Limited growth during the lag phase of a growth curve is due to the need for cells to

2.13.2.2 Healthy and Active Inoculum

In order to achieve exponential phase in less time, microbes should have a short lag period, that is, they take less time to adapt to the environmental conditions. This is possible only with healthy and actively growing microbial growth. Healthy and active growth can be obtained by providing microbes with proper medium, necessary conditions, and a good monitoring system [27, 43]. The initial size of the inoculum influences the duration of the lag period, which is represented by the mathematical equation [16]

λn=−1μlog⁡(∑i=1nαi)

where n is the size of inoculum. It has been demonstrated that the expected log value with initial cell number n is always greater than the population with double (2n) initial cell number.

Age and Growth Rate

It has been shown that exponential-phase cells of S. typhimurium are much more sensitive to freeze–thaw stress than stationary-phase cells. This, however, is not a generally recognized phenomenon. Sensitivity of Pseudomonas to freezing, at different phases of growth, is dependent on freezing rate. At a lower cooling rate (≤10 °C min−1), exponential-phase cells were more sensitive, but at a higher rate (≥100 °C min−1), stationary-phase cells were more sensitive. Cells of S. typhimurium grown at 25 °C are more resistant to freezing stress than cells grown at 30 °C. This may be due to changes in membrane properties as a function of growth temperature or it may reflect the different growth rates at midexponential phase, which are 0.25 and 0.17 h−1 at 37 and 25 °C, respectively.

2.2 Preparation of algal suspensions

The H. pluvialis having green color under exponential phase was used to be centrifuged at 3000g for 5 min at a room temperature and washing with the fresh medium. After three cycles of centrifugation and washing, the suspension was diluted consecutively to make different concentrations of algal suspensions using fresh medium. The measurement of dry cell weight was carried out by drying 5ml of the suspension at 60 °C in a drying oven for 24 h after being filtered through a pre-dried and pre-weighed 0.45 μm nitrocellulose membrane filter (Millipore, USA). The algal suspensions with different cell concentrations were shaken for 2 h at 170 rpm and 25 °C in a dark condition in order to remove any residual effects of previously exposed light. When needed, nitrogen gas was bubbled to decrease the concentration of dissolved oxygen. The resulting suspensions were used to measure the oxygen production rate.

Growth Phase

With respect to the growth phase of bacteria, exponential phase cells differ in their sensitivity to irradiation compared with stationary phase cells. During the exponential phase of growth, bacteria are rapidly multiplying and exhibit greater sensitivity to irradiation when they are actively proliferating. Also, during the exponential phase, the bacterial chromosomes may exhibit two or more replication forks as additional rounds of DNA replication start before the initial round is completed. This phenomenon is not observed in stationary-phase cells. The relatively greater sensitivity of exponential-phase cells to irradiation compared with stationary-phase cells might be attributed to the greater amount of DNA that become exposed to radiation to cause more damage for the cells to repair. Also, because exponential-phase cells are rapidly multiplying due to increased metabolic rate, they are likely to generate more reactive oxygen species (ROS) compared with stationary-phase cells. Metabolically generated ROS plus ROS formed from radiolysis of water can overwhelm the organism's antioxidant capacity and result in cell death due the organism's inability to repair cellular lesions caused by ROS.

2.2 Mathematical modelling

Two segregated populations are formulated as pre-stationary and post-exponential phase viable cells. They are distributed in volume and represented by nc and na, respectively. Their dynamic behavior is described by the following population balances:

(1)Accumlationgrowthdivisiondeathtransitiontona∂ncvt∂t+∂∂vgcvsncvt+Γcv sncvt+Dsncvt+Γtvsncvt+FinV1−xancvtdilution=2∫vminvmaxP vv′Γcv′sbirthnc v′tdv′

(2)Accumlationgrowthdeathdilutiontransitionfromnc∂navt∂t+∂∂vgavsnavt+Dsnavt+FinVxanavt=Γtvsncvt

The second stage of the model shown in Eq. (2) represents post-exponential phase dynamics in an environment of low asparagine availability. Unlike Eq. (1), this equation has no division function and the birth term is the transition from the previous stage. This assumption agrees with our experimental data as feeding during the stationary and decline phases appears to maintain cell viability rather than increase cell density.

The initial distribution of viable cell population is given in Eq. (3) by Generalised Extreme Value for cycling cells and zero for the stationary phase cells. This distribution fits our data well in MATLAB® distribution fitting tools. The boundary conditions are given in Eq. (4), which signifies that no cell has volume of zero at any time.

(3)ncv0=1σ1+ε(v−μσ)−1ε−1e−1+ε(v−μσ)−1 ε;nav0=0

(4)nc0t=0;na0t=0

There are outliers in cell size, such as cell aggregates and fragments observed particularly in late stage culture. When analysing our data we limited the range of diameter for viable cells between 10 and 22 μm based on previous observations and the literature (Kiehl et al., 2011). Cell volume was normalised and presented using a probability density function.

The two population growth rates, gc(v,s) and ga(v,s), are functions of cell volume, asparagine and ammonia concentrations as given in the following equations:

gjvs=μj−maxfj−limfinhv;fj−lim= AsnAsn+kj−Asn; finh=kAmmAmm+kAmm;j=c,a

The reduction of asparagine below a minimum limit results in cell growth decrease with the population entering stationary phase. In this phase, most cells are at the G0/G1 phase of the cell cycle, while growth is suppressed by the accumulation of toxic metabolites and limiting substrate availability (Fan et al., 2015). The inhibition term finh is assumed to have the same effect on both populations. Both the limitation and inhibition terms obey Monod kinetics. Transition and division rates are expressed through the same generalised equation:

(6)Γj vs=2e−(v‐vcε)2gjνsεπ1+ erfcvcε;j=c,t

The term gt(v,s) in the transition rate is directly proportional to the factor ft

(7)gtvs=μt−maxftv;ft=ktAsn+kt

which is almost zero at the lag and early exponential phase but as asparagine concentration reaches the minimum limit, the cells rapidly shift to the second phase. The cell division function, Eq. (6), requires a volumetric mean, vc, and standard deviation, ε, of cells at division. This mean has been determined iteratively, as it depends on the chosen distribution, to mimic the initial self-similar cell distribution. A commonly used standard deviation is around 0.125 (Mantzaris et al., 1999). The transition function also requires the input of cycling cells mean for the birth of stationary phase thus is identical to the mean volume of cycling cells. The death function is given by Eq. (8). It depends on extracellular ammonia and asparagine concentrations, with the last term accounting for cell lysis.

(8)Ds=kdmaxe(−μmax fc‐limfinhkd0)−kι

Cell density is calculated by integrating the distributions of both viable cell populations from minimum to maximum cell volume as shown in Eq. (9). The fraction of cells in the stationary phase at any instance is given by Eq. (10). This fraction is used in Eq. (1) and Eq. (2) to consider the feeding effect on the cell number; assuming a well-mixed bioreactor. Similarly, Eq. (11) calculates the total dead cell density.

(9)Nc=∫vminvmaxncvtdv;Na=∫vminvmaxnavtdv

(10)xa=NaNa+Nc

(11)dNddt=∫vminvmaxDsn avt+ncvtdv

The following equations represent the dynamics of asparagine, ammonia, mAb and HCP concentrations. Asparagine is consumed by the two populations at different rates as shown in Eq. (12). Ammonia is mostly produced initially then consumed by the cells to synthesise glutamine. In Eq. (13), for the sake of simplicity, we assume that cycling cells produce the ammonia whereas cells at stationary phase consume it. The two populations produce mAbs at different rates according to Eq. (14). The HCPs are coming initially from viable cells as secreted proteins and then released from dead cells into the supernatant (Eq. (15)).

(12)dAsndt=−μ c−maxfc−limfinhYc−AsnNc−μa−maxfa−lim finhYa−AsnNa+Fin VCF−Asn

(13)dAmmdt =Yc−Ammμc−maxfc−lim finhNc−μa−maxfa− limfinhYa−AmmNa

(14)dmAbdt=Yc−mabμ c−maxfc−limfinhNc+Ya−mabμa−maxfa−limfinhNa

(15)dHCPsdt =Yc−HCPμc−maxfc−lim finhNc+Ya−HCPμa− maxfa−limfinhNa+ Yd−HCPkdmaxe(−μmax fc−linfinhkd0)Nd

Solution

To solve the present problem Table 4.1 is made from the date reported in Fig. 4.1.

Table 4.1. Values of Cell Concentrations, Substrate Content, and Logarithm of Biomass During a Batch Submerged Process Employing a Strain of Lactobacillus acidophilus

Note that negatives values for ln X simply correspond to the natural logarithmic of decimal value and obviously do not alter the values to determine the corresponding parameters, v. gr. μmax. A graphic representation of ln X vs. t allows a much easier estimate of the different questions asked in the problem and a clearer picture of the process.

The reader should compare Fig. 4.2 with Fig. 4.1.

Calculations:

Beginning the logarithmic phase: From the constructed graphic, it is observed that the exponential phase begins 4 h after the beginning of the fermentation.

Time at fermentation should be stopped because biomass synthesis is the only purpose of the fermentation: It is the corresponding time at the end of the exponential phase. From Fig. 4.2 it can be seen that the logarithmic phase ended at 10 h. This is the time when fermentation must be stopped. Going further is unproductive as we are concerned with biomass production only.

Yield based on substrate consumption (YXS):

YXS =S0−StXt−X0=2.45−0.0810.0−5.1=0.4837

g of biomass/g of substrate consumed (as overall, dimensionless).

Expressed as (%); (YXS) = 48.37%

It must be observed that to determine the yield, the final values in the yield expression correspond to the end of the logarithmic or exponential phase (in our case at 10 h). If we would consider all the time the fermentation ran, the estimate for the yield would be 30.54%. This fact is very important to take into account. It indicates that fermentation should be stopped at 10 h. After that time, the endogenous process starts to become more important and consumed sugars are employed in a greater quantity than in the exponential phase for this purpose. The reader must consider that in case a metabolite is the principal aim of the process, the analysis would be different mainly in a case where secondary metabolites are produced.

The initial stationary phase: From the graphic, it is taken at 14 h.

Maximum specific growth rate (μ): The maximum specific growth rate that is reached in this process corresponds to the specific growth rate in the logarithmic or exponential phase. From Eq. (4.5), it is obvious that the best way to estimate this value is to make a lineal regression with minimum squared adjustment for ln X vs. t in time interval between 4 and 10. The slope corresponding to line fixing is the value of the specific growth rate. This value is constant during the whole phase and maximum (μmax = μ). In our case:

μmax=0.540h−1

r2=0.9945

(It should be noted that the estimate was made considering only four points. Undoubtedly a better estimate could be done if there were more points to consider.)

Time in which biomass duplicates:

This time is already calculated from Eq. (4.7), hence

td=0.6930.540h−1=1.28h

1.29.2 Translational Machinery

In the early stages of culture, cells focus energy into division and growth, resulting in a lag between growth curves and rP production. As cells reach the mid-exponential phase of growth, much of the energy resource of the cell is diverted into protein synthesis via mRNA translation and global protein synthesis. When a culture approaches maximum cell concentration, a number of environmental stresses, such as nutrient deprivation and endoplasmic reticulum (ER) stress, are encountered and perceived. One mechanism by which mammalian cells respond to such environmental, ER, and other stresses encountered as a result of the demands of high-level expression of a rP is to modulate mRNA translation rates and hence global protein synthesis rates. Much of this control is imparted by (de)phosphorylation of key factors of the mRNA translational machinery with a potential outcome being a reduction in recombinant mRNA translation and hence rP synthesis. Therefore, in order to maximize rP synthesis, differences in the rate of mRNA translation throughout the entire culture must be determined and optimized through each culture phase, although this is rather difficult to achieve.

mRNA translation is comprised of three main steps – initiation, elongation, and termination – each of which requires ribosomes, mRNA, energy, and a number of additional factors. Translation initiation is the most complex of the steps and depends upon the assembly and coordinated action of multiple initiation factors, many of which consist of multiple subunits (Figure 2). Consequently, the initiation step is rate limiting for translation and provides the cell with a key control point in the gene expression pathway.

In yeast cells, it has been shown that the copy numbers per cell of the eukaryotic initiation factors (eIFs) and their subunits are spread over an approximately 30-fold range. Knowledge of the stoichiometry of initiation factors not only gives a better insight into translation initiation as a whole process but also provides key information on the impact of individual eIFs in translational regulation [15]. In mammalian cells, the stoichiometry of the eIFs remains to be determined, although a number of studies have shown that changes in levels of individual eIFs or their subunits are implicated in malignant transformation and changes in cell growth in cancer. Despite the stoichiometry of the mammalian eIFs being as-yet unknown, a number of key control points of translation initiation have been well studied in mammalian cells.

The phosphorylation status of several eIFs tightly regulates translation initiation. The best characterized of these are eIF2α [8] and eIF4E-binding protein (4E-BP) [10] phosphorylation (see Figure 2). eIF2 is a trimeric protein which joins with the initiator methionyl-tRNA (Met-tRNA(i)) and guanosine triphosphate (GTP) to form the ternary complex and bring Met-tRNA(i) onto the 40S ribosomal subunits (tRNA, transfer RNA). During each cycle of translation initiation, the GTP associated with eIF2 is hydrolyzed to guanosine diphosphate (GDP) and subsequently the eIF2/GDP complex is released. To participate in another round of translation, the GDP must be exchanged for a GTP molecule. This exchange is accomplished with the help of the guanine nucleotide exchange factor (GEF) eIF2B. In times of cellular stress, the eIF2α subunit is hyperphosphorylated at Ser51 and forms an inhibitory complex with eIF2B, thus preventing the assembly of the ternary complex and translation initiation. As eIF2 normally occurs in excess of eIF2B, and has a higher affinity for eIF2B in its phosphorylated form, only a small proportion of eIF2 needs to be phosphorylated to inhibit nucleotide exchange and thus cap-dependent initiation. The phosphorylation event can be carried out by one of four protein kinases (PKR-like endoplasmic reticulum kinase (PERK), heme-regulated inhibitory kinase (HRI), general control nonderepression-2-kinase (GCN2), and interferon-induced protein kinase (PKR)), each of which responds to different cellular stresses. The level of phosphorylated eIF2α has been shown to increase toward the end of mammalian cell culture, at the same point at which there was a marked increase in secreted rP. Phosphorylated eIF2α levels may therefore act as an indicator of cellular stress perception, which could be monitored during rP production and used to inform feeding and engineering strategies [14].

eIF4E is a member of the cap-binding complex (eIF4F) which binds the 7-methyl GTP-cap structure of mRNA for cap-dependent translation. Inhibition of cap binding of eIF4E is a potential control point for translation initiation both through eIF4E phosphorylation and through its interaction with the 4E-BPs. The members of the 4E-BP family inhibit translation by competing for the eIF4G-binding site of eIF4E. Affinity of the 4E-BP for eIF4E is reduced by its hyperphosphorylation. The hyperphosphorylation can be induced by a variety of stimuli, including hormones, mitogens, and growth factors, via a number of signaling pathways such as the mammalian target of rapamycin (mTOR) pathway. The converse of this is hypophosphorylation of 4E-BP when there is nutrient or growth factor deprivation [7]. Hypophosphorylation of 4E-BPs increases their affinity for eIF4E, inhibiting cap-dependent translation in times of stress. In a recent study investigating the impact of cellular energy on rP production capacity, it was shown that upon addition of adenosine to a culture the level of cellular adenosine triphosphate (ATP) increased, cell growth was arrested and average specific productivity was increased 2.5-fold. Under these conditions, hypophosphorylation of 4E-BP1 is expected due to the activation of the adenosine monophosphate-activated protein kinase (AMPK) and subsequent inhibition of the mTOR pathway of 4E-BP1 phosphorylation. However, the high levels of ATP kept 4E-BP1 hyperphosphorylated, probably by a direct interaction of ATP with the mTOR pathway. The hyperphosphorylation allowed translation to continue and increased average specific productivity to be achieved, suggesting that the manipulation of the repression of translation by pathways involving 4E-BP may improve rP yield under stress conditions [3].

The eIFs are not the only cellular machinery critical to the rate of translation. The number of ribosomes present in the cell can also limit translational capacity. Ribosome biogenesis in mammalian cells is a complex process during which RNA polymerases I (45S processed to 18S, 28S, and 5.8S) and III (5S) transcribe rRNA species in different cellular compartments. Additionally, RNA polymerase II transcribes a large number of mRNAs, approximately 80 of which are translated to ribosomal proteins. At any one time, a significant proportion of ribosomal RNA (rRNA) genes in a cell is transcriptionally silent. Ribosome assembly begins in the nucleolus before transport out through the nucleus into the cytoplasm where the final activation of the large subunit occurs (for review see Reference [4]). In yeast, it has been shown that engineering of a gene BMS1, whose product is required for 18S ribosome biogenesis, altered the ratio of 60S:40S subunits from 1:1 to 2:1 and correspondingly 25S:18S subunits from 2:1 to 3:1, resulting in a high-yielding phenotype. These data suggest that the balance of cellular ribosomal components is critical to efficient rP production [1]. Furthermore, a study showed that, in mammalian cells producing the model rPs, luciferase and human placental secreted alkaline phosphatase (SEAP), protein yield was increased two- to fourfold when ribosome synthesis was enhanced. The increase in ribosome synthesis was achieved using an epigenetic engineering approach to limit the silencing of rRNA genes by knockdown of a subunit of the nucleolar remodeling complex (NoRC) which normally represses rDNA transcription via histone modification and DNA methylation [11].

Exponential phase

Following a period during which the growth rate of the cells gradually increases, the cells grow at a constant, maximum rate and this period is known as the log, or exponential, phase and the increase in biomass concentration will be proportional to the initial biomass concentration.

dxdt∝x

where x is the concentration of microbial biomass (g dm−3), t is time (h), d is a small change.

This proportional relationship can be transformed into an equation by introducing a constant, the specific growth rate (μ), that is, the biomass produced per unit of biomass and takes the unit per hours. Thus:

(2.1)dxdt =μx

On integration Eq. (2.1) gives:

(2.2)xt=x0eμt

where x0 is the original biomass concentration, xt is the biomass concentration after the time interval, t hours, e is the base of the natural logarithm.

On taking natural logarithms, Eq. (2.2) becomes:

(2.3)lnxt=ln x0+μt

Thus, a plot of the natural logarithm of biomass concentration against time should yield a straight line, the slope of which would equal to μ. During the exponential phase nutrients are in excess and the organism is growing at its maximum specific growth rate, μmax. It is important to appreciate that the μmax value is the maximum growth rate under the prevailing conditions of the experiment, thus the value of μmax will be affected by, for example, the medium composition, pH, and temperature. Typical values of μmax for a range of microorganisms are given in Table 2.1.

Table 2.1. Some Representative Values of μmax (Obtained Under the Conditions Specified in the Original Reference) for a Range of Organisms

It is easy to visualize the exponential growth of single celled organisms that replicate by binary fission. Indeed, animal and plant cells in suspension culture will behave very similarly to unicellular microorganisms (Griffiths, 1986; Petersen & Alfermann, 1993). However, it is more difficult to appreciate that mycelial organisms, which grow only at the apices of the hyphae, also grow exponentially. The filamentous fungi and the filamentous bacteria (particularly the genus Streptomyces) are significant fermentation organisms and thus an understanding of their growth is important. Plomley (1959) was the first to suggest that filamentous fungi have a “growth unit” that is replicated at a constant rate and is composed of the hyphal apex (tip) and a short length of supporting hypha. Trinci (1974) demonstrated that the total hyphal length of a mycelium and the number of tips increased exponentially at approximately the same rate indicating that a branch is initiated when a certain hyphal length is reached. Robinson and Smith (1979) demonstrated that it is the volume of a fungal hypha rather than simply the length, that is, the branch initiation factor and Riesenberger and Bergter (1979) confirmed the same observation for Streptomyces hygroscopicus. Thus, branching in both fungi and streptomycetes is initiated when the biomass of the hyphal growth unit exceeds a critical level. This is equivalent to the division of a single celled organism when the cell reaches a critical mass. Hence, the rate of increase in hyphal mass, total length, and number of tips is dictated by the specific growth rate and:

dxdt =μx,

dHdt=μH,

dA dt=μA

where H is total hyphal length and A is the number of growing tips. Although the growth of both filamentous fungi and streptomycetes are described by identical kinetics, the mechanisms associated with apical growth differ. The movement of materials to the fungal growing tip is dependent on a microtubule-based transport system (Egan, McClintock, & Reck-Peterson, 2012), whereas that in Streptomyces is facilitated by the coiled coil protein DivIVA that recruits other proteins to the growing site forming multiprotein assemblies termed polarisomes (Flardh, Richards, Hempel, Howard, & Butner, 2012).

In submerged liquid culture (shake flask or fermenter), a mycelial organism may grow as dispersed hyphal fragments or as pellets (as shown in Fig. 2.2) and whether the culture is filamentous or pelleted can have a significant influence on the products produced by a mycelial organism (Krull et al., 2013). As discussed in more detail in Chapter 6, the key factors influencing hyphal morphology in submerged culture are the concentration of spores in the inoculum, medium design, and shear conditions. The influence of morphology on culture rheology and oxygen supply is discussed in Chapter 9. The growth of pellets will be exponential until the density of the pellet results in diffusion limitation. Under such limitation, the central biomass of the pellet will not receive a supply of nutrients, nor will potentially toxic products diffuse out. Thus, the growth of the pellet proceeds from the outer shell of biomass that is the actively growing zone and was described by Pirt (1975) as:

M1/3=kt+M01/3

where M0 and M are the mycelium mass at time 0 and t, respectively. Thus, a plot of the cube root of mycelial mass against time will give a straight line, the slope of which equals k.

It is possible for new pellets to be generated by the fragmentation of old pellets and, thus, the behavior of a pelleted culture may be intermediate between exponential and cube root growth.

2.4 Analysis of the modified Gompertz equation

The growth curve of the microorganism is shown in Fig. 2.6. The growth rate of microorganisms changed regularly with time, which can be divided into the delay period, logarithmic growth phase (exponential phase), stable period, and decay period. The curve can be described by three parameters: maximum slope μmax: maximum slope of point t; delay time λ, that is, the intercept on the x-axis at t; asymptote A: the maximum value that can be achieved during the growth process.

In microbiology, there are many models used to describe the growth of bacteria under different environmental conditions, most of which only draw a curve including the mathematical parameters a, b, c, and rarely include organisms.

(2.3)dXdt=μxorXi=X0eμ

(2.4)μ=lnXt−lnX0 t

where µ is the specific growth rate (h−1); Xt is the concentration of microbial cells after incubation in t time; and X0 is the cell concentration of the initial microorganism.

Although the above formula can be used to estimate the specific growth rate of bacteria, the delay period and the growth-halt period situation cannot be properly described. The growth kinetics model of microorganisms is rewritten with A, μmax, and λ, where the modified Gompertz equation is the simplest and could describe the four stages of microbial growth. The derivation process is as follows.

The Gompertz equation is:

(2.5)y=ae−e(b−ct)

Derivation of Eq. (2.5):

(2.6)y′ =ac·e−e(b−ct)·e(b−ct)

Second derivation of Eq. (2.5):

(2.7)y′′=ac2·e−e(b−ct)·e(b−ct)·[e(b−ct)−1]

when t=ti,

(2.8)d2ydt2=0→ti=bc

The maximum specific growth rate, μmax, can be calculated using the following formula:

(2.9)μm=(dydt)ti=ace

c in Eq. (2.9) can be expressed as:

(2.10)c=μmea

The tangent equation is:

(2.11)y=μmt+ae−μm ti

Λ is the intercept on the time axis, therefore:

(2.12)0=μmλ+a e−μmti

Calculation of Eqs. (2.8), (2.9), and (2.12) can obtain:

(2.13)λ=( b−1)c

(2.14)b=μmeaλ+1

When the asymptotic value is reached, t tends to infinity:

(2.15)t→∞:y→aA=a

(2.16)y=Ae−e[(μme/A)(λ−t)+1]

The modified Gompertz equation can be used in statistics to describe bacterial growth, such as that of Lactobacillus plantarum, Lactobacillus acidophilus, acetogens, and methanogens. This equation can also be used to describe the production of the product in the anaerobic culture system, in which part of the substrate is converted in to new cells and partly converted in to hydrogen and carbon dioxide. The modified Gompertz equation is used to describe the formation of methane in anaerobic fermentation systems.

The modified Gompertz equation is used to describe the hydrogen production process. After the equation fitting, the reaction delay time, the maximum hydrogen production rate, and the hydrogen production rate of hydrogen are measured, which are consistent with the experimental results.

(2.17)H=Hmax·e −e[(Rme/P)( λ−t)+1]

where H is the cumulative hydrogen production (mL); λ is the hydrogen production delay time (h); Hmax is the maximum cumulative hydrogen production (mL); Rm is the maximum hydrogen production rate (mL/h); and e=2.718281828.

As production of hydrogen is an accumulation process during fermentation, the volume of hydrogen produced at each sampling time needs to be calculated using the following mass balance formula:

(2.18)VH,iVH,i−1+0.5VG,i(CH,i+CH,i−1)+VH(CH,i−CH,i−1)

where VH,i, VH,i−1 are the accumulated hydrogen volume during the i-th test and i−1-th test (mL); CH, i, CH,i−1 are the hydrogen volume concentration during the i-th test and i−1-th test (%); VG,i is the drainage volume of the i-th time gas measure; and VH is the headspace volume (200 mL) in serum bottles of fermentation hydrogen production.

The methane volume can be calculated by the following equation:

(2.19)VH,i VH,i−1+0.5VG,i(CH,i+CH,i−1)+VH(CH,i−CH,i−1)

where VH,i, VH,i−1 are the accumulated methane volume during the i-th test and i−1-th test, mL; CH,i, CH,i−1 are the methane volume concentration during the i-th test and i−1-th test, %; V G,i is the drainage volume of the i-th time gas measure; and VH is the headspace volume (200 mL) in serum bottles of fermentation hydrogen production.

The methane inhibition ratio (IR) can be calculated by (2.20).

The IR of the anaerobic bacteria inhibitor to sludge methane production is as follows:

(2.20)IR(%)=A−BA×100 %

where IR is the inhibition rate of CH4 production (%); A denotes, after n hours of anaerobic fermentation, the cumulative methane production (mL) from black experiment sludge; and B denotes, after n hours (observation period) of anaerobic fermentation, the maximum cumulative methane production (mL) when adding the anaerobic bacteria inhibitor.

Brevibacterium linens

Brevibacterium linens, which is the type species of the genus Brevibacterium, is Gram positive with both rod and coccoid forms. Cells of older cultures (3–7 days) are composed of coccoid cells, whereas cells in the exponential phase are characterized by their irregular rod shapes. Brevibacterium linens is an obligate aerobe that does not produce acid from lactose. The microorganism grows well at neutral pH. Growth also occurs in the pH range 6.5–8.5 and in NaCl concentrations up to 15%. Brevibacterium linens strains produce colonies that are yellow to deep orange-red, on a variety of media.

Brevibacterium linens has long been recognized as an important dairy microorganism because of its ubiquitous presence on the surface of a variety of smear surface-ripened cheeses, such as Limburger, Munster, Brick, Tilsiter, and Appenzeller. Brevibacterium linens is a strictly aerobic microorganism, with a rod-coccus growth cycle, with temperature growth optimum of 20–30 °C.

The growth of B. linens on the surface is thought to be an essential prerequisite for the development of the characteristic color, flavor, and aroma of smear surface-ripened cheeses. The growth of B. linens also is stimulated by vitamin production by the yeasts during growth. The major factors that influence the distinctive characteristics of smear surface-ripened cheeses and the number, type, and growth rate of the surface microflora are the physical and chemical characteristics intrinsic to the cheese (pH, water activity, redox potential, composition, and size), the environmental parameters (ripening temperature, relative humidity), and the technological conditions during manufacture (ripening time, degree of mechanization, and microflora of cheese equipment).

Surface-ripened cheeses (Table 2) can be defined as varieties with desirable microbial growth on the surface that plays a key role in the development of the characteristic flavor of the cheese. Surface-ripened cheeses can be differentiated, according to the types of microorganism growing on their surface, into cheeses with mold and those with yeasts and bacteria. In the latter, surface ripening is the result of the symbiotic growth of the bacteria and yeasts.

Table 2. Varieties of surface-ripened cheese

Yeasts are present in higher concentrations during the earlier stages of the ripening process, because they can develop at rather low temperatures and at relatively high humidities. They also can tolerate the low pH and high NaCl concentration at the cheese surface. The yeast flora is composed mainly of Debaryomyces, Candida, and Torulopsis, and it plays a key role in the transformation of the environment on the cheese surface. They yeast flora uses lactic acid as a carbon source, transforming it to H2O and CO2. As a result, the pH of the cheese surface is increased considerably from close to 5.0 to about 5.9. The yeasts also stimulate the growth of Brevibacterium linens and of micrococci through the synthesis of vitamins, including riboflavin, niacin, and pantothenic acid. The yeast flora disappears after 1–20 days, giving way to the micrococci and B. linens.

The micrococci isolated from surface-ripened cheeses have been identified as Micrococcus caseolyticus and Micrococcus freudenreichii. It is believed that micrococci play a role in the proteolysis of cheese and in flavor development. Brevibacterium linens, along with microorganisms of the genus Arthrobacter, forms the predominant flora of the smear of surface-ripened cheeses. Through their various metabolic activities, these microorganisms cause changes in the texture of the cheese and play a key role in the development of its characteristic flavor.