{"id":41,"date":"2022-01-11T01:14:26","date_gmt":"2022-01-11T01:14:26","guid":{"rendered":"https:\/\/books.gw-project.org\/groundwater-microbiology\/chapter\/cell-growth-and-environment\/"},"modified":"2022-01-13T05:53:14","modified_gmt":"2022-01-13T05:53:14","slug":"cell-growth-and-environment","status":"publish","type":"chapter","link":"https:\/\/books.gw-project.org\/groundwater-microbiology\/chapter\/cell-growth-and-environment\/","title":{"raw":"2.2 Cell Growth and Environment","rendered":"2.2 Cell Growth and Environment"},"content":{"raw":"
\r\n

While prokaryotes are abundant and widely distributed in nature, their growth rates and metabolic functions are sensitive to environmental conditions. This includes physical and chemical parameters such as temperature, pressure, pH, oxidation-reduction (redox) potential, ionic strength, and nutrient availability. For some environments with extreme conditions, such as high temperature or low pH, prokaryotes are the only form of life capable of survival and growth.<\/p>\r\n

Of all environmental properties, temperature exerts a particularly strong effect on prokaryotic growth. This is because chemical and metabolic reaction rates increase with temperature following the Arrhenius relationship as shown in Equation 1.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle k=Ae^{-E_{a}\/RT}[\/latex]<\/td>\r\n(1)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
k<\/em><\/td>\r\n=<\/td>\r\nreaction rate coefficient (1\/T)<\/td>\r\n<\/tr>\r\n
A<\/em><\/td>\r\n=<\/td>\r\ncollision frequency factor (1\/T)<\/td>\r\n<\/tr>\r\n
E<\/em>a<\/em><\/sub><\/td>\r\n=<\/td>\r\nactivation energy of the reaction (ML2<\/sup>)\/(T2<\/sup> mol)<\/td>\r\n<\/tr>\r\n
R<\/em><\/td>\r\n=<\/td>\r\nuniversal gas constant (ML2<\/sup>)\/(T2 <\/sup>\u00b0K mol)<\/td>\r\n<\/tr>\r\n
T<\/em><\/td>\r\n=<\/td>\r\nabsolute temperature (\u00b0K)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Prokaryotes typically grow best near a characteristic optimal temperature. The optimal growth temperature of psychrophilic (cold-loving) prokaryotes is around 10\u00b0C, whereas thermophiles (heat-loving) prefer temperatures above 40\u00b0C. Mesophilic prokaryotes grow well at midrange temperatures between 20 and 40\u00b0C. At the extremes, prokaryotes survive at temperatures as low as \u221220\u00b0C and as high as 120\u00b0C, provided water is maintained in a liquid state by dissolved salts and high pressure, respectively.<\/p>\r\n

Exposure to high pressures tends to impede the growth of prokaryotes that are accustomed to atmospheric pressure. But among those that live in high pressure deep-ocean and subsurface environments, microbes classified as both barotolerant (able to tolerate high pressures) and barophilic (requiring high pressures to function) have been found. These prokaryotes are able to stabilize their cytoplasmic membranes by altering the fatty acid composition of the phospholipids to compensate for extreme pressure gradients between the inside and outside of the cells.<\/p>\r\n

Defined as the negative logarithm of the molar proton (hydrogen ion, H+<\/sup>) concentration, pH is regarded as a master variable in chemistry and biology. pH is defined in Equation 2.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\npH = \u2212log[H+<\/sup>]<\/td>\r\n(2)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

This is because protons are involved in almost all types of chemical and metabolic reactions, including acid-base, aqueous complexation, surface adsorption, and redox reactions. The vast majority of prokaryotes are quite comfortable growing in the circumneutral pH range of most natural waters, from around 5.7 for pristine meteoric water to about 8.0 for seawater. Acidophiles are adapted to grow at pH\u00a0<\u00a03.0, for example in acid drainage from mines and acidic hot springs. At the other end of the pH spectrum, alkaliphiles occur at pH\u00a0>\u00a010 in saline alkaline lakes and calcareous alkali soils.<\/p>\r\n

Environmental redox potentials measured with a platinum electrode are often discussed in terms of the presence (aerobic, oxic) or absence (anaerobic, anoxic) of oxygen. This is an oversimplification of the electrochemical meaning of redox potential (Eh<\/em>), which is defined relative to the standard hydrogen electrode for a generic half-cell reaction involving oxidant ox<\/em> and conjugate reductant red<\/em> (Equation 3) by the Nernst equation (Equation 4).<\/a><\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nox<\/em> + nH<\/em>+<\/sup> + ne<\/em>\u2212<\/sup> = red<\/em><\/td>\r\n(3)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle Eh = Eh^{0}+\\frac{2.303RT}{nF}\\textup{log}\\frac{[ox][H^{+}]^{n}}{[red]}[\/latex]<\/td>\r\n(4)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Based on the Nernst equation, high redox potentials (Eh<\/em>) are indicative of oxidizing conditions (greater abundance of oxidized chemical species), whereas lower Eh<\/em> values correspond to reducing conditions (reduced chemical species dominate). Moreover, Eh<\/em> tends to decrease with increasing pH because of the logarithmic dependence on proton concentration. When the concentrations of ox<\/em> and red<\/em> are equal at pH\u00a0=\u00a00 (so-called standard conditions), then Eh<\/em> equals the standard half-cell potential E<\/em>h<\/em>0<\/sup>.<\/em><\/p>\r\n

The use of platinum electrodes to measure environmental redox potentials is historically based on the work of C.E. Zobell with marine sediments (Zobell, 1946). However, sediments and groundwater systems are seldom at thermodynamic equilibrium with respect to oxidation-reduction reactions. In addition, many important oxidants (such as molecular oxygen) and reductants (such as organic carbon) do not react reversibly on platinum electrodes. For these reasons, Eh<\/em> measurements have not proven to be quantitatively meaningful in aqueous environments, including groundwater systems (Lindberg and Runnells, 1984).<\/p>\r\n

When it comes to prokaryotic growth, the distinction between aerobic (molecular oxygen present) versus anaerobic (molecular oxygen low or absent) conditions is more important than whether a specific environment is oxidizing or reducing. Many prokaryotes, and nearly all eukaryotes, require oxygen for survival and growth. The lower limit for these strict aerobes is approximately 1 percent (referred to as the Pasteur Point) of the atmospheric oxygen concentration (pO<\/em>2<\/em><\/sub>\u00a0=\u00a00.21\u00a0atm); however, a vast number of other prokaryotes can grow in the absence of oxygen as either facultative or strict anaerobes (Stolper et al., 2010). This is the main reason why complex prokaryotic communities thrive in environments isolated from direct contact with the atmosphere, such as within sediments and groundwater systems.<\/p>\r\n

The ionic strength of natural waters has multiple implications for prokaryotic growth, especially in terms of water activity and osmotic balance. As a measure of the concentration of ions in solution, molar ionic strength I<\/em> (mole\/L) is calculated for n<\/em> ionic species as shown in Equation 5.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle I=\\frac{1}{2}\\sum_{i=1}^{n}c_{i}{z_{i}}^{2}[\/latex]<\/td>\r\n(5)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n
c<\/em>i<\/em><\/sub><\/td>\r\n=<\/td>\r\nmolar concentration of ion species i<\/em> (mol\/L2<\/sup>)<\/td>\r\n<\/tr>\r\n
z<\/em>i<\/em><\/sub><\/td>\r\n=<\/td>\r\nion charge (dimensionless)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Because it is not always possible (or feasible) to obtain a complete chemical analysis of all dissolved ions in solution, a convenient approximation for molar ionic strength as a function of total dissolved solids (TDS<\/em> in mg\/L) is given by Equation 6.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\nI<\/em> = (2.5 \u00d7 10\u22125<\/sup>) TDS<\/em><\/td>\r\n(6)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

An increase in ionic strength causes the solution to shift away from ideal behavior, making ion and molecular interactions more dependent on activities (dimensionless effective concentrations, a<\/em>i<\/em><\/sub>) rather than absolute concentrations. Considering the concentration of chemical species i<\/em> in solution relative to a standard concentration c<\/em>p<\/em><\/sub> (taken as unity for a pure phase) and the corresponding activity coefficient \u03b3<\/em>i<\/em><\/sub> (which decreases as a function of increasing ionic strength), activity is calculated as shown in Equation 7.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle a_{i}=\\gamma _{i}\\frac{c_{i}}{c_{p}}[\/latex]<\/td>\r\n(7)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

For prokaryotes, higher ionic strengths and lower solute activities may impede growth by slowing down rates of chemical and metabolic reactions (Small et al., 2001). A far more serious consequence is the decrease in water activity that accompanies an increase in TDS<\/em> and ionic strength. In fact, few prokaryotes can tolerate water activities much below 0.98, which approximately corresponds to the salinity of seawater. At lower water activities, water is drawn out of cells by osmosis thereby disrupting normal cellular growth. Nevertheless, some prokaryotes (halophiles) manage to grow in brines (>\u00a020 percent NaCl by weight) at extremely low water activity levels (down to about 0.80).<\/p>\r\n

The growth of prokaryotes generally implies an increase in the number of individual cells (Allan and Waclaw, 2019). Under ideal laboratory conditions with an unlimited supply of nutrients, the differential rate of increase in cell numbers with respect to time (t<\/em>) depends on the frequency of cell division, specified by the growth rate constant (\u03bc<\/em>), and the number of prokaryotes that are growing (<\/span>\u039d<\/em>)<\/span> as shown by Equation 8.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle \\frac{dN}{dt}=\\mu N[\/latex]<\/td>\r\n(8)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

Integration yields the familiar exponential growth equation (Equation 9), that is the progressive increase in prokaryotic cell numbers over time (Figure\u00a05).<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle N_{t}=N_{0}e^{\\mu t}[\/latex]<\/td>\r\n(9)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

with a characteristic doubling time T<\/em>\u00a0=\u00a0ln(2)\/<\/em>\u03bc<\/em>\u00a0=\u00a00.693\/<\/em>\u03bc<\/em> (Allan and Waclaw, 2019).<\/p>\r\n

\"a)\u00a0Illustration<\/p>\r\n

Figure<\/strong>\u00a0<\/strong>5<\/strong>\u00a0<\/strong>-<\/strong>\u00a0<\/strong>a)\u00a0Illustration of microbial growth and the exponential increase in cell numbers as a function of time. b)\u00a0A plot of the natural logarithm of cell numbers as a function of time, where the growth rate constant \u03bc<\/em> is the slope of the line.<\/p>\r\n

A major limitation of the exponential growth model is that it does not take into account the influence of nutrient availability on prokaryotes growth rate. This situation is described by the extended Monod equation as shown in Equation 10.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle \\mu =\\frac{(\\mu _{max}+m)S}{(K_{s}+S)}-m[\/latex]<\/td>\r\n(10)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nwhere:\r\n\r\n\r\n\r\n\r\n\r\n\r\n
\u03bc<\/em>max<\/em><\/sub><\/td>\r\n=<\/td>\r\nmaximum growth rate constant (1\/T)<\/td>\r\n<\/tr>\r\n
S<\/em><\/td>\r\n=<\/td>\r\nconcentration of a single limiting nutrient concentration (i.e., where other nutrients are in excess) (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
K<\/em>s<\/em><\/sub><\/td>\r\n=<\/td>\r\nnutrient concentration that corresponds to one half of \u00b5<\/em>max<\/em><\/sub> (M\/L3<\/sup>)<\/td>\r\n<\/tr>\r\n
m<\/em><\/td>\r\n=<\/td>\r\nmaintenance energy coefficient of metabolic processes that keep cells alive (1\/T) (Figure 6)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

\"Graph<\/p>\r\n

Figure\u00a0<\/strong>6<\/strong>\u00a0<\/strong>-<\/strong>\u00a0<\/strong>The dependence of growth rate constant \u00b5<\/em> as a function of substrate concentration according to the extended Monod equation. As the substrate concentration increases, the value of \u00b5<\/em> asymptotically approaches the maximum growth rate constant \u00b5<\/em>max<\/em>. The substrate concentration, equal to K<\/em>S<\/em><\/sub>, corresponds to the point at which \u00b5<\/em> is equal to one half of (\u00b5<\/em>max<\/em>\u00a0-\u00a0m<\/em>). The minimum substrate concentration required for maintenance energy is equivalent to S<\/em>min<\/em><\/sub>.<\/p>\r\n

The Monod equation indicates an increasing supply of nutrients promotes a higher frequency of cell division and faster growth rates; however, there is a finite metabolic limit to how fast cells can grow (\u00b5<\/em>max<\/em><\/sub>) beyond which growth rates become independent of nutrient availability. There is also a minimum substrate concentration (<\/span>S<\/em>min<\/em><\/sub>) imposed by maintenance energy requirements. At S<\/em>min<\/em><\/sub>, cell growth comes to a stop (\u03bc<\/em>\u00a0=\u00a00<\/em>). Rearrangement of Equation\u00a010 for cells staying alive but not growing yields Equation 11.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle S_{min}=\\frac{mK_{s}}{\\mu _{max}}[\/latex]<\/td>\r\n(11)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

In natural environments, particularly groundwater systems, nutrient concentrations are normally much closer to S<\/em>min<\/em><\/sub> than K<\/em>S<\/em><\/sub>. Under such near starvation conditions, prokaryotes grow slowly if at all (Hoehler and Jorgensen, 2013; LaRowe and Amend, 2015, 2019). Cell numbers are typically low and tend to remain constant over time in a balance between cell growth and loss of cells owing to death or physical removal from the system. In this situation, the change in cell numbers over time takes the form of Equation\u00a012.<\/a><\/p>\r\n\r\n\r\n\r\n\r\n
<\/td>\r\n[latex]\\displaystyle \\frac{dN}{dt}=\\mu N-k_{d}N=(\\mu -k_{d})N[\/latex]<\/td>\r\n(12)<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n

A decay constant k<\/em>d<\/em><\/sub> is added to account for the rate at which cell numbers are lost (Allan and Waclaw, 2019). If the rates of growth and loss are equal, cell numbers will not change over time. This situation is representative of a steady-state condition. When the growth rate is greater than the loss rate, cell numbers will increase. On the other hand, cell numbers will decrease if the growth rate is less than the rate at which cells are lost.<\/p>\r\n

Although the Monod relationship takes nutrient supply<\/em> into account, it does not address the issue of nutrient quality<\/em>. Essential nutrients required for cell growth include sources of carbon, nitrogen, phosphorus, sulfur, potassium, magnesium, calcium, oxygen, and iron. Trace nutrients include elements such as manganese, copper, cobalt, zinc, and molybdenum. All of these nutrients can be obtained to meet the specific growth requirements of different prokaryotic microorganisms from a vast assortment of organic and inorganic materials. But availability alone does not make one nutrient compound any better than another. Other factors come into play including molecular size and structure, solubility, and ionic charge. For instance, the nutritional value of large insoluble materials is generally lower than that of smaller soluble molecules. Similarly, branching and ring structures in the carbon backbone of complex organic compounds are restrictive to metabolic processing. When it comes to uptake of ionic nutrients, cells must rely on active transport because ions cannot diffuse freely across the cytoplasmic membrane.<\/p>\r\n

Prokaryotic cells are mostly water (80 percent), so their bulk density is nearly the same as the density of water. This makes prokaryotes rather buoyant, which permits free and unconfined planktonic growth in aqueous suspension (Figure\u00a07a). It also makes prokaryotes susceptible to advective transport and dispersion as suspended particles in moving water. <\/a>Some prokaryotes are well adapted to planktonic growth and can survive long periods of starvation under the dilute nutrient-poor conditions that prevail in most natural waters; however, the reality is that most prokaryotes grow in biofilms attached to surfaces (McDougald et al., 2012; Marshall, 2013). These adherent prokaryotic communities consist mainly of EPS and other biopolymers that immobilize living cells on surfaces (Figure\u00a07b). In comparison to their planktonic counterparts, prokaryotes growing in biofilms benefit directly from solid-liquid interfacial forces, such as surface tension and ion adsorption, which contribute to the accumulation and increased metabolic accessibility of nutrients.<\/p>\r\n

\"a)\u00a0Epifluorescence<\/p>\r\n

Figure\u00a0<\/strong>7<\/strong>\u00a0<\/strong>-<\/strong>\u00a0<\/strong>a)\u00a0Epifluorescence photomicrograph of planktonic bacteria from a freshwater sample. Scale bar\u00a0=\u00a020\u00a0\u03bc<\/em>m. b)\u00a0Thin-section transmission electron micrograph showing microcolonies of epilithic biofilm bacteria (indicated by arrows) surrounded by large amounts of fibrous extracellular polymeric substances. Scale bar\u00a0=\u00a01.0\u00a0\u03bc<\/em>m.<\/p>\r\n

As a general rule, the numerical abundance of living organisms increases with decreasing size. The smallest and most abundant biological entities in nature are viruses, followed by prokaryotes, then eukaryotes. On average, the number of viruses suspended in a typical sample of surface or shallow groundwater approaches 107<\/sup> per mL, followed by 105<\/sup> prokaryotes per mL and 102<\/sup> single cell eukaryotic organisms per mL (Kyle et al., 2008). Total numbers are even higher in soils and sediment samples, which can contain up to 1010<\/sup> viruses, 109<\/sup> prokaryotes, and 105<\/sup> eukaryotes per gram. This implies that a great majority of the microorganisms in subsurface environments grow in adherent biofilms on mineral surfaces (McDougald et al., 2012; Marshall, 2013).<\/p>\r\n\r\n<\/div>","rendered":"

\n

While prokaryotes are abundant and widely distributed in nature, their growth rates and metabolic functions are sensitive to environmental conditions. This includes physical and chemical parameters such as temperature, pressure, pH, oxidation-reduction (redox) potential, ionic strength, and nutrient availability. For some environments with extreme conditions, such as high temperature or low pH, prokaryotes are the only form of life capable of survival and growth.<\/p>\n

Of all environmental properties, temperature exerts a particularly strong effect on prokaryotic growth. This is because chemical and metabolic reaction rates increase with temperature following the Arrhenius relationship as shown in Equation 1.<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle k=Ae^{-E_{a}/RT}\"<\/td>\n(1)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n\n\n\n
k<\/em><\/td>\n=<\/td>\nreaction rate coefficient (1\/T)<\/td>\n<\/tr>\n
A<\/em><\/td>\n=<\/td>\ncollision frequency factor (1\/T)<\/td>\n<\/tr>\n
E<\/em>a<\/em><\/sub><\/td>\n=<\/td>\nactivation energy of the reaction (ML2<\/sup>)\/(T2<\/sup> mol)<\/td>\n<\/tr>\n
R<\/em><\/td>\n=<\/td>\nuniversal gas constant (ML2<\/sup>)\/(T2 <\/sup>\u00b0K mol)<\/td>\n<\/tr>\n
T<\/em><\/td>\n=<\/td>\nabsolute temperature (\u00b0K)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Prokaryotes typically grow best near a characteristic optimal temperature. The optimal growth temperature of psychrophilic (cold-loving) prokaryotes is around 10\u00b0C, whereas thermophiles (heat-loving) prefer temperatures above 40\u00b0C. Mesophilic prokaryotes grow well at midrange temperatures between 20 and 40\u00b0C. At the extremes, prokaryotes survive at temperatures as low as \u221220\u00b0C and as high as 120\u00b0C, provided water is maintained in a liquid state by dissolved salts and high pressure, respectively.<\/p>\n

Exposure to high pressures tends to impede the growth of prokaryotes that are accustomed to atmospheric pressure. But among those that live in high pressure deep-ocean and subsurface environments, microbes classified as both barotolerant (able to tolerate high pressures) and barophilic (requiring high pressures to function) have been found. These prokaryotes are able to stabilize their cytoplasmic membranes by altering the fatty acid composition of the phospholipids to compensate for extreme pressure gradients between the inside and outside of the cells.<\/p>\n

Defined as the negative logarithm of the molar proton (hydrogen ion, H+<\/sup>) concentration, pH is regarded as a master variable in chemistry and biology. pH is defined in Equation 2.<\/a><\/p>\n\n\n\n
<\/td>\npH = \u2212log[H+<\/sup>]<\/td>\n(2)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

This is because protons are involved in almost all types of chemical and metabolic reactions, including acid-base, aqueous complexation, surface adsorption, and redox reactions. The vast majority of prokaryotes are quite comfortable growing in the circumneutral pH range of most natural waters, from around 5.7 for pristine meteoric water to about 8.0 for seawater. Acidophiles are adapted to grow at pH\u00a0<\u00a03.0, for example in acid drainage from mines and acidic hot springs. At the other end of the pH spectrum, alkaliphiles occur at pH\u00a0>\u00a010 in saline alkaline lakes and calcareous alkali soils.<\/p>\n

Environmental redox potentials measured with a platinum electrode are often discussed in terms of the presence (aerobic, oxic) or absence (anaerobic, anoxic) of oxygen. This is an oversimplification of the electrochemical meaning of redox potential (Eh<\/em>), which is defined relative to the standard hydrogen electrode for a generic half-cell reaction involving oxidant ox<\/em> and conjugate reductant red<\/em> (Equation 3) by the Nernst equation (Equation 4).<\/a><\/a><\/p>\n\n\n\n
<\/td>\nox<\/em> + nH<\/em>+<\/sup> + ne<\/em>\u2212<\/sup> = red<\/em><\/td>\n(3)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n\n\n\n
<\/td>\n\"\displaystyle Eh = Eh^{0}+\frac{2.303RT}{nF}\textup{log}\frac{[ox][H^{+}]^{n}}{[red]}\"<\/td>\n(4)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Based on the Nernst equation, high redox potentials (Eh<\/em>) are indicative of oxidizing conditions (greater abundance of oxidized chemical species), whereas lower Eh<\/em> values correspond to reducing conditions (reduced chemical species dominate). Moreover, Eh<\/em> tends to decrease with increasing pH because of the logarithmic dependence on proton concentration. When the concentrations of ox<\/em> and red<\/em> are equal at pH\u00a0=\u00a00 (so-called standard conditions), then Eh<\/em> equals the standard half-cell potential E<\/em>h<\/em>0<\/sup>.<\/em><\/p>\n

The use of platinum electrodes to measure environmental redox potentials is historically based on the work of C.E. Zobell with marine sediments (Zobell, 1946). However, sediments and groundwater systems are seldom at thermodynamic equilibrium with respect to oxidation-reduction reactions. In addition, many important oxidants (such as molecular oxygen) and reductants (such as organic carbon) do not react reversibly on platinum electrodes. For these reasons, Eh<\/em> measurements have not proven to be quantitatively meaningful in aqueous environments, including groundwater systems (Lindberg and Runnells, 1984).<\/p>\n

When it comes to prokaryotic growth, the distinction between aerobic (molecular oxygen present) versus anaerobic (molecular oxygen low or absent) conditions is more important than whether a specific environment is oxidizing or reducing. Many prokaryotes, and nearly all eukaryotes, require oxygen for survival and growth. The lower limit for these strict aerobes is approximately 1 percent (referred to as the Pasteur Point) of the atmospheric oxygen concentration (pO<\/em>2<\/em><\/sub>\u00a0=\u00a00.21\u00a0atm); however, a vast number of other prokaryotes can grow in the absence of oxygen as either facultative or strict anaerobes (Stolper et al., 2010). This is the main reason why complex prokaryotic communities thrive in environments isolated from direct contact with the atmosphere, such as within sediments and groundwater systems.<\/p>\n

The ionic strength of natural waters has multiple implications for prokaryotic growth, especially in terms of water activity and osmotic balance. As a measure of the concentration of ions in solution, molar ionic strength I<\/em> (mole\/L) is calculated for n<\/em> ionic species as shown in Equation 5.<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle I=\frac{1}{2}\sum_{i=1}^{n}c_{i}{z_{i}}^{2}\"<\/td>\n(5)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n
c<\/em>i<\/em><\/sub><\/td>\n=<\/td>\nmolar concentration of ion species i<\/em> (mol\/L2<\/sup>)<\/td>\n<\/tr>\n
z<\/em>i<\/em><\/sub><\/td>\n=<\/td>\nion charge (dimensionless)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Because it is not always possible (or feasible) to obtain a complete chemical analysis of all dissolved ions in solution, a convenient approximation for molar ionic strength as a function of total dissolved solids (TDS<\/em> in mg\/L) is given by Equation 6.<\/a><\/p>\n\n\n\n
<\/td>\nI<\/em> = (2.5 \u00d7 10\u22125<\/sup>) TDS<\/em><\/td>\n(6)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

An increase in ionic strength causes the solution to shift away from ideal behavior, making ion and molecular interactions more dependent on activities (dimensionless effective concentrations, a<\/em>i<\/em><\/sub>) rather than absolute concentrations. Considering the concentration of chemical species i<\/em> in solution relative to a standard concentration c<\/em>p<\/em><\/sub> (taken as unity for a pure phase) and the corresponding activity coefficient \u03b3<\/em>i<\/em><\/sub> (which decreases as a function of increasing ionic strength), activity is calculated as shown in Equation 7.<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle a_{i}=\gamma _{i}\frac{c_{i}}{c_{p}}\"<\/td>\n(7)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

For prokaryotes, higher ionic strengths and lower solute activities may impede growth by slowing down rates of chemical and metabolic reactions (Small et al., 2001). A far more serious consequence is the decrease in water activity that accompanies an increase in TDS<\/em> and ionic strength. In fact, few prokaryotes can tolerate water activities much below 0.98, which approximately corresponds to the salinity of seawater. At lower water activities, water is drawn out of cells by osmosis thereby disrupting normal cellular growth. Nevertheless, some prokaryotes (halophiles) manage to grow in brines (>\u00a020 percent NaCl by weight) at extremely low water activity levels (down to about 0.80).<\/p>\n

The growth of prokaryotes generally implies an increase in the number of individual cells (Allan and Waclaw, 2019). Under ideal laboratory conditions with an unlimited supply of nutrients, the differential rate of increase in cell numbers with respect to time (t<\/em>) depends on the frequency of cell division, specified by the growth rate constant (\u03bc<\/em>), and the number of prokaryotes that are growing (<\/span>\u039d<\/em>)<\/span> as shown by Equation 8.<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle \frac{dN}{dt}=\mu N\"<\/td>\n(8)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

Integration yields the familiar exponential growth equation (Equation 9), that is the progressive increase in prokaryotic cell numbers over time (Figure\u00a05).<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle N_{t}=N_{0}e^{\mu t}\"<\/td>\n(9)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

with a characteristic doubling time T<\/em>\u00a0=\u00a0ln(2)\/<\/em>\u03bc<\/em>\u00a0=\u00a00.693\/<\/em>\u03bc<\/em> (Allan and Waclaw, 2019).<\/p>\n

\"a)\u00a0Illustration<\/p>\n

Figure<\/strong>\u00a0<\/strong>5<\/strong>\u00a0<\/strong>–<\/strong>\u00a0<\/strong>a)\u00a0Illustration of microbial growth and the exponential increase in cell numbers as a function of time. b)\u00a0A plot of the natural logarithm of cell numbers as a function of time, where the growth rate constant \u03bc<\/em> is the slope of the line.<\/p>\n

A major limitation of the exponential growth model is that it does not take into account the influence of nutrient availability on prokaryotes growth rate. This situation is described by the extended Monod equation as shown in Equation 10.<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle \mu =\frac{(\mu _{max}+m)S}{(K_{s}+S)}-m\"<\/td>\n(10)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

where:<\/p>\n\n\n\n\n\n\n
\u03bc<\/em>max<\/em><\/sub><\/td>\n=<\/td>\nmaximum growth rate constant (1\/T)<\/td>\n<\/tr>\n
S<\/em><\/td>\n=<\/td>\nconcentration of a single limiting nutrient concentration (i.e., where other nutrients are in excess) (M\/L3<\/sup>)<\/td>\n<\/tr>\n
K<\/em>s<\/em><\/sub><\/td>\n=<\/td>\nnutrient concentration that corresponds to one half of \u00b5<\/em>max<\/em><\/sub> (M\/L3<\/sup>)<\/td>\n<\/tr>\n
m<\/em><\/td>\n=<\/td>\nmaintenance energy coefficient of metabolic processes that keep cells alive (1\/T) (Figure 6)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\"Graph<\/p>\n

Figure\u00a0<\/strong>6<\/strong>\u00a0<\/strong>–<\/strong>\u00a0<\/strong>The dependence of growth rate constant \u00b5<\/em> as a function of substrate concentration according to the extended Monod equation. As the substrate concentration increases, the value of \u00b5<\/em> asymptotically approaches the maximum growth rate constant \u00b5<\/em>max<\/em>. The substrate concentration, equal to K<\/em>S<\/em><\/sub>, corresponds to the point at which \u00b5<\/em> is equal to one half of (\u00b5<\/em>max<\/em>\u00a0–\u00a0m<\/em>). The minimum substrate concentration required for maintenance energy is equivalent to S<\/em>min<\/em><\/sub>.<\/p>\n

The Monod equation indicates an increasing supply of nutrients promotes a higher frequency of cell division and faster growth rates; however, there is a finite metabolic limit to how fast cells can grow (\u00b5<\/em>max<\/em><\/sub>) beyond which growth rates become independent of nutrient availability. There is also a minimum substrate concentration (<\/span>S<\/em>min<\/em><\/sub>) imposed by maintenance energy requirements. At S<\/em>min<\/em><\/sub>, cell growth comes to a stop (\u03bc<\/em>\u00a0=\u00a00<\/em>). Rearrangement of Equation\u00a010 for cells staying alive but not growing yields Equation 11.<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle S_{min}=\frac{mK_{s}}{\mu _{max}}\"<\/td>\n(11)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

In natural environments, particularly groundwater systems, nutrient concentrations are normally much closer to S<\/em>min<\/em><\/sub> than K<\/em>S<\/em><\/sub>. Under such near starvation conditions, prokaryotes grow slowly if at all (Hoehler and Jorgensen, 2013; LaRowe and Amend, 2015, 2019). Cell numbers are typically low and tend to remain constant over time in a balance between cell growth and loss of cells owing to death or physical removal from the system. In this situation, the change in cell numbers over time takes the form of Equation\u00a012.<\/a><\/p>\n\n\n\n
<\/td>\n\"\displaystyle \frac{dN}{dt}=\mu N-k_{d}N=(\mu -k_{d})N\"<\/td>\n(12)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

A decay constant k<\/em>d<\/em><\/sub> is added to account for the rate at which cell numbers are lost (Allan and Waclaw, 2019). If the rates of growth and loss are equal, cell numbers will not change over time. This situation is representative of a steady-state condition. When the growth rate is greater than the loss rate, cell numbers will increase. On the other hand, cell numbers will decrease if the growth rate is less than the rate at which cells are lost.<\/p>\n

Although the Monod relationship takes nutrient supply<\/em> into account, it does not address the issue of nutrient quality<\/em>. Essential nutrients required for cell growth include sources of carbon, nitrogen, phosphorus, sulfur, potassium, magnesium, calcium, oxygen, and iron. Trace nutrients include elements such as manganese, copper, cobalt, zinc, and molybdenum. All of these nutrients can be obtained to meet the specific growth requirements of different prokaryotic microorganisms from a vast assortment of organic and inorganic materials. But availability alone does not make one nutrient compound any better than another. Other factors come into play including molecular size and structure, solubility, and ionic charge. For instance, the nutritional value of large insoluble materials is generally lower than that of smaller soluble molecules. Similarly, branching and ring structures in the carbon backbone of complex organic compounds are restrictive to metabolic processing. When it comes to uptake of ionic nutrients, cells must rely on active transport because ions cannot diffuse freely across the cytoplasmic membrane.<\/p>\n

Prokaryotic cells are mostly water (80 percent), so their bulk density is nearly the same as the density of water. This makes prokaryotes rather buoyant, which permits free and unconfined planktonic growth in aqueous suspension (Figure\u00a07a). It also makes prokaryotes susceptible to advective transport and dispersion as suspended particles in moving water. <\/a>Some prokaryotes are well adapted to planktonic growth and can survive long periods of starvation under the dilute nutrient-poor conditions that prevail in most natural waters; however, the reality is that most prokaryotes grow in biofilms attached to surfaces (McDougald et al., 2012; Marshall, 2013). These adherent prokaryotic communities consist mainly of EPS and other biopolymers that immobilize living cells on surfaces (Figure\u00a07b). In comparison to their planktonic counterparts, prokaryotes growing in biofilms benefit directly from solid-liquid interfacial forces, such as surface tension and ion adsorption, which contribute to the accumulation and increased metabolic accessibility of nutrients.<\/p>\n

\"a)\u00a0Epifluorescence<\/p>\n

Figure\u00a0<\/strong>7<\/strong>\u00a0<\/strong>–<\/strong>\u00a0<\/strong>a)\u00a0Epifluorescence photomicrograph of planktonic bacteria from a freshwater sample. Scale bar\u00a0=\u00a020\u00a0\u03bc<\/em>m. b)\u00a0Thin-section transmission electron micrograph showing microcolonies of epilithic biofilm bacteria (indicated by arrows) surrounded by large amounts of fibrous extracellular polymeric substances. Scale bar\u00a0=\u00a01.0\u00a0\u03bc<\/em>m.<\/p>\n

As a general rule, the numerical abundance of living organisms increases with decreasing size. The smallest and most abundant biological entities in nature are viruses, followed by prokaryotes, then eukaryotes. On average, the number of viruses suspended in a typical sample of surface or shallow groundwater approaches 107<\/sup> per mL, followed by 105<\/sup> prokaryotes per mL and 102<\/sup> single cell eukaryotic organisms per mL (Kyle et al., 2008). Total numbers are even higher in soils and sediment samples, which can contain up to 1010<\/sup> viruses, 109<\/sup> prokaryotes, and 105<\/sup> eukaryotes per gram. This implies that a great majority of the microorganisms in subsurface environments grow in adherent biofilms on mineral surfaces (McDougald et al., 2012; Marshall, 2013).<\/p>\n<\/div>\n","protected":false},"author":1,"menu_order":2,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-41","chapter","type-chapter","status-publish","hentry"],"part":84,"_links":{"self":[{"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/pressbooks\/v2\/chapters\/41","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":7,"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/pressbooks\/v2\/chapters\/41\/revisions"}],"predecessor-version":[{"id":255,"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/pressbooks\/v2\/chapters\/41\/revisions\/255"}],"part":[{"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/pressbooks\/v2\/parts\/84"}],"metadata":[{"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/pressbooks\/v2\/chapters\/41\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/wp\/v2\/media?parent=41"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/pressbooks\/v2\/chapter-type?post=41"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/wp\/v2\/contributor?post=41"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/books.gw-project.org\/groundwater-microbiology\/wp-json\/wp\/v2\/license?post=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}