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

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.

www.nature.com/scientificreports/ analysis 21 ). 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 e z and the effective stress σ' z at depth z (for η = 1/3-See related example 21,22 ): Finally, we obtain the void ratio profile e z = 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 μ d [m] is a function of the void ratio e z and the specific surface S s defined as the ratio between the surface area of particles A s and their mass, S s = A s /(ρ m V m ) [m 2 /g] 18,23 , 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 S s and the asymptotic void ratio e L (see Supplementary Fig. S1): For large rotund particles, the specific surface S s → 0 while the asymptotic void ratio tends to e L → 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. S2-S6). Figure 1 shows the standard deviation σ d [ln(d/µm)] plotted against the mean pore size μ d [ln(d/µm)]. The trend reveals a surprisingly strong relationship across all sediments and intact rocks: σ d /μ d ≈ 0.4, from nm-size pores in shales to mm-size pores in sandy sediments (previously observed for a small set of sediments 18 ).
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 lognormal distribution assuming σ d /μ d ≈ 0.4 simplifies to (see inset in Fig. 1): 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 e z -z profiles (Eqs. 1-3). The fitted asymptotic void ratio e L allows the estimation of the specific surface S s (Eq. 5). Then, the mean pore size μ d (z) at depth z is computed from the local void ratio e z and the sediment specific surface S s (Eq. 4, Supplementary Table S1). We complete the probabilistic pore size analysis by invoking the strong correlation σ d /μ d = 0.4 between the mean pore size μ d and the standard deviation σ d (  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 c fl and the sediment porosity n determine the cell counts in coarse-grained sediments c = c fl ·[e z / (1 + e z )] = c fl ·n z [refer to Eqs. (6) and (7)].  www.nature.com/scientificreports/ We followed the same methodology to analyze all 116 profiles in the database (a total of 2696 measurements- Supplementary Table S3 and Figs. S8-S121). Figure 3a presents the complete dataset. We use the fitted asymptotic void ratio e L to discriminate cell count profiles and cluster bio-habitats into three distinct groups: (1) green data points correspond to sandy and silty sediments (e L < 2, S s < 1.1 m 2 /g, and LL < 30), (2) black data points show intermediate plasticity sediments (e L = 2-5, S s = 10-70 m 2 /g, and LL ≈ 50-to-120), and (3) red data points represent very high plasticity clayey sediments (e L > 5, S s > 120 m 2 /g, and LL > 140). For completeness, the values in parentheses include the estimated specific surface S s 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).

Results in
Cell counts in sediments vary across > 8 orders of magnitude (Fig. 3a), and the overall depth distribution deviates from previously suggested trends 4,5,24 (black line 24 : log 10 [cell counts] = 8.05-0.68·log 10 [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 c fl 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 e L and S s -Eq. 5).
Our depth dependent cell count analysis identifies two parameters of particular significance: the cell concentration in the pore fluid c fl and the asymptotic void ratio e L , i.e., sediment type. Figure 4 presents cumulative distributions for the asymptotic void ratio e L and the cell concentration in the pore fluid c fl 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 e L fall between 2.4 ≤ e L ≤ 4.8 for 68% of data (mean value e L = 3.6- Fig. 4a). This suggests a prevalence of intermediate plasticity sediments at the studied sites. www.nature.com/scientificreports/ Intermediate plasticity sediments with asymptotic void ratios in the range of 2 ≤ e L ≤ 5 tend to host life with the highest cell volume density c fl . In these sediments, the inferred cell concentrations in the pore fluid varies between c fl = 10 7.8 and 10 10.2 cells/cm 3 for 68% of the data (mean value c fl = 10 9 cells/cm 3 ; Fig. 4b), and can reach volume saturation levels found in dense biofilms at ~ 10 11 cells/cm 3 . (Note: biofilm concentrations are typically reported in areal density; a high biofilm density of 10 7 cells/cm 2 corresponds to 10 11 cells/cm 3 for biofilm layers separated at 1 μm; for comparison, the packing of micron-size spheres in simple cubic configuration corresponds to the ratio cm 3 /μm 3 that is 10 12 cells/cm 3 ). These cell counts are orders of magnitude higher than in the water column in most oceans, which ranges between 2 × 10 4 and 5 × 10 5 [cells/cm 3 ] 9,25-27 .

Discussion and implications
Active microorganisms require traversable pore throats larger than the nominal b ≈ 1 μm size 28 . Pores and pore throats also limit the advective nutrient transport. In fact, the 1 μm size correlates with a hydraulic conductivity k h ≈ 0.1-to-10 cm/day 29 . We can anticipate low flow velocities v = k h ·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 others 2,30 .
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 sediments [31][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 S s . 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 depth 35,36 . In fact, fractures can be active bio-reactors within rock masses.