Surface Thermodynamics Approach to Mycobacterium tuberculosis (M-TB) – Human Sputum Interactions

This research work presents the surface thermodynamics approach to M-TB/HIV-Human sputum interactions. This involved the use of the Hamaker coefficient concept as a surface energetics tool in determining the interaction processes, with the surface interfacial energies explained using van der Waals concept of particle interactions. The Lifshitz derivation for van der Waals forces was applied as an alternative to the contact angle approach which has been widely used in other biological systems. The methodology involved taking sputum samples from twenty infected persons and from twenty uninfected persons for absorbance measurement using a digital Ultraviolet visible Spectrophotometer. The variables required for the computations with the Lifshitz formula were derived from the absorbance data. The Matlab software tools were used in the mathematical analysis of the data produced from the experiments (absorbance values). The Hamaker constants and the combined Hamaker coefficients were obtained using the values of the dielectric constant together with the Lifshitz equation. The absolute combined Hamaker coefficients A132abs and A131abs on both infected and uninfected sputum samples gave the values of A132abs = 0.21631×10-21 Joule for M-TB infected sputum and A132abs = 0.18825×10-21 Joule for M-TB/HIV infected sputum. The significance of this result is the positive value of the absolute combined Hamaker coefficient which suggests the existence of net positive vanderwaals forces demonstrating an attraction between the bacteria and the macrophage. This however, implies that infection can occur. It was also shown that in the presence of HIV, the interaction energy is reduced by 13% conforming adverse effects observed in HIV patients suffering from tuberculosis.


I. INTRODUCTION
HE World Health Organization (WHO) declared tuberculosis (TB) as a global emergency in 1993. Unfortunately, the efforts made by the Stop TB Strategy were not enough to impede the occurrence of 1.3 million deaths in 2009 [1]. However, WHO estimates that the number of cases per capita peaked at 2004 and is slowly falling [2]. Nonetheless, the battle against TB is far from being over, since Mycobacterium tuberculosis (the main causative agent of TB) proved to be highly adaptive [3] and capable of evading the current strategies for treatment of about half million cases of multi-drug-resistant TB (MDR-TB) that were reported in 2007, including cases of extensively drug-resistant TB (XDR-TB) [2], and the more recently reported totally drug-resistant strains (TDR-TB) [4], [5].
Several reviews so far have been reported the incidences of TB cases, a particular report surveyed that out of 134 countries only 35 showed declination of cases of around 5% per year based on per capita rate [6]. This survey considered the data from 1998 to 2007. Different surveillance analysis and mathematical modeling studies recommended reduction of TB incidences per capita is around 1% per year, further suggesting diminution of cases by 2015. It is being predicted that growth of the world population of approximately 2% per year may be an important reason for increment of TB cases [2]. All these previous reports showing the presence of lacunae in the existing management approaches for TB and the inadequate effectiveness of public health systems, with special reference to underdeveloped countries. In spite of the availability of anti-TB drugs developed over the last five decades, one-third of the world's population retains a dormant or latent form of Mycobacterium tuberculosis (M-TB). In addition, drugs such as Rifampicin have high levels of adverse effects making them prone to patient incompliance. Another important problem with most of the anti-mycobacterials is their inability to act upon latent forms of the bacillus. To compound the problem further, the complex (vicious) interactions between the HIV and TB makes the treatment of co-infected patients even more challenging [5], [7].
In this study, M-TB is conceptualized as particle dispersed in a liquid (the sputum) and interacting with another particle (macrophage). The bacterium attaches itself on the surface of the macrophage cell before penetrating and attacking it. If the surface of the macrophage cell is such that it will repel the bacteria, access of the bacteria into the alveoli of the cell would have been denied. Thus, the initial actions actually take place on the surface of the cell and of the bacteria.
It is a well-known fact that surface property determination of interacting particles leads to the further understanding of the mechanism of interactions. A common area of contact is established once two particles meet each other. In such process, a certain portion of each particle gets displaced through work. Work responsible for the displacement of a unit area is known as surface free energy. The consecutive impact on the surface is known as surface thermodynamic effects. To attain the equilibrium such impacts are changed in a slow pace. In this particular study, similar concepts have been the combined m of (8), the nt ε of that eq urement of the putum, uninfec um. same laboratory with proper safety measures to avoid being infected.
The glass slide of 25.4mm x 76.2 x1.2mm was used for the preparation of test surfaces. A dropper was used to draw each of the Sputum samples from the container and smeared carefully on a slide to ensure even distribution of the sputum samples on the slides. Three slides were prepared for each of the twenty sputum samples and smeared with the samples for absorbance measurements. The slide preparations and sample smearing were done at the same laboratory (Chest Clinic/Laboratory, Anambra State University Teaching Hospital, Awka). The samples were allowed to dry naturally at room temperature because exposing the prepared slides to the sun is likely to cause oxidation and the surface energy might be increased unconditionally. All the well prepared and dried surfaces were covered with microscopic cover slip, ready for the experiment.

C. Measurements
Absorbance measurements were done on all the positive and negative sputum components of all sixty samples (TB infected, TB uninfected, TB/HIV co-infected and macrophage sputum samples). A digital Ultraviolet Visible Spectrophotometer (UV/VIS MetaSpecAE1405031Pro) was used in the measurements. The measurements of absorbance and transmittance were done at Bioengineering Labouratory of the department of Mechanical Engineering, NnamdiAzikiwe University, Awka. The absorbance values of the samples were measured over a range of wavelength spanning between 230 and 950 Å. The data collected were used in calculating the Hamaker coefficients using the Lifshitz formula. Fig. 3 shows an interesting pattern for M-TB positive sputum. The absorbance of the individual twenty M-TB infected sputum samples steeply increased as the wavelength increased until a critical wavelength of 320Å, where the peak value was attained. A further increase in the wavelength saw at first a sudden and latter a gradual decrease in the absorbance values. This peak value falls within the visible range of ultraviolet radiation which is between 300 -600Å.

A. Results
The peak values of absorbance range between 0.2918 and 0.7877 (0.2918 ≤ ā ≤ 0.7877). These values are listed for each sample in Table I. It is interesting though, that at the lower wavelengths of between 230-290Å some negative absorbance values were recorded.  Fig. 4 shows a similar pattern as that of Fig. 3 with the peak value occurring at the wavelength of 320Å which corresponds exactly with that of Fig. 3. However, the peak absorbance values are of the range 0.0206 and 0.0736 (0.0206 ≤ ā ≤ 0.0736). It is interesting though, that at the lower wavelengths of between 230 -260Å some negative absorbance values were recorded (see Table I). Fig. 5 reveals an interesting pattern for M-TB/HIV positive Sputum. The absorbance of the respective twenty M-TB/HIV co-infectious sputum samples systematically increased as the wavelength increased until a critical wavelength of 290Å, where a peak value was accomplished. A further increase in the wavelength saw at first a steady decrease in absorbance until a minimum was attained. As wavelength increases, a progressive increase in absorbance values was recorded and latter a gradual decrease follows. These peak values of absorbance fall within the visible range of the ultraviolet radiation which is between 300 -600Å. The peak values of absorbance range between 0.0231 and 0.0498 (0.0231≤ ā ≤ 0.0498) (see Table I) except sample 17 which showed a steady increase as wavelength increased until 410Å and steeply decreased as wavelength increased. The value of absorbance recorded is obviously a faulty one, this could be explained against the possibility of some experimental error or as a result of some sputum related disease conditions like diabetes, Hepatitis etc. it is interesting though, that at the lower wavelengths of between 230-260Å some negative absorbance values were recorded.  Table I). Sample 15 showed a marked departure in its response from the rest until the wavelength of 560Å and latter decreased systematically as wavelength increased. The continuous increase and latter decrease in the absorbance value recorded is clearly a defective one. This could be explained against the possibility of some experimental or machine error or as a result of some disease related conditions like diabetes, Hepatitis etc.
The peak value of the absorbance for M-TB negative sputum of Fig. 7 was obtained at the wavelength of 320Å and ranges as 0.2657 ≤ ā ≤ 1.2501 (see Table I). The reaction here also follows the earlier patterns with the various twenty samples showing moderately conformed characteristics. An exception to the rule is found with sample 19 which showed a drop down decrease from the pattern exhibited by the rest of the samples. This again could be explained against machine error.  Table  I).

B. Comparison between the Peak Absorbance Values of M-TB Positive, M-TB/HIV Positive and Negative Sputum Components
From results presented in Figs. 3-8 summarized in Table I; it could be seen that the peak absorbance values of the various sputum samples and components vary in magnitude revealing the notable effect of the bacteria on them. The comparison between the positive and negative samples of the macrophages is imperative to this research. This is because Mycobacterium Tuberculosis actually attacks the macrophages by attaching itself to the macrophage cells. Table I reveals also the degree of variation between similar infected and uninfected sputum components at a glance for a clearer understanding.   Table I

C. Computation of Absolute Hamaker Coefficients
To be able to use the absorbance data to calculate the Hamaker coefficients using the Lifshitz theorem of (10), there is a need to evaluate the dielectric constant of the equation. Some relevant equations are required as presented below.From the information of light absorbance, reflection and transmittance, it could be seen that; ā + T + R = 1 (13) where; ā is absorbance, T is transmittance, and R is reflectance. Also, from the information of light absorbance and transmittance; With the values of ā determined from absorbance experimental results, and substituting the values of ā into (14) to obtain T, R could easily be derived by substituting the values of ā and T into (13).
To find a value for the refractive index, n employing the mathematical relation [21]; A value for the extinction coefficient, k is obtained from; where;  is the absorption coefficient defined as follows; Substituting the value, of (17) into (16); The dielectric constant, ε could thus be given by the formula [22] For the real part; (19) For the imaginary part; 2 (20) With these values, it is possible to determine using the relevant equations.
Equation (10) was used to obtain for each interacting system, by approximate change of variables. MATLAB computation tools were used. This involved the numerical integration of (10) for each wavelength from 230 to 950 for all the twenty samples in each category. The results are given on Table II. A 33 , which serves as the energy of sputum as an intervening medium, is seen in M-TB data to be reduced by infection from 0.4247x10 -21 J to 0.23067x10 -21 J by a factor of about 45.7%. In M-TB/HIV co-infection, the reduction is from 0.4247x10 -21 J to 0.28812x10 -21 J, a factor of about 32.2%. The reduction is lower in M-TB/HIV co-infection probably because of the interaction between HIV and TB. For the combined Hamaker coefficient, the value is 0.21631x10 -21 J for M-TB and 0.18825x10 -21 J for M-TB/HIV. This result is as expected. HIV has the tendency to reduce the energy on the surface of a given material, in this case by about 13%, conforming adverse effects observed in HIV patients with tuberculosis.
Note that the values of A 132 are all positive showing that attraction exists between the macrophage and the TB particles. The effect of the infection can only be abated if a drug, in the form of additive is added that can change the value of A 132 to negative under that condition, mutual repulsion will occur and it will be expected that, in principle, the TB bacteria will not attack the macrophage. were actually infected. The absolute Hamaker coefficient A 131 =0.10165x10 -21 Joule gives the interaction energy among the macrophage cells in the sputum while A 232 is the interaction energy among the TB particles in the sputum (i.e. A 232 is the energy of interaction among the TB particles or among the TB/HIV particles in sputum). A 232 for TB/HIV coinfection is less than that for TB alone. Reduction in energy in the presence of HIV confirms the adverse effect when TB and HIV occur simultaneously in a patient. Reduction in energy leads to reduction in CD4 in HIV patient and hence greater prospect for death. This is so since a positive Hamaker value for any interacting system implies an attraction between the interacting bodies or particles while a negative Hamaker coefficient means repulsive van der Waals forces hence the interacting bodies would repel each other.
This research concludes that there is a prospect of finding remedy for the M-TB/HIV pandemic if further work towards defining the conditions of the system that could render the absolute combined Hamaker coefficient negative and the additive(s) to the system (in form of drugs) as the intervening medium that could accomplish this condition. That, as expected, may be the much desired way out for drug resistant strains of the M-TB bacteria.