# The critical role of pore size on depth-dependent microbial cell counts in sediments

## Abstract

Cell counts decrease with sediment depth. Typical explanations consider limiting factors such as water availability and chemistry, carbon source, nutrients, energy and temperature, and overlook the role of pore size. Our analyses consider sediment self-compaction, the evolution of pore size with depth, and the probability of pores larger than the microbial size to compute the volume fraction of life-compatible pores. We evaluate cell counts vs. depth profiles gathered at 116 sites worldwide. Results confirm the critical role of pore size on cell counts in the subsurface and explain much of the data spread (from ~ 9 orders of magnitude range in cell counts to ~ 2 orders). Cells colonize pores often forming dense biofilms, thus, cell counts in pores are orders of magnitude higher than in the water column. Similar arguments apply to rocks.

## Introduction

Bioactivity has been found at sediment depths in excess of 1000 m1,2,3. Overall, cell counts decrease with depth2,4,5,6,7; typical explanations include limiting factors such as water availability and chemistry, carbon source, nutrients, energy and temperature8,9,10,11,12,13,14,15. Some studies have also recognized the critical role of pore size on microbial life and the need for interconnected and traversable habitable spaces16,17,18. A previous experimental study and related analyses identified three distinct regions defined by particle size and sediment depth: “active and motile” for coarse silts and sands at all depths, and either “trapped” or “membrane punctured” for clay-controlled sediments19. Still, the role of pore size as a limiting factor to microbial activity in sediments remains unnoticed or overlooked.

Here, we analyze cell counts versus depth data gathered at 116 sites as part of the global Ocean Drilling Program ODP, Integrated Ocean Drilling Program IODP, and other expeditions. Our goal is to assess the role of pore size on microbial cell counts in marine sediments.

## Analyses

A detailed description of the analytical approach follows. Additional details, the complete dataset and references can be found in the Supplementary Information associated to this manuscript.

### From sediment self-compaction to cell counts

The equilibrium analysis of a sediment slice of thickness dz at depth z predicts that the effective stress gradient dσ'z/dz is a function of the local void ratio ez (Note: the void ratio ez is the volume of voids Vv normalized by the volume of the solid mineral phase Vm):

$$\frac{{d\sigma_{z}^{^{\prime}} }}{dz} = \rho_{w} \left[ {\frac{{G_{s} - 1}}{{1 + e_{z} }}} \right]g$$
(1)

where gravitational acceleration is g = 9.81 m/s2 and the specific gravity Gs = ρm/ρw is the ratio between the mineral density ρm and water density ρw. The sediment void ratio ez decreases with depth z as the vertical effective stress σ'z increases. We adopt an asymptotically-correct exponential compaction model, where the void ratio decreases from the asymptotic maximum value eL at the water-seabed interface where σ'z = 0, to the limiting void ratio eH at very high effective stress20:

$$e_{z} = e_{H} + \left( {e_{L} - e_{H} } \right)\exp \left[ { - \left( {\frac{{\sigma_{z}^{^{\prime}} }}{{\sigma_{c}^{^{\prime}} }}} \right)^{\eta } } \right]$$
(2)

The characteristic effective stress is typically between σ'c = 500 and 3000 kPa, and the model parameter η reflects the sensitivity of the void ratio to effective stress (Note: most sediments exhibit η = 1/3—See related analysis21). The solution of the differential Eq. (1) with the constitutive model in Eq. (2) results in the following implicit equation that relates the void ratio ez and the effective stress σ'z at depth z (for η = 1/3—See related example21,22):

$$z = \frac{{\left( {1 + e_{H} } \right)}}{{\left( {G_{s} - 1} \right)\rho_{w} g}}\sigma_{z}^{^{\prime}} + 3\frac{{\left( {e_{L} - e_{H} } \right)}}{{\left( {G_{s} - 1} \right)\rho_{w} g}}\sigma_{c}^{^{\prime}} \left\{ {\left[ {\left( {\frac{{\sigma_{z}^{^{\prime}} }}{{\sigma_{c}^{^{\prime}} }}} \right)^{\frac{2}{3}} + 2\left( {\frac{{\sigma_{z}^{^{\prime}} }}{{\sigma_{c}^{^{\prime}} }}} \right)^{\frac{1}{3}} + 2} \right] \cdot \exp \left[ { - \left( {\frac{{\sigma_{z}^{^{\prime}} }}{{\sigma_{c}^{^{\prime}} }}} \right)^{\frac{1}{3}} } \right] - 2} \right\}$$
(3)

Finally, we obtain the void ratio profile ez = f (z) with depth z by replacing a selected effective stress σ'z in both Eqs. (3) and (2).

### Mean pore size

The geometrical analysis of various sediment fabrics shows that the mean pore size μd [m] is a function of the void ratio ez and the specific surface Ss defined as the ratio between the surface area of particles As and their mass, Ss = As/(ρmVm) [m2/g]18,23,

$$\mu_{d} = k\frac{{e_{z} }}{{S_{s} \rho_{m} }}$$
(4)

where the k-factor reflects the soil fabric (see geometric analyses and values for various fabrics in the Supplementary Table S1). Furthermore, our database shows a strong correlation between the specific surface Ss and the asymptotic void ratio eL (see Supplementary Fig. S1):

$$e_{L} = 0.9 + 0.03\frac{{S_{s} }}{{[{\text{m}}^{2} /{\text{g}}]}}$$
(5)

For large rotund particles, the specific surface Ss → 0 while the asymptotic void ratio tends to eL → 0.9 which corresponds to the loose, simple cubic packing of monosize spherical particles.

### Pore size distribution (Soils and rocks)

We compiled a large database of pore size distributions measured from a wide range of soils (39 specimens) and intact rocks (44 specimens), and fitted each dataset with a log-normal distribution (Supplementary Table S2 and Figs. S2S6). Figure 1 shows the standard deviation σd [ln(d/µm)] plotted against the mean pore size μd [ln(d/µm)]. The trend reveals a surprisingly strong relationship across all sediments and intact rocks: σd/μd ≈ 0.4, from nm-size pores in shales to mm-size pores in sandy sediments (previously observed for a small set of sediments18).

### Cell count in sediments

The pore size d must be larger than the cell size b [m]. Consequently, cell counts per sediment unit volume must relate to the probability of pores P(d ≥ b). The probability P(d ≥ b) for a log-normal distribution assuming σd/μd ≈ 0.4 simplifies to (see inset in Fig. 1):

$$P(d \ge b) = \int\limits_{\ln b}^{\infty } {\exp \left\{ { - \frac{2.5}{4}\left[ {\ln \left( {\frac{d}{{\mu_{d} }}} \right) + 0.05} \right]^{2} } \right\}{\text{d}} d}$$
(6)

Finally, the cell count c [cells/cm3] in a sediment at depth z depends on: (1) the cell concentration cfl [cells/cm3] in the pore fluid within the pores, (2) the sediment void ratio ez (Eqs. 2 and 3), and (3) the probability P(d ≥ b) (Eq. 6) for a given mean pore size μd (Eq. 4) and standard deviation σd/μd = 0.4 (Fig. 1):

$$c = c_{fl} \cdot \left( {\frac{{e_{z} }}{{1 + e_{z} }}} \right) \cdot P(d \ge b)$$
(7)

where porosity n = e/(1 + e). We adopt a nominal cell size b = 1 µm for all analyses presented in this manuscript.

### Implementation

We use the effective stress dependent, asymptotically correct self-compaction model to match the reported void ratio versus depth ez-z profiles (Eqs. 13). The fitted asymptotic void ratio eL allows the estimation of the specific surface Ss (Eq. 5). Then, the mean pore size μd(z) at depth z is computed from the local void ratio ez and the sediment specific surface Ss (Eq. 4, Supplementary Table S1). We complete the probabilistic pore size analysis by invoking the strong correlation σd/μd = 0.4 between the mean pore size μd and the standard deviation σd (Fig. 1, Supplementary Table S2 and Figs. S2S6). While there is variability, we adopt a single σd/μd ≈ 0.4 for all analyses to avoid additional degrees of freedom (The Supplementary Fig. S7 shows the effect of σd/μd on predicted cell counts—all other parameters are kept constant). Finally, we estimate cell count profiles c(z) [cells/cm3] using a single value of cell concentration in the pore fluid cfl for the full profile at each site (Eq. 7).

## Results

Results in Fig. 2 show the fitted compaction model and predicted cell counts for various marine sediments. Computed trends fit the compiled data well. In particular, there is a significant reduction in cell count with depth for high specific surface sediments (yellow and red data points). By contrast, pore size is not the limiting factor for microbial cell counts in silty or sandy sediments (low specific surface—blue data points). In fact, the cell count in the pore fluid cfl and the sediment porosity n determine the cell counts in coarse-grained sediments c = cfl·[ez/(1 + ez)]  = cfl·nz [refer to Eqs. (6) and (7)].

We followed the same methodology to analyze all 116 profiles in the database (a total of 2696 measurements—Supplementary Table S3 and Figs. S8S121). Figure 3a presents the complete dataset. We use the fitted asymptotic void ratio eL to discriminate cell count profiles and cluster bio-habitats into three distinct groups: (1) green data points correspond to sandy and silty sediments (eL < 2, Ss < 1.1 m2/g, and LL < 30), (2) black data points show intermediate plasticity sediments (eL = 2–5, Ss = 10–70 m2/g, and LL ≈ 50-to-120), and (3) red data points represent very high plasticity clayey sediments (eL > 5, Ss > 120 m2/g, and LL > 140). For completeness, the values in parentheses include the estimated specific surface Ss and liquid limit LL, where the liquid limit LL is a gravimetric water content of a water–sediment mixture at the paste-slurry transition. Data clustering by sediment type highlights the role of sediment texture and effective stress-dependent pore size on microbial cell counts in the subsurface (For clarity, cell count data for the different void ratio categories are presented in the Supplementary Fig. S122).

Cell counts in sediments vary across > 8 orders of magnitude (Fig. 3a), and the overall depth distribution deviates from previously suggested trends4,5,24 (black line24: log10[cell counts]  = 8.05–0.68·log10[depth/m]).

Figure 3b shows the ratio between measured and predicted (Eq. 7) cell counts versus depth. Data points collapse onto a single trend within ± one log cycle (standard deviation σ = 0.52). The contraction in the spread from Fig. 3a to Fig. 3b reflects the extent to which observed cell counts can be justified by pore size as a limiting factor. The remaining spread reflects physical factors (e.g., sediment layering and heterogeneity, non-constant cell concentration in the pore fluid cfl with depth due to nutrient availability and environmental conditions such as temperature), experimental difficulties (e.g., cell counts and void ratio measurements), inherent uncertainties in the analysis and material parameters (e.g., validity of correlations, adopted nominal cell size, and correlation between eL and Ss—Eq. 5).

Our depth dependent cell count analysis identifies two parameters of particular significance: the cell concentration in the pore fluid cfl and the asymptotic void ratio eL, i.e., sediment type. Figure 4 presents cumulative distributions for the asymptotic void ratio eL and the cell concentration in the pore fluid cfl obtained by fitting the analytical model to void ratio and cell count profiles at each of the 116 sites. The fitted asymptotic void ratio values eL fall between 2.4 ≤ eL ≤ 4.8 for 68% of data (mean value eL = 3.6—Fig. 4a). This suggests a prevalence of intermediate plasticity sediments at the studied sites.

Intermediate plasticity sediments with asymptotic void ratios in the range of 2 ≤ eL ≤ 5 tend to host life with the highest cell volume density cfl. In these sediments, the inferred cell concentrations in the pore fluid varies between cfl = 107.8 and 1010.2 cells/cm3 for 68% of the data (mean value cfl = 109 cells/cm3; Fig. 4b), and can reach volume saturation levels found in dense biofilms at ~ 1011 cells/cm3. (Note: biofilm concentrations are typically reported in areal density; a high biofilm density of 107 cells/cm2 corresponds to 1011 cells/cm3 for biofilm layers separated at 1 μm; for comparison, the packing of micron-size spheres in simple cubic configuration corresponds to the ratio cm3/μm3 that is 1012 cells/cm3). These cell counts are orders of magnitude higher than in the water column in most oceans, which ranges between 2 × 104 and 5 × 105 [cells/cm3]9,25,26,27.

## Discussion and implications

Active microorganisms require traversable pore throats larger than the nominal b ≈ 1 μm size28. Pores and pore throats also limit the advective nutrient transport. In fact, the 1 μm size correlates with a hydraulic conductivity kh ≈ 0.1-to-10 cm/day29. We can anticipate low flow velocities v = kh·i given the typically low hydraulic gradients in nature i < 1.0; therefore, the ensuing advective-reactive regime hinders nutrient transport and bio-activity, as reported by others2,30.

A small fraction of fines can be sufficient to fill the pore space between coarse grains, control the pore size and eventually limit microbial cell counts. The Revised Soil Classification System RSCS recognizes the critical role of fines on mechanical and fluid flow properties in sediments31,32,33,34. For example, the fines fraction required to fill the pores in a sandy sediment is within the range of 12% for kaolinite, 7% for illite, and 2% for bentonite. Consequently, the detailed analysis of bioactivity in sediments must carefully consider the presence of fines and their mineralogy.

Data compiled in this study and the mecho-geometrical probabilistic analyses provide strong evidence for the critical role of pore size on microbial cell counts in sediments (together with other limiting factors such as water, carbon source, nutrients and temperature). The sediment type and effective-stress dependent pore size analysis adequately capture the decreasing cell counts with depth, and highlight the controlling role of the sediment specific surface Ss. Similarly, pore size emerges as a critical limiting factor for life in rocks as well; for example, it is unlikely that active life will take place in the small pores of intact shales (Fig. 1), however, life may indeed thrive in large carbonate vugs. Furthermore, we expect to find microbial activity in most fractures, even at depth35,36. In fact, fractures can be active bio-reactors within rock masses.

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## Acknowledgements

Gabrielle. E. Abelskamp edited the manuscript. Support for this research was provided by the KAUST Endowment at King Abdullah University of Science and Technology.

## Author information

Authors

### Contributions

J.P. and J.C.S. have contributed equally to all parts of the study and manuscript.

### Corresponding author

Correspondence to J. Carlos Santamarina.

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Park, J., Santamarina, J.C. The critical role of pore size on depth-dependent microbial cell counts in sediments. Sci Rep 10, 21692 (2020). https://doi.org/10.1038/s41598-020-78714-3

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