Electron Ionization Cross Section in relation to dosage of medicine-Antimicrobial drugs

Electron Ionization Cross Section in relation to dosage of medicine-Antimicrobial drugs By (1 S.Kavitha, 2 V.R. Murthy,,3 K.R.S. Samba Siva Rao)1(Research Scholar, Dept. of Biotechnology, Acharya Nagarjuna University, Guntur. Andhra Pradesh. India, 2(Prof.& Head, Dept. of Physics (P.G. Course), T.J.P.S. College, Guntur. Andhra Pradesh. India. (3 Prof. & Head, Dept. of Biotechnology, Acharya Nagarjuna University, Guntur. Andhra Pradesh. S.,*Corresponding author


Physical parameters such as molecular polarizability, diamagnetic susceptibility, and molecular electron ionisation cross section are important parameters bearing some dependence on the dosage of the medicine through the electron transfer of the medicine in the process of diagnosis. Hence they are analysed and used in calculating the dosage of few anti-microbial drugs, in particular Quinolones. Data collected on Plasma protein binding Bioavailability, Half-life period and Log P show dependence on Q and is expressed in the form of a mathematical equation. The dosage thus calculated by above parameters has a good agreement with the suggested dosage values. For example Ciprofloxacin has the reported dosage value1.0grms/day against the calculated dosage value 0.849grams /day. In case of other drug Lomefloxacin, the calculated value is 0.394 grams /day against the reported value 0.4 grams /day. Similar observation was done in case of other quinolones compounds also. The present method enables a new approach in finding out the drug activity and is preferred to the highly theoretical approaches involving quantum mechanical methods.

Key words: Dosage, Half Life Period, Electron Ionisation cross section.

Introduction: The quinolones are potent synthetic chemotherapeutic, broad-spectrum antibiotics 1, 2. Since the introduction of Nalidixic acid in 1962 3, 4 several structural modifications have resulted in second, third and fourth generation antibiotics. With the recent introduction of agents such as Gatifloxacin and Moxifloxacin, the traditional gram-negative coverage of fluroquinolones has been expanded to include specific gram positive organisms5.Community acquired pneumonia is the sixth leading cause of death in the United States. Even with optimal therapy, this illness is associated with mortality rates of approximately 15 percent.6

Therapeutic uses of fluoroquinolones include the following: 1) For serious acute cases of pyelonephritis or bacterial prostatis, where the patient may need to be hospitalised, fluoroquinolones such as Ciprofloxacin, 7oflaxacin, lomefloxacin, enofloxacin, levofloxacin and gatifloxacin are recommended.8 2) Due to excellent penetration into prostatic tissue, norfloxacin, levofloxacin,ciprofloxacin and iflaxacinhave eradication rates of 67 to 91%.9,7 3) The U.S.Food and drug administrationhas labelled gatifloxacin, moxifloxacin, sparfloxacin and levofloxacin for use in the treatment of acute sinusitis.10For severe forms of community aqured pneumonia , the fluroquinolones are associated with improved treatment rates.11 4) In case of sexually transmitted diseases, a single dose of ciprofloxacin or ofloxacin is considered as alternative treatment in for example patients with pencillin allergy.12 5) Fluroquinolones in combination with other drugs such as ofloxacin plus metronidazole or Cefoxitin and ciprofloxacin plus clindamycin 7,10 are used to relieve pelvic inflammatory, Diabetic food infections etc. Norfloxacin or ciprofloxacin are used in the treatment of traveller’s diarrhea and certain other infections such as typhoid fever and Vibrio cholera. Adverse events: Although quinolones are well tolerated and relatively safe, certain adverse effects are 13, 14 common. Gastro intestinal and Central nervous system 15,16 effects are the most frequent adverse events occurring in 2 to 20 per cent of patients 17-22.Other adverse effects such as QTC prolongation, 23,24 hepatotoxicity, tendon rupture, cardiovascular toxicity, disturbed blood glucose levels 25,26 certain dermatologic effects etc.

Mechanism of fluoroquinolones: Fluoroquinolones interfere with bacterial DNA metabolism by the inhibition of two enzymes, Topoisomerase II (Syn. DNA gyrase) and Topoisomerase IV. In gram-negative organisms DNA gyrase is the primary target, where as in Gram -positive bacteria topoisomerase IV was recently found to be most affected. The function of DNA gyrase is to introduce supercoils into the linear DNA double helix, which results in the highly condensed three dimensional structure of the DNA usually present inside the cell. The function of topoisomerase IV is involved in the separation process of the DNA daughter chains after chromosome duplication. DNA gyrase and Topoisomerase IV have a very similar protein structure, each composed of two sub units(Gyr-A and gyr-B). The Gyr-A subunits of this enzyme were proposed to initially bind to the double stranded DNA helix. In an ATP-dependent process, described as intermediate gate opening step-, both DNA strands are leaved at certain 4 base pair staggered sites. The 5’ends of the DNA chain are thereby bound covalently to Tyrosine 122 residues with in the Gyr-A-subunits. Gyr-B-subunits are probably responsible for the ATP-dependent releasing process of the DNA. Two quinolones molecules self-assemble inside the pocket in dimer structure 27 and attach to the gyrase -DNA complex electrostatically, which stabilizes the intermediate stage of this reaction step. Permanent gaps in the DNA strands induce synthesis of repair enzymes (exonucleases) initiating uncoordinated repair process, which results in irreversible damage to the DNA and, finally, cell death. 28, 29

Methodology: A knowledge of Molecular polarizability, diamagnetic susceptibility, Molecular electron ionisation cross section reflects on transport mobility, activity and the vigour of the electron associate with the interaction of the medicine with the electrons released from host cell(or effected cell) of the body during the reaction .Hence an investigation of these properties leading to the dosage of the few anti-microbial drugs (Quinolones) is taken up in the present investigation. The above parameters are obtained through quantum mechanical approach of Lippincott, Bond Polorizability and Bond Refractivity of Le Fevre. The diamagnetic susceptibility for these systems is evaluated using Rao &Murthy’s method. The molecular electron ionization cross section is then evaluated from diamagnetic susceptibility using modified Kevan’s formula of Murthy et al. The electron ionization cross section along with the data of Protein binding, Bioavailability, Log P,& Half-life are taken from Wikipedia are used in the present investigation.30 The related work of drug dosage activity through molecular electron ionization cross- section and medical parameters like bioavailability, protein binding etc., has been reported by Murthy et al in a few medicinal systems. 31, 32, 33 The present paper deals with the evaluation of dosages of a few anti-microbial drugs (Quinolones). The information regarding the Molecular polarizability obtained by Lippincott method, Bond polarizability and Bond refractivity, diamagnetic susceptibility and molecular electron ionisation cross section was given in already accepted previous papers31, 32, 33, 34

?aP = 4nA/ao [(R2/4) + (1/2(CR)2)]2 x e-(XA-XB)2/4 (1)

?an = ? fj aj (2)

? 2 a- = n df ?2j/?j2 (3)

aM=1/3[?aP+? a n +? 2 a-] (4)

aM=?[3/4pN?](R8) (5)

aM= n1 a(c=c) + n2 a(c-c) +———– ——–=Ojnjaj (6)

?M = ? m s1aM (7)

Q (in 10-16cm2)=0.278n ?M ( 8)

Molecular polarizablility can be calculated by Lippincott method, Bond refraction method and Bond polarizability method. The aM by Lippincott method is evaluated with help of parallel component (?a?p), Perpendicular component (?2a-) and ?a?n .The parallel Component?a?p, is based on parameters i.e. A, CR, ao are taken from Lippincott35 are given in the equation(1).The values of bond lengths required for evaluating?a?p are taken from CRC Hand book of Physics and Chemistry.36 Similarly the perpendicular component is given in the equation(3).The electronegativity and atomic polarizability values are taken from the reference.36Thus calculated ?a?p, ?a?n and ?2a- are given in table I. Finally from these values aM is measured by the formula (4). Molecular polarizabilty obtained by other methods i.e Bond polarizablity and Bond refraction methods are given table II. The values needed to calculate the mean molecular polarizabilty -aM’ from Bond refractivities and Bond polarizabiltes are taken from Le Fevre37.and expressed in 10-25cm3.

The diamagnetic susceptibility -?M’ is calculated with the help of equation 7. The -aM’ values obtained by three methods i.e. Lippincott, Bond polarizablity and Bond refraction are inserted in the given equation which gives the ?M. The necessary data required for the calculation of -s’ Covalency factor taken from reference. 38

The covalency factor is calculated as s=[s1 1/n1. s2 1/n2——–s n 1/n8-]1/2 (9) s=e-(XA-XB)2/4 Where XA and XB are electronegativity of the bond A- B respectively and n1, n2 are the bond orders. Calculation of ?M is immediately followed by -Q’, Electron ionisation cross section which only needs the ?M value. The ?M and -Q’ values obtained by Lippincott Bond polarizablity and Bond refraction are shown in the table III. Practical approach for diamagnetic susceptibility through vibrational magnetometer technique is under progress. Of the three methods -Q’ obtained by Bond polarizablities are taken as standard because, this method is found to be sensitive to conformational changes than the other two methods. In table IV, the calculated values of Electron ionisation cross section -Q’ along with other medicinal parameters are given. These include Protein binding, Bioavailability, Log P and Half life period of some anti-microbial (Quinolones). The data required are taken from Wikepedia30. By calculating the -Q’, an attempt has been done in studying the activity of a drug and further its interaction with the target molecule. Finally with the help of the expression 10, dosage of antimicrobial drugs is calculated and compared with the reported dosage values taken from reference 30. The results are given in the table V.

=((Q/D)2/3LLogP) va/5 (10)

Where, Q – Electron ionisation cross section D-Dosage of the drug L- is the Half-life period Log P -Hydrophobicity a= (PB)(BA)/6ms

Where, m – the no.of unsaturation bonds PB -Protein binding BA-Bioavailabilty s- the Covalency factor

Results and Discussion: A keen observation of the dosages of the medicinal compounds calculated and reported show he following features. The calculated dosage of Prefloxacin is 0.825 grams per day against the reported dosage value 0.8grams per day. Similarly Lomefloxacin and Sparfloxacin has the calculated value 0.394 grams per day and 0.211 grams per day compared with the reported dosage value0.4 grams and 0.222grams per day. Good agreement regarding the dosage values were observed in case of other medicinal compounds also. An analytical approach on Q and medicinal parameters reveal some observations .Generally the medicinal compounds having similarity in their structure are analysed. In case of Quinolones (Antimicrobial drugs) ,Prefloxacin has the -Q’valuei.e3.03×10-16 cm2 less than Lomefloxacin Q value11. 27×10-16 cm2 But increased half-life period 8.6hrs than half life period of Lomefloxacin 3 to 5 hrs. Similarly for Nalidixic acid the half life is 1.1to2.5hrsless than the Ciprofloxacin h alflife period i.e.3 to 4 hrs. Compared to the -Q’ values of Nalidixic acid (12.23×10-16 cm2) and Norfloxacin (8.33×10-16 cm2). An attempt has been made in analysing the relation between Log P (Hydrophobicity) and ‘Q’ Electron ionization cross section. The hydrophobicity of Sparfloxacin is2.5 compared with the hydrophobicity value of Moxifloxcin 2.9 against the -Q’ value Sparfloxacin11.806×10-16 cm2 and Moxifloxacin 9.459 x10-16 cm2. Similar observations is done in case of Prefloxacin and Lomefloxacin. From the above data it is hypothesized that lower the hydrophobic nature of the drug higher may be the interaction of the drug with the target molecule and finally the activity of drug molecule i.e. Electron ionization cross section. Comparison of -Q’, Electron ionisation cross section value and the dosage value reflect some useful and supporting view to the above analysis. In case of Sparfloxacin Q value ( 11.806×10-16 cm2). The reported dosage value is0.22grams per day againt the lower Moxifloxacin Q value 9.459 x10-16 cm2 and higher dosage value 0.4grams per day respectively. Similarly Lomefloxacin (Q value11. 27×10-16 cm2) has 0.4grmas per day to Prefloxacin (Q’valueless than Lomefloxacin i.e3.03×10-16 cm2) dosage value 0.8 grams per day. Rigorous work is under study in order to understand the relation between -Q’, dosage and other medicinal parameters of other medicinal compounds.

A plausible explanation for this behaviour may be given as follows. An increase in electron transportation activity reflected by higher electron ionization cross section will tender the chemical reaction to be faster. Hence an incidence of electron from the donor to the place of malignity will make the process curing faster. Thus very little dosage of the medicine will be sufficient. A long continued impingement of the electrons on the malgn cells might develop saturation effects. Hence the life time of the drug for limited time suggested. Thus an increase in Q explains lower half life and lower dosage. A continued dosage of such medicine might result in undesirable toxic effects. Rigorous work is under study in order to understand the relation between -Q’, dosage and other medicinal parameters of other medicinal compounds.

Inference: The present method hints at study of important physical parameters like refractivity and electron ionization cross section through simple molecular structure. An elucidation of Q and its use with other medicinal parameters yield a new method of obtaining medicinal dosage. Thus the present method of arriving at medicinal dosage through physical parameters n, k ,Q give a novel approach of equation of dosage and looking at it from molecular level of interactions. This approach has the superiority over the already available sophisticated medicinal methods which involve highly theoretical quantum mechanical modelling, highly computive modelling or highly sophisticated physicochemical methods of drug analysis.

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TABLE-1 Molecular Polarizabilities of Anti-microbial drugs(Quinolones) by Lippincott method in 10-25cm3

S.NoName of the drug?a?p?a?n?2a- 1Nalidixic acid469.19117.784231.208 2Norfloxacin645.04924.96346.985 3Ciprofloxacin691.86624.956272.072 4Sparfloxacin768.94024.956272.072 5Moxifloxacin862.9924.703329.746 6Prefloxacin680.24320.756306.652 7Lomefloxacin687.93520.756269.383

TABLE-II Molecular Polarozablities (aM) in 10-25cm3 S. NoName of the drugaM by Lippincott methodaM by Bond PolarizablityaM by Bond Refraction 1Nalidixic acid231.208266.244247.319 2Norfloxacin315.907346.985333.101 3Ciprofloxacin329.631366.252342.97 4Sparfloxacin385.709383.183378.339 5Moxifloxacin405.814423.115421.671 6Prefloxacin335.894354.352352.635 7Lomefloxacin326.025347.852347.166

TABLE-III The Diamagnetic Susceptibilities (in 106CGS units) and Molecular Electron Ionisation cross section (in10-16cm2)of certain Anti-microbial drugs(Quinolones) ? M in 106CGS units Qin10-16cm2 S.NoName of the drugByByByByByBy LippincottBond PolarizabilityBondLippincottBond PolarizabilityBond Refraction method Refractionmethod 1Nalidixic acid56.41764.96760.3411.43313.16612.23 2Norfloxacin38.98942.82541.1127.9028.6798.332 3Ciprofloxacin65.82373.14668.49512.3414.82413.881 4Sparfloxacin59.39959.10158.25612.03811.97811.806 5Moxifloxacin44.9246.83546.6779.1049.4929.46 6Prefloxacin14.25415.03814.9642.8893.0483.033 7Lomefloxacin53.85155.74855.63810.91411.29511.276

TABLE-IV Electron Ionisation cross section (in10-16cm2 ) and other medicinal parameters

S.NoName of the drugQ PB BALog PHalf Life(hrs) 1Nalidixic acid12.23093962.11.1-2.51.383 2Norfloxacin8.33215502.13-41.1383 3Ciprofloxacin13.88130502.53-51.176 4Sparfloxacin11.80650502.5201.272 5Moxifloxacin9.45986-92402.9121.477 6Prefloxacin3.033251002.48.61.450 7Lomefloxacin11.2760.725502.13-51.335

TABLE-V Drug dosage (in grams/day) S. NoName of the druga’Calculated dosages grams/dayReported dosages grams/day 1Nalidixic acid0.0951.3834.0334.0 2Norfloxacin0.0091.1380.6510.80 3Ciprofloxacin0.0131.1790.8491.0 4Sparfloxacin0.0261.2730.2110.222 5Moxifloxacin0.0491.4750.4090.40 6Prefloxacin0.0691.4490.8250.8 7Lomefloxacin0.0371.3350.3940.4