**9. Calculation of the t1/2 values for the cleavage reactions of atenolol prodrugs ProD 1-2**

The effective molarity (EM) parameter is a commonly tool used to predict the efficiency of intramolecular reactions when bringing two functional groups such as an electrophile and a nucleophile in a close proximity. Intramolecularity is usually measured by the effective molarity parameter. The effective molarity is defined as the rate ratio (kintra/kinter) for corre‐ sponding intramolecular and intermolecular processes driven by identical mechanisms. Ring size, solvent and reaction type are the major factors affecting the EM value. Ring-closing reactions *via* intramolecular nucleophilic addition are much more efficient than intramolecular proton transfer reactions. EM values in the order of 109 -1013 M were determined for intramo‐ lecular processes occurring through nucleophilic addition. Whereas for proton transfer processes values of less than 10 M were measured for proton transfer processes until recently where values of 1010 was documented by Kirby on the hydrolysis of some enzyme models [60,78-84].

For obtaining the EM values for processes **34**-**42** and atenolol **ProD1**-**2** the kinetic and ther‐ modynamic parameters for their corresponding intermolecular process, **Inter** (Figure 8) were calculated.

Using equations 1-4, equation 5 was derived, and describes the EM term as a function of the difference in the activation energies of the intra-and the corresponding inter-molecular processes. The calculated EM values for processes **34**-**42** and **ProD 1**-**2** were calculated using equation 5.

$$\mathbf{EM} = \mathbf{k}\_{\mathrm{intra}} / \mathbf{k}\_{\mathrm{inter}} \tag{1}$$

$$
\Delta \mathbf{G}^{\ddagger}\_{\text{inter}} = \text{-RT } \ln \mathbf{k}\_{\text{inter}} \tag{2}
$$

$$
\Delta \mathbf{G}^{\ddagger}\_{\text{intra}} = \text{-RT } \ln \mathbf{k}\_{\text{intra}} \tag{3}
$$

$$
\Delta \mathbf{G}^{\ddagger}\_{\text{intra}} \text{ - } \Delta \mathbf{G}^{\ddagger}\_{\text{inter}} = \text{-RT } \ln \mathbf{k}\_{\text{intra}} / \mathbf{k}\_{\text{inter}} \tag{4}
$$

$$\text{Min EM} = \left\langle \Delta \mathbf{G}^{\ddagger}\_{\text{intra}} \cdot \Delta \mathbf{G}^{\ddagger}\_{\text{inter}} \right\rangle \text{/RT} \tag{5}$$

Where T is the temperature in Kelvin and R is the gas constant.

#### **Figure 8.** Acid catalyzed hydrolysis for process **Inter**.

**O**

of the phenolic group in paracetamol with the bitter taste receptors. Similarly, it is expected that blocking the amine group in atenolol with a suitable linker might inhibit the hydrogen bonding between the amine group in atenolol and its bitter taste receptors and hence masking

The proposed atenolol prodrugs, atenolol **ProD 1** and atenolol **ProD 2**, have a hydroxyl and carboxylic acid groups (hydrophilic moiety) and the rest of the prodrug molecule is a lipophilic moiety (Figure 7), where the combination of both groups ensures a moderate hydrophilic

It is worth noting that the HLB value of atenolol prodrug will be largely determined on the pH of the physiological environment by which the prodrug is exposed to. For example, in the stomach pH, the atenolol prodrugs, **ProD 1** and **ProD 2,** will exist in the free carboxylic acid form whereas in the blood circulation the carboxylate form will be dominant. It was planned that atenolol **ProD 1**-**ProD 2** (Figure 7) will be formulated as sodium salts since the carboxylate form is expected to be quite stable in neutral aqueous medium. However, upon dissolution in the stomach (pH less than 3) the proposed prodrugs will exist mainly as a carboxylic acid form

**H2O**

**H2O**

**O**

**H**

**Atenolol**

**Atenolol**

**H**

**H**

**Me**

**O**

**O**

**Maleic anhydride**

**O**

**O**

**O**

**Methylmaleic anhydride**

the drug's bitterness [132].

418 Application of Nanotechnology in Drug Delivery

lipophilic balance (HLB).

**N**

**OH**

**O N**

**O**

**prodrugs ProD 1-2**

**OH**

**Atenolol ProD 2**

**Me Me OH O**

**Atenolol ProD 1**

**Me Me OH O**

**O**

**H**

**Me**

**H**

**H**

**O**thus enabling the acid-catalyzed hydrolysis to commence.

**O**

**NH2**

**NH2**

**9. Calculation of the t1/2 values for the cleavage reactions of atenolol**

The effective molarity (EM) parameter is a commonly tool used to predict the efficiency of intramolecular reactions when bringing two functional groups such as an electrophile and a nucleophile in a close proximity. Intramolecularity is usually measured by the effective

**O**

**Figure 7.** Acid-catalyzed hydrolysis for atemolol ProD 1 and atenolol ProD 2.

The calculated EM values from eq. 5 for processes**34**-**38** were correlated with the corresponding EM values [101] (Figure 9a). Good correlation with a correlation coefficient of r=was obtained. The correlation results demonstrate that processes **35** and **37**werethe most efficient among **34**-**38**, whereas process **4** was the least. The discrepancy in the rates of processes **35** and **38**on one hand and process **37** on the other hand is might be attributed to strain effects.

In addition, for further support to the credibility of our DFT calculations the calculated free activation energies (∆GBW‡ ) were correlated with the corresponding experimental free activa‐ tion energies (Exp ∆G‡ ). Good correlation was obtained with R value of 0.96 (Figure 9b).

Utilizing eq. 6 obtained from the correlation of log krelvs. ∆G‡ and the experimental t1/2 value measured for process **2** (t1/2=1 second) [103], the t1/2 values for atenolol **ProD 1** and atenolol **ProD 2** at pH 2 were calculated and their values were65.3 hours and 11.8 minutes, respectively.

$$
\log k\_{rel} = -0.44\,\Lambda G^\ddagger + 13.53\tag{6}
$$

**Figure 9.** (a) log calculated effective molarity vs. experimental effective molarity for processes **34-38**. (b) DFT calculat‐

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ed activation energy (kcal/mol) vs. experimental activation energy (kcal/mol) for processes **34-38**.

**Figure 10.** First order hydrolysis plot of atenolol **ProD 1** in (a) 1N HCl, (b) buffer pH 2 and (c) buffer pH 5.

#### **10. In vitro intraconversion of atenolol ProD 1 to the parent drug atenolol**

Kinetics of the acid-catalyzed hydrolysis for atenolol **ProD 1** was carried out in an aqueous buffer in a similar manner to that done by Kirby on N-alkylmaleamic acids **34**-**38**. This is in order to examine whether atenolol prodrug is hydrolyzed in aqueous medium and to what extent, suggesting its fate in the system. Acid-catalyzed hydrolysis of atenolol **ProD 1** was investigated in four different aqueous media: 1 N HCl and buffers pH 2, pH 5 and pH 7.4. Under the experimental conditions, atenolol **ProD 1** was hydrolyzed to release the parent drug, atenolol, (Figure 10) as was evident by HPLC measurements. At constant pH and temperature, the reaction displayed strict first order kinetics as the *k*obs was fairly constant and a straight line was obtained on plotting log concentration of residual atenolol prodrug verses time. The rate constant (*k*obs) and the corresponding half-lives (t1/2) for atenolol prodrug **ProD 1** in the different media were calculated from the linear regression equation correlating the log concentration of the residual prodrug verses time. The kinetic data, *k*obs and t1/2 values, are listed in Table 1. 1N HCl, pH 2 and pH 5 were selected to examine the intraconversion of atenolol **ProD 1**in pH as of stomach, because the mean fasting stomach pH of adult is approximately 1-2 and increases up to 5 following ingestion of food. In addition, buffer pH 5 mimics the beginning of the small intestine environment. The medium at pH 7.4 was selected to examine the intraconversion of the tested prodrug in the blood circulation system. Acid-catalyzed hydrolysis of atenolol **ProD 1** was found to be higher in 1N HCl than at pH 2 and 5 (Figure 10). At 1N HCl atenolol **ProD 1** was intraconverted to release the parent drug in 2.53 hour. On the other hand, at pH 7.4, the prodrug was entirely stable and no release of the parent drug was observed. Since the *pKa* of the carboxylic group of atenolol **ProD1** is in the range of 3-4, it is expected at pH 5 the anionic form of the prodrug will be dominant and the percentage of the free acid form that expected to undergo hydrolysis will be relatively low. At 1N HCl and pH 2 most of the prodrug will exist as the free acid form, whereas at pH 7.4 most of the prodrug will be in the anionic form. Thus, the difference in rates at the different pH buffers.

The calculated EM values from eq. 5 for processes**34**-**38** were correlated with the corresponding EM values [101] (Figure 9a). Good correlation with a correlation coefficient of r=was obtained. The correlation results demonstrate that processes **35** and **37**werethe most efficient among **34**-**38**, whereas process **4** was the least. The discrepancy in the rates of processes **35** and **38**on

In addition, for further support to the credibility of our DFT calculations the calculated free

Utilizing eq. 6 obtained from the correlation of log krelvs. ∆G‡ and the experimental t1/2 value measured for process **2** (t1/2=1 second) [103], the t1/2 values for atenolol **ProD 1** and atenolol **ProD 2** at pH 2 were calculated and their values were65.3 hours and 11.8 minutes, respectively.

**10. In vitro intraconversion of atenolol ProD 1 to the parent drug atenolol**

Kinetics of the acid-catalyzed hydrolysis for atenolol **ProD 1** was carried out in an aqueous buffer in a similar manner to that done by Kirby on N-alkylmaleamic acids **34**-**38**. This is in order to examine whether atenolol prodrug is hydrolyzed in aqueous medium and to what extent, suggesting its fate in the system. Acid-catalyzed hydrolysis of atenolol **ProD 1** was investigated in four different aqueous media: 1 N HCl and buffers pH 2, pH 5 and pH 7.4. Under the experimental conditions, atenolol **ProD 1** was hydrolyzed to release the parent drug, atenolol, (Figure 10) as was evident by HPLC measurements. At constant pH and temperature, the reaction displayed strict first order kinetics as the *k*obs was fairly constant and a straight line was obtained on plotting log concentration of residual atenolol prodrug verses time. The rate constant (*k*obs) and the corresponding half-lives (t1/2) for atenolol prodrug **ProD 1** in the different media were calculated from the linear regression equation correlating the log concentration of the residual prodrug verses time. The kinetic data, *k*obs and t1/2 values, are listed in Table 1. 1N HCl, pH 2 and pH 5 were selected to examine the intraconversion of atenolol **ProD 1**in pH as of stomach, because the mean fasting stomach pH of adult is approximately 1-2 and increases up to 5 following ingestion of food. In addition, buffer pH 5 mimics the beginning of the small intestine environment. The medium at pH 7.4 was selected to examine the intraconversion of the tested prodrug in the blood circulation system. Acid-catalyzed hydrolysis of atenolol **ProD 1** was found to be higher in 1N HCl than at pH 2 and 5 (Figure 10). At 1N HCl atenolol **ProD 1** was intraconverted to release the parent drug in 2.53 hour. On the other hand, at pH 7.4, the prodrug was entirely stable and no release of the parent drug was observed. Since the *pKa* of the carboxylic group of atenolol **ProD1** is in the range of 3-4, it is expected at pH 5 the anionic form of the prodrug will be dominant and the percentage of the free acid form that expected to undergo hydrolysis will be relatively low. At 1N HCl and pH 2 most of the prodrug will exist as the free acid form, whereas at pH 7.4 most of the prodrug will be in the anionic form.

Thus, the difference in rates at the different pH buffers.

) were correlated with the corresponding experimental free activa‐

‡ *log k* 0.44 13.53 *rel* =- D + *G* (6)

). Good correlation was obtained with R value of 0.96 (Figure 9b).

one hand and process **37** on the other hand is might be attributed to strain effects.

activation energies (∆GBW‡

420 Application of Nanotechnology in Drug Delivery

tion energies (Exp ∆G‡

**Figure 9.** (a) log calculated effective molarity vs. experimental effective molarity for processes **34-38**. (b) DFT calculat‐ ed activation energy (kcal/mol) vs. experimental activation energy (kcal/mol) for processes **34-38**.

**Figure 10.** First order hydrolysis plot of atenolol **ProD 1** in (a) 1N HCl, (b) buffer pH 2 and (c) buffer pH 5.


from the intestinal tract, better capacity for reaching effective concentrations at the sites of action and a more rapid capacity for penetrating the cellular wall of Gram-negative microor‐ ganisms. Amino-penicillins are frequently prescribed agents for the oral treatment of lower respiratory tract infections and are generally highly effective against S. pneumonia and nonβ-lactamase-producing H. influenza. Amoxicillin is mostly common antibiotics prescribed for children. It has high absorption after oral administration which is not altered and affected by the presence of food. Amoxicillin dose reaches Cmax about 2 hours after administration and is quickly distributed and eliminated by excretion in urine (about 60%-75%). The antibacterial effect of amoxicillin is extended by the presence of a benzyl ring in the side chain. Because amoxicillin is susceptible to degradation by β-lactamase-producing bacteria, which are resistant to a broad spectrum of β-lactam antibiotics, such as penicillin, for this reason, it is often combined with clavulanic acid, a β-lactamase inhibitor. This increases effectiveness by reducing its susceptibility to β-lactamase resistance. Amoxicillin has two ionizable groups in the physiological range (the amino group in α-position to the amide carbonyl group and the carboxyl group). Amoxicillin has a good pharmacokinetics profile with bioavailability of 95% if taken orally, its half-life is 61.3 minutes and it is excreted by the renal and less than 30 % bio-

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Cephalexin is a first-generation cephalosporin antibiotic, which was chosen as the model drug candidate to obtain dosage with improved stability, palatability and attractive pediatric elegance, cost effective with ease of administration. Cephalosporins are the most widely used for treatment of skin infections because of their safety profile, and their wide range of activity against both gram positive and gram negative microorganism. Cephalexin is also used for the treatment of articular infections as a rational first-line treatment for cellulitis, it is a useful alternative to penicillins hypersensitivity, and thought to be safe in a patient with penicillin allergy but caution should always be taken, that's because cephalexin and other first-genera‐ tion cephalosporins are known to have a modest cross-allergy in patients with penicillin hypersensitivity. In addition, cephalexin is also effective and used in the treatment of group A β-hemolytic streptococcal throat infections. Cephalexin works by interfering with the bacter‐ ia's cell wall formation, causing it to rupture, and thus killing the bacteria. The compound is zwitterionbywhichitcontainsbothabasicandanacidicgroup,theisoelectricpointofcephalexin in water is approximately 4.5 to 5. Cephalexin has a good pharmacokinetic profile by which it is well absorbed, 80% excreted unchanged in urine within 6 hours of administration. Cephalex‐ in'shalf-life is0.5-1.2hoursanditis excreted*via* the renal.Itisusedforthe treatmentofinfections includingotitismedia,streptococcalpharyngitis,boneandjointinfections,pneumonia,cellulitis

and UTI, and so it may be used to prevent bacterial endocarditis [142-145].

Cefuroxime axetil is a semi-synthetic, broad-spectrum cephalosporin antibiotic for oral administration. Cefuroxime axetil is an orally active antibacterial agent though its absorption is incomplete. The range of its bioavailability is 25-52%. The axetil moiety is metabolized to acetaldehyde and acetic acid. Peak plasma concentration is reached 2-3 hours after an oral

transformed in the liver [140-142].

**11.2. Cephalexin**

**11.3. Cefuroxime axetil**

In 1N HCl and at pH 2, 5 and 7.4

**Table 1.** The observed k value and t1/2 of atenolol **ProD 1**
