**8. Shape variations during active or exponential phase of growth**

The most classical form of tubercle bacilli is a slender rod shape that seen in stained smears. They have smooth, homogenous cytoplasm with clear-cut and well-define outlines. The first electron microscope images of the tubercle bacilli were obtained in 1939 in the laboratories of the Technische Hochschule, Berlin.

von Borries and E. Ruska (1939) published electron micrographs of the avian strain of tubercle bacilli magnified 26,000 times. The cytoplasm of these bacilli contained dark bodies of different sizes. Later on, Lembke and Ruska (1940), culture the bacilli on petragnani medium and observed up to eight large bodies inside the cytoplasm of bacilli. Rosenblatt, Fullam and Gessler (1942) in their studies of tubercle bacilli in the electron microscope, confirmed many earlier observation and added some new data, particularly concerning the internal structure of bacilli. The bacilli varied in size. The size of the strain H37 sub-cultured at Columbia University varied from 4.3µ X 0.4µ to 1.0µ X 0.2µ. The cell wall was always present (sometimes it was as thick as 0.03µ) and contained granules. The internal structure showed dense nuclear masses within the granular cytoplasm. The density of the cytoplasm varied; it contained many granules and vacuoles of different sizes. Later on it became clear that the cytoplasm of young cells is dense, the basic dyes stain it deeply and uniformly, and it contains vacuoles and hyper chromic bodies. The cell protoplast was seen surrounded by a 0.023µ thick and ductile cell wall. The cytoplasm itself was covered with a thin cytoplasmic membrane which closely adhered to the cell wall (Rosenblatt *et al*., 1942; Knaysi *et al*., 1950; Werner, 1951; Draper, 1982). In rod like bacilli, the process of cell division resembles that of most grams –positive bacteria (figure, 2). In the equatorial zone of the cell, on the inner side of the cell wall, a double cell plate was formed. The growth of this plate proceeded till the mother cell wall was divided into two daughter cells. The separation of newly formed cells occurred between these plates, which then covered the poles of the right and left cells. Before the cytoplasm divided, the division of cellular bodies was observed (Edwards, 1970; Nishiura *et al*, 1970; Dhal, 2004).

The other types of cell shape (V or Y - shape bacilli) occurs in lower frequency (Dahl, 2004; Farnia *et al* 2010). The V-shape bacilli are caused by snapping post-fission movements (Krulwich and Pate, 1971). The term "snapping division" was first described by Kurth (1898) and has been reported by many other investigators. Upon completion of cell division, one or both of the two daughter cells suddenly swing around, bringing their distal ends closer together while still remaining attached by a small region at their proximal ends. The exact mechanism responsible for snapping postfission movements is not clear. Bisset (1955) claimed that all so-called postfission movements were nothing but artifacts due to mechanical stress on the dividing cells (e.g., cells growing between solid agar and a cover slip) and would not occur if the same cells were grown in liquid cultures. Sguros (1957)

stress conditions (Velayati *et al*., 2009,2011; Farnia *et al*., 2010). Briefly, the reported morphological variation in *M. tuberculosis* are classified into two categories; those which frequently seen at exponential phase of growth that is rod, V, Y-shape, branched or buds, and those that are seen occasionally under stress or environmental conditions which are

The most classical form of tubercle bacilli is a slender rod shape that seen in stained smears. They have smooth, homogenous cytoplasm with clear-cut and well-define outlines. The first electron microscope images of the tubercle bacilli were obtained in 1939 in the laboratories

von Borries and E. Ruska (1939) published electron micrographs of the avian strain of tubercle bacilli magnified 26,000 times. The cytoplasm of these bacilli contained dark bodies of different sizes. Later on, Lembke and Ruska (1940), culture the bacilli on petragnani medium and observed up to eight large bodies inside the cytoplasm of bacilli. Rosenblatt, Fullam and Gessler (1942) in their studies of tubercle bacilli in the electron microscope, confirmed many earlier observation and added some new data, particularly concerning the internal structure of bacilli. The bacilli varied in size. The size of the strain H37 sub-cultured at Columbia University varied from 4.3µ X 0.4µ to 1.0µ X 0.2µ. The cell wall was always present (sometimes it was as thick as 0.03µ) and contained granules. The internal structure showed dense nuclear masses within the granular cytoplasm. The density of the cytoplasm varied; it contained many granules and vacuoles of different sizes. Later on it became clear that the cytoplasm of young cells is dense, the basic dyes stain it deeply and uniformly, and it contains vacuoles and hyper chromic bodies. The cell protoplast was seen surrounded by a 0.023µ thick and ductile cell wall. The cytoplasm itself was covered with a thin cytoplasmic membrane which closely adhered to the cell wall (Rosenblatt *et al*., 1942; Knaysi *et al*., 1950; Werner, 1951; Draper, 1982). In rod like bacilli, the process of cell division resembles that of most grams –positive bacteria (figure, 2). In the equatorial zone of the cell, on the inner side of the cell wall, a double cell plate was formed. The growth of this plate proceeded till the mother cell wall was divided into two daughter cells. The separation of newly formed cells occurred between these plates, which then covered the poles of the right and left cells. Before the cytoplasm divided, the division of cellular bodies was observed

The other types of cell shape (V or Y - shape bacilli) occurs in lower frequency (Dahl, 2004; Farnia *et al* 2010). The V-shape bacilli are caused by snapping post-fission movements (Krulwich and Pate, 1971). The term "snapping division" was first described by Kurth (1898) and has been reported by many other investigators. Upon completion of cell division, one or both of the two daughter cells suddenly swing around, bringing their distal ends closer together while still remaining attached by a small region at their proximal ends. The exact mechanism responsible for snapping postfission movements is not clear. Bisset (1955) claimed that all so-called postfission movements were nothing but artifacts due to mechanical stress on the dividing cells (e.g., cells growing between solid agar and a cover slip) and would not occur if the same cells were grown in liquid cultures. Sguros (1957)

round, oval , ultra-virus, spore like, and cell wall defiant or L-forms.

of the Technische Hochschule, Berlin.

(Edwards, 1970; Nishiura *et al*, 1970; Dhal, 2004).

**8. Shape variations during active or exponential phase of growth**

suggested that V-forms resulted from "germ tube extrusions" from each of a pair of attached arthrospores and were not due to postfission movements. More studies have demonstrated that snapping division or V-forms could arise by any of three methods: (I) germination of adjacent coccoid elements, (ii) subpolar germination (budding) of rods, and (iii) snapping postfission movements (Starr and Khan, 1962). In mycobacterium, during septum formation the plasma membrane and inner cell wall grow inward but the outer cell wall layer remains intact. Upon completion of septum formation with a cross-wall, the inner layer may continue to grow and thus exert pressure upon the outer cell wall layer. The outer layer eventually ruptures first on one side of the cell, and the two daughter cells bend in on the side where the outer layer is still intact forming a "V-form (Dahl,2004; Farnia *et al*,2010; Malhotra *et al*., 2010)

Mycobacterium is known to form a "Y-shaped "cells with branches more interior to the cells and of greater length figure 3. Brieger *et al* in 1954, was among the first scientist who demonstrate the branching in the reproductive cycle of *M. avium*. He showed that young culture of bacilli when first transplanted to fresh medium it consists mainly of short coccoid rods. These elongate into filaments (8-10µ) which continue to divide and grow during a phase of filamentous proliferation. The filaments usually have two fully

Fig. 2. Atomic force microscopy shows the V-shape *M. tuberculosis* during exponential phase of growth

Morphological Characterization of *Mycobacterium tuberculosis* 157

of the cause of tuberculosis", he described that "under certain conditions, some bacilli contain several spores, in most cases there are two to four of them; oval in form, they are distributed, in uniform intervals, along the axis of the bacilli(1882). Following Koch discovery, Malassez and Vignal (1883) had described, the small "coccoid bodies " which cause tuberculosis infection and named them as cell wall deficient forms (CWD-forms) of tuberculosis. Later on, Spengler (1903, 1905), were among the first scientist who could demonstrated that in older cultures and frequently in sputa, apparently in response to adverse environmental conditions, the smooth cell takes on a fragmented appearance. Much (1907) was able to reproduce granules in the inside of the bacilli as well as scattered around them. These granules, according to Much, cannot be stained by the Ziehl- Neelsen technique but may generate new tubercle bacilli. Later on 1909, Fontes revealed how he had applied double staining to the bacilli, namely Ziehl- Neelson's carbolfuchsin staining and the Gram treatment. In this way he tried to differentiate the pathogenic tubercle bacilli, containing Much granules, from the apathogenic ones without these granules. In 1910, Fontes described the multiplication through division of these granules in the inside of a cell and on its outside and applied the term "virus" to this formation. Fontes described the application to the tubercule bacillus of the well –known method of separating the virus from the substrate by filtering the material through a bacterial filter. He inoculated a guinea pig with the filtered caseous material and transplanted the organs of this animal into a fresh one. When after five months of observation the animal was killed, the autopsy revealed the infiltration of round cells, granules, and occasional acid-fast bacilli in the lymph nodes and the lungs. After years of oblivion, the early works of Fontes were rediscovered by Vandremer (1923). He repeated the Fontes filtration experiments and confirmed the development of acid –fast bacilli on media and in animals inoculated with these filtrates. Calmette (1926) advanced the theory on the role of the the tuberculosis " ultra-virus" in the development of certain forms of the diseases. However, Negre *et al* (1933) denied the existence of filterable forms of the mycobacteria. Few years later, Vera and Rettger (1939) studied four strains of *M. tuberculosis*(hominis), "Koch", 607, 75 and H37 in micro-culture by Hill hanging block technique. This method was employed to permit observation of individual cells and their progeny over long periods of time using lucida drawings camera. They could demonstrate various forms which have been described in the literature at one time or another. When they cut off air supply, different variants developed very soon. The bacilli swelled slightly, the cytoplasm become less clear and smooth. The swelling commonly occurred at the ends of cells, so the clubs and dumbbell shapes were formed; cells often became spoon shaped. These swollen structures became increasingly refractive and more sharply delimited, until finally there was a definite superficial resemblance to spores. At the similar time, the ability of the tubercle bacillus to survive environmental hardship in culture was documented by Corper and Cohn in a study published in 1933. In another study, McCune and other colleagues (1965, 1966), showed the capacity of tubercle bacilli to survive in mouse tissue after sterilization. In this model, out bred mice were infected intravenously with 105 colonyforming units of the H37Rv strain of *M. tuberculosis*. They were immediately treated for a period of 12 weeks with the antimycobacterial drugs isonizid (INH) and pyrazinamide (PZA). For 4-6 week period after withdrawal of therapy, the mice showed no evidence of cultivable tubercle bacilli (sterile state). But, 12 weeks after INH and PZA treatment was withdrawn, one-third of the mice developed full-blown active TB, with nearly two-thirds

developed dense bodies in polar positions and in some organisms a number of smaller are also seen scattered among the cellular units and apparently associated with them. The final stage in the reproductive cycle led to a massive production of small rods. At this phase the filaments suddenly break down into masses of short rods which elongate to form the new generation and the cycle is complete. Under electron microscope, it was seen that the filaments were quite separate, and there was no true branching and that the mycelia appearance was produced because the filaments often remained stuck together. In another study, Mizuguchi Y *et al* (1985) showed β-Lactam antibiotics at low concentration induced filamentous cells in the *M. avium-intracellular* complex. Although, the mechanisms of induction of filamentous cells appeared to be different according to the drugs used. Ampicillin induces filaments by inhibiting the septation in a manner similar to its effect on *E. coli,* whereas cephazolin induces filaments but does not inhibit septation. In *M. tuberculosis,* branches were first seen as a small bud that does not grow to any appreciable size before breaking off as a separate cell. Few studies suggested that *M. tuberculosis* grows from the ends of bacilli and not along the length of the cylinder as seen in other well-characterized rod shape bacteria (Thanky *et al*., 2007). This might be true for susceptible isolates, but recently Farnia *et al* (2010) showed that in highly drug resistance strains i.e., XDR-TB and Totally or Extremely drug resistant isolates (TDR or XXDR-TB), branches produce along the cylinder. In fact, about 20 -24% of cells in XDR and XXDR-TB bacilli were dividing by branching, respectively.

Fig. 3. Transmission Electron Microscopy shows Y-Shape *M. tuberculosis* at exponential phase of growth


*2.2. Plant Sample Collection and Identification*

The seeds of *M. pruriens* were purchased from a local market in Kanchanaburi province and kindly provided by *Chao-Phraya Abhaibhubejhr* Hospital *Foundation*. The plant materials were compared with the authentic specimens at the Bangkok Herbarium (BK), Botany Section, Botany and Weed Science Division, Department of Agriculture. The voucher specimen (RSU-MP-KP01) was kept in the Department of Pharmacognosy, College of Pharmacy, Rangsit University for future reference.


5. The Gershgorin circle theorem

The Gershgorin circle theorem first version was published by S. A. Gershgorin in 1931 [9]. This theorem may be used to bind the spectrum of a complex matrix, and its statement is the following:

Theorem (Gershgorin)

Once again, the ODE system can be written as , where the MP-matrix is:

It is easy to observe that the outgoing flux Φ0 only appears in the last entry of the MP-matrix and the incoming flux Φ0 only is involved in the first entry of vector B. These facts—particularly the first one—are relevant when applying the Gershgorin circle theorem, which will be exposed

The Gershgorin circle theorem first version was published by S. A. Gershgorin in 1931 [9]. This theorem may be used to bind the spectrum of a complex matrix, and its statement is the

In the previous ODE system, the independent vector is:

Figure 5. Three tanks with all the possible connections.

50 Matrix Theory-Applications and Theorems

in the next section.

following:

5. The Gershgorin circle theorem

ð18Þ

ð19Þ

If is an matrix, with entries being , and is the sum of the non-diagonal entry modules in the th row, then every eigenvalue of lies within at least one of the closed disks , called Gershgorin disks.

This theorem was widely used in previous book chapters [6, 10, 11] in order to obtain new results about matrices corresponding to chemical problems.

Here, the main purpose is to apply this theorem to MP-matrices as a method to bind their eigenvalues, depending on the characteristics of the MP ODE system, and, even more, the compartment considered.

For instance, if we consider the MP corresponding to Figure 5, the first ODE of Eq. (17) can be expressed as dC1 dt ¼ Φ0 V1 C0 þ Φ21 V1 C2 þ Φ31 V1 C3 � ð Þ Φ12þΦ13 V1 C1

This equation—which obviously corresponds to an input tank—gives the first row of the MPmatrix (Eq. (18)) that can be written as � ð Þ Φ12 þ Φ13 V1 Φ21 V1 Φ31 V1 .

The Gershgorin disk corresponding to this row is centered at a11 ¼ � ð Þ Φ12þΦ13 V1 < 0 with radius R1 ¼ Φ21þΦ31 V1 .

Now, if a flux balance is performed in this input tank, we have this equation: Φ0 þ Φ21 þ Φ31 ¼ Φ12 þ Φ13, and then Φ21 þ Φ31 < Φ12 þ Φ13 (at least if we consider the nontrivial case Φ0 > 0). As a consequence of this fact, j j a11 > R1, and the Gershgorin disk will look like the one schematized in Figure 6.

Now, if the second ODE of Eq. (17) is considered, this equation can be written as dC2 dt ¼ Φ12 V2 C1 þ Φ32 V2 C3 � ð Þ Φ21þΦ23 V2 C2.

This internal tank equation corresponds to the second row of the MP-matrix (Eq. (18)): Φ12 V2 � ð Þ Φ21 þ Φ23 V2 Φ32 V2 .

Figure 6. The Gershgorin disk corresponding to an input tank.

The Gershgorin disk corresponding to this row is centered at a22 ¼ � ð Þ Φ21þΦ23 V2 < 0 with radius R2 ¼ Φ12þΦ32 V2 .

Since every eigenvalue lies within at least one of the Gershgorin disks, it follows that

As stated in Section 3, if there is no recirculation, then the ODE system has only negative

eigenvalues of the form , for all Then, in this case all the

In a previous work [6], it was proved that in an open MP, with three or less compartments, with or without recirculation, all the corresponding ODE system solutions are asymptotically stable. It is important to analyze if this result can be generalized or not, when closed systems and/or tanks with more than three compartments are considered. For this purpose, we will start with

In an open system, if the ith tank is an input one, then the diagonal entry of the ith row is aii < 0

If Φai, Φbi, ⋯, Φni are the incoming fluxes from other tanks of the system, ΦiA, ΦiB, ⋯, ΦiJ are the

0 are the incoming fluxes from outside the system, then the

0C0 þ … þ Φs

Square Matrices Associated to Mixing Problems ODE Systems

http://dx.doi.org/10.5772/intechopen.74437

53

0Cs (20)

Vi for k ¼ i, and

Cp (21)

PΦij

and aii j j > Ri being the sum of the non-diagonal entry modules of that row.

dt ¼ ΦaiCa þ … þ ΦniCn � ΦiA þ … þ ΦiJ � �Ci þ Φ1

Φni Vi Cn � PΦij Vi

Ci þ

Vi ¼ aii j j, which proves the theorem.

PΦp 0 Vi

Vi for k 6¼ i, �

0 ¼ PΦij, which implies PΦki < PΦij, and then:

Ca þ … þ

PΦij

Eq. (20) implies that the ith row of the MP-matrix has entries: Φki

PΦki Vi <

In the following section, these results—among others—will be generalized.

6. The general form of MP-matrices and new results

corresponding ODE system solutions will be asymptotically stable.

the following theorem.

outgoing fluxes, and Φ1

Vi dCi

This equation gives.

0, Φ2

dCi dt ¼ Φai Vi

Vi Cp is part of the independent term.

A flux balance gives PΦki þ PΦp

Vi < 0 and also Ri ¼

corresponding ODE can be written as

0, ⋯, Φs

Theorem 1

Proof

PΦp 0

aii ¼ �

PΦij

Now, if a flux balance is performed in this internal tank, we have this equation: Φ12 þ Φ32 ¼ Φ21 þ Φ23, and then j j a22 ¼ R2, and the corresponding Gershgorin disk will look like the one schematized in Figure 7.

Finally, if the third ODE of Eq. (17) is considered, this equation can be written as dC3 dt ¼ Φ13 V3 C1 þ Φ23 V3 C2 � ð Þ Φ31þΦ32þΦ0 V3 C3.

This output tank equation corresponds to the third row of the MP-matrix Eq. (18): Φ13 V3 Φ23 V3 � ð Þ Φ31 þ Φ32 þ Φ0 V3 .

The Gershgorin disk corresponding to this row is centered at the point a33 ¼ � ð Þ Φ31þΦ32þΦ0 V3 < 0 with radius R3 ¼ Φ13þΦ23 V3 .

The flux balance in this case gives Φ13 þ Φ23 ¼ Φ31 þ Φ32 þ Φ0, and then j j¼ a33 R3, and the corresponding Gershgorin disk will look like as the one schematized in Figure 7.

Taking into account all these results, the Gershgorin circles for the MP of Figure 5 are shown in Figure 8.

Figure 7. The Gershgorin disk corresponding to an internal tank.

Figure 8. Gershgorin circles for a three-tank system with recirculation.

Since every eigenvalue lies within at least one of the Gershgorin disks, it follows that

In the following section, these results—among others—will be generalized.


*4.9. Pro-MMP-2 Assay*

Pro-MMP-2 activation in the culture supernatants, peritoneal neutrophils and IFN-γ or LPS were measured using a gelatin zymography kit (Cosmo Bio, Tokyo, Japan) according to the manufacturer's instructions. The gelatin zymography products were electrophoresed on 2% agarose gels, stained with 0.5 mg/mL ethidium bromide and observed with a ultraviolet transilluminator. Images were analyzed using Image J version 1.51 (National Institutes of Health, MD, USA).


*5.2. Results*

In this section, all experiments are repeated five times based on randomly split datasets (refer to Section 5.1.1), and the mean result will be provided.

### 5.2.1. Effect of Knowledge Embedded Sample Model

From Figure 4, we can get a rough impression that the linear separability of knowledge embedded sample is better than raw SM data. Table 3 presents further the detailed performance of raw SM data samples and knowledge-embedded samples. By comparing XGBoost and SSAE in both sample models, all metrics of both algorithms are improved obviously. It demonstrates that knowledge of electricity measurement is very helpful for NTL recognition. Particularly, knowledge embedded sample model plays a more important role to SSAE because it allows SSAE learning more advanced features from mass samples. On the contrary, SSAE could not learn any knowledge from raw SM data, and the performance of SSAE is similar to XGBoost.

**Table 3.** Comparison about sample embedded knowledge or not.