (D'Hondt et al., 2011) and is used to derive rates of POC degradation. These data are coupled to a non-linear regression model for cell abundance, thus providing POC degradation rate per cell per depth (or equivalent sediment age). It is then assumed that cells are utilizing all energy derived from the oxidation of POC exclusively for maintenance (Bradley et al., 2018a). Based on these cal- • Physiology. The three states of dormancy resolved in the model (B 2-4 ) are intended to represent a gradient of reduced metabolic activity rather than the existence of three distinct biological states, and additional or fewer physiological states may be included depending on the nature of the organisms and environment to be studied. It might also be useful to base microbial activity on thermodynamic factors or a measure of Gibbs energy, with thresholds and requirements based on an electron-equivalent basis (e.g., Dale, Regnier, & Van Cappellen, 2006). Furthermore, the activation of dormant cells (i.e., transition from B 2-4 to B 1 ) and its mathematical formulation is not tested in the present setting, due to the continual worsening of conditions with increased burial at SPG. The nature of reactivation, as well as the rates associated with it, therefore, warrant further testing, which should draw from both laboratory and modelling studies (e.g., Morono et al., 2011;Stolpovsky, Fetzer, Van Cappellen, & Thullner, 2016;Stolpovsky et al., 2011;Takano et al., 2010;Trembath-Reichert et al., 2017).
• Treatment of POC. We use a simple 1G approach to resolve organic carbon. 1G approaches have been widely applied to a range of sedimentary environments, are often favoured for sake of minimizing complexity and the number of parameters, and are suitable where the degradability of POC compounds does not vary widely (Arndt et al., 2013). However, unlike multi-G and continuum approaches, a 1G model cannot capture the heterogeneity of sedimentary POC compounds and their various reactivity, as well as the various factors affecting POC degradation rate (Arndt et al., 2013). Nevertheless, the predictive capability of a more complex approach remains limited by the availability of appropriate measurements and data (e.g., molecular characterization of POC compounds, mineral-POC interactions, microbial functional groups), the level of mechanistic understanding of organic matter degradation rates in the environment and knowledge of appropriate parameter values. The 1G modelling approach implemented here is sufficient to provide a good fit between model results and measurements of cellular carbon and organic carbon concentration at SPG, while enabling us to focus our analyses on the novel components of the microbial model (i.e., bioenergetics and physiological state transitions). We suggest that the POC at SPG is likely to be comprised of a highly non-reactive residual fraction of sedimentary organic matter (Bradley et al., 2018b), and thus may be appropriately lumped into a single pool (Arndt et al., 2013).
Future iterations of this modelling framework might, however, expand on the treatment of POC to incorporate multiple or infinite pools.

| CON CLUS I ON S AND OUTLOOK
Microorganisms buried in SPG sediments undergo minimal to no new biomass growth; they transition to dormancy (with no reactivation over millions of years) and utilize substrate rather than biomass to meet their energetic demand for maintenance. By exploring dormancy and basal maintenance power requirements in a quantitative framework, it is clear that a microorganism's ability to transition between active and dormant physiological states, as well as the need to meet energetic maintenance power demand by exogenous strategies, are key factors in enabling its survival over long timescales. Thus, in the oligotrophic deep biosphere, the fitness of a microorganism may not be determined by its growth, but rather its ability simply to stay alive. Furthermore, the quantity of buried POC and the cost of maintenance activities set the ultimate limit on the duration that microorganisms can survive in a dormant state before endogenous catabolism results in rapid loss of cellular biomass. Recognizing the role of dormancy while quantifying the basal power requirement of organisms is critical to understanding how microorganisms endure unfavourable environments and to setting a limit on how long these organisms may survive in oligotrophic settings.

ACK N OWLED G M ENTS
We thank Sandra Arndt (l'Universitélibre de Bruxelles) for insightful discussion on the modelling approach. We also thank two anonymous reviewers, whose comments and suggestions helped improve the manuscript significantly.