For the following drug molecule fragments, chemists are attempting to improve their properties in specific aspects by optimizing the side chain group $R$:

- Drug molecule 1: Increase lipophilicity

<MultiModal>![SMILES：CC(C)(NCC(O[R])COC1=NSN=C1N2CCOCC2)C](/media/uploads/2676f3dc-70b3-4bc1-adb4-0a8a9f4ad9b8.png)</MultiModal>

- Drug molecule 2: Increase lipophilicity

<MultiModal>![SMILES：CCCC(C(O[R])=O)NC(C)C(N1C(C(O)=O)CCC1)=O](/media/uploads/596cdf91-8ee0-47b8-a366-fad077d25259.png)</MultiModal>

- Drug molecule 3: Increase water solubility

<MultiModal>![SMILES：C[C@]12[C@@]([C@H](OC(C3=CC=CC=C3)=O)[C@]4(O)C[C@H](OC([C@@H]([C@H](C5=CC=CC=C5)NC(C6=CC=CC=C6)=O)[R])=O)CC(C4(C)C)[C@@H](OC(C)=O)C2=O)([H])[C@@](CO7)(OC(C)=O)[C@H]7C[C@@H]1O](/media/uploads/1f0e2e31-8f8c-4bbc-bc91-94577988b230.png)</MultiModal>

- Drug molecule 4: Increase specificity for the site of action:

<MultiModal>![CC12CCC(=O)C=C2CCC3C4CC[C@](C(=O)C[R])(C4(C)CC(=O)C31)O](/media/uploads/12986ddf-ce98-4cb9-ad4d-68065d8309a8.png)</MultiModal>

From the following numbered side chain groups, find the groups that can achieve specific property improvements (each side chain group corresponds to one and only one drug molecule fragment, and one drug molecule fragment may correspond to multiple side chain groups). The number of each side chain group is marked below, where $R$ represents the position connected to the drug molecule fragment:

<MultiModal>![SMILES从1到5依此为：CCCC([R])=O、[R]OC(OCC(O)=O)=O、O[C@H]1[C@@H](CO)O[C@@H](O[R])[C@H](O)[C@H]1O、CC[R]、[R]CC1=CC=CC=[N+]1C.CC(=O)[O-]](/media/uploads/9aa607dc-40fb-409c-9a9c-b3bd1edebfac.png)</MultiModal>

Let the sequence of drug molecule numbers be $a_{1\sim 4}$, and the sequence of side chain group numbers be $b_{1\sim 5}$. Calculate $x_{ij} =\dfrac{a_i}{b_j}$ for each pairing relationship, and further calculate the sum of all $x_{ij}$ as $z$. Select the correct value of $z$.
对于以下药物分子片段，化学家试图通过优化侧链基团 $R$ ，以改善其在特定方面的性质：

- 药物分子 1：增加脂溶性

<MultiModal>![SMILES：CC(C)(NCC(O[R])COC1=NSN=C1N2CCOCC2)C](/media/uploads/2676f3dc-70b3-4bc1-adb4-0a8a9f4ad9b8.png)</MultiModal>

- 药物分子  2：增加脂溶性

<MultiModal>![SMILES：CCCC(C(O[R])=O)NC(C)C(N1C(C(O)=O)CCC1)=O](/media/uploads/596cdf91-8ee0-47b8-a366-fad077d25259.png)</MultiModal>

- 药物分子  3：增加水溶性

<MultiModal>![SMILES：C[C@]12[C@@]([C@H](OC(C3=CC=CC=C3)=O)[C@]4(O)C[C@H](OC([C@@H]([C@H](C5=CC=CC=C5)NC(C6=CC=CC=C6)=O)[R])=O)CC(C4(C)C)[C@@H](OC(C)=O)C2=O)([H])[C@@](CO7)(OC(C)=O)[C@H]7C[C@@H]1O](/media/uploads/1f0e2e31-8f8c-4bbc-bc91-94577988b230.png)</MultiModal>

- 药物分子 4：提高作用部位特异性：

<MultiModal>![CC12CCC(=O)C=C2CCC3C4CC[C@](C(=O)C[R])(C4(C)CC(=O)C31)O](/media/uploads/12986ddf-ce98-4cb9-ad4d-68065d8309a8.png)</MultiModal>

请从以下编号的侧链基团中，找出能够实现特定性质改善的基团（每个侧链基团对应且只对应一个药物分子片段，一个药物分子片段可能对应多个侧链基团），每个侧链基团的编号在下方标出，其中 $R$ 表示与药物分子片段相连的位置：

<MultiModal>![SMILES从1到5依此为：CCCC([R])=O、[R]OC(OCC(O)=O)=O、O[C@H]1[C@@H](CO)O[C@@H](O[R])[C@H](O)[C@H]1O、CC[R]、[R]CC1=CC=CC=[N+]1C.CC(=O)[O-]](/media/uploads/9aa607dc-40fb-409c-9a9c-b3bd1edebfac.png)</MultiModal>

记药物分子编号的序列为 $a_{1\sim 4}$，侧链基团编号序列为 $b_{1\sim 5}$，计算每对配对关系的 $x_{ij} =\dfrac{a_i}{b_j}$，进一步计算所有 $x_{ij}$ 加和 $z$，选择正确的 $z$ 值。
4.68
4.77
4.93
5.05
5.68
6.53
6.93
None of the above options are accurate
4.68
4.77
4.93
5.05
5.68
6.53
6.93
以上选项均不准确
Match the drug molecular fragments with the side chain groups as follows:

Drug Molecules 1 & 2: Increase lipophilicity, typically achieved by introducing nonpolar hydrocarbon chains or esterifying to mask polar groups (e.g., -OH or -COOH).

<Checkpoint>[Increasing lipophilicity requires masking polar groups](0.5)</Checkpoint>

Side chain 1 (butyryl) and side chain 4 (ethyl) are both nonpolar groups that effectively increase lipophilicity. Side chain 1 (butyryl) can acylate hydroxyl groups to form esters, while side chain 4 (ethyl) can esterify carboxyl groups to form esters.

<Checkpoint>[Side chain 1 (butyryl) and side chain 4 (ethyl) increase lipophilicity](0.5)</Checkpoint>

The $R$ group of Drug Molecule 2 is attached to a carboxyl group ($\mathrm{-COOH}$). Converting it to an ethyl ester (attaching side chain 4) is a classic method in medicinal chemistry to enhance lipophilicity and oral bioavailability. Therefore, Molecule 2–Side Chain 4 is a reasonable match.

<Checkpoint>[Molecule 2 matches with Side Chain 4](1)</Checkpoint>

The $R$ group of Drug Molecule 1 is attached to a hydroxyl group (-OH). Esterification (attaching side chain 1) can also effectively mask polarity and increase lipophilicity. Therefore, Molecule 1–Side Chain 1 is a reasonable match.

<Checkpoint>[Molecule 1 matches with Side Chain 1](1)</Checkpoint>

Drug Molecule 3: Increase water solubility. For a very large and highly lipophilic molecule (a paclitaxel analog), strongly polar, ionizable, or charged groups need to be introduced to significantly increase its water solubility.

Side chain 2 (containing carboxyl), side chain 3 (glucose), and side chain 5 (quaternary ammonium salt) are all polar or charged groups that increase water solubility. According to the given information, "each side chain group corresponds to and only corresponds to one drug molecular fragment, while a drug molecular fragment may correspond to multiple side chain groups." At least one of these three must correspond to Drug Molecule 4. Consider Drug Molecule 4 first.

Drug Molecule 4: Improve site-specificity. Enhance the drug's targeting to specific tissues or cells (e.g., tumor cells). A common strategy is to utilize transporters highly expressed on the surface of these cells, such as glucose transporters (GLUTs). Side chain 3 is a glucose group. Linking the drug to glucose enables its preferential uptake by cells with high GLUT expression, achieving targeted delivery.

<Checkpoint>[Side chain 3 (glucose) enables preferential uptake by cells with high GLUT expression](1)</Checkpoint>

Thus, Molecule 4–Side Chain 3 is a standard strategy to achieve this goal.

<Checkpoint>[Molecule 4 matches with Side Chain 3](1)</Checkpoint>

Therefore, to increase the water solubility of Drug Molecule 3, side chain 2 or 5 can be introduced.

<Checkpoint>[Molecule 3 matches with Side Chain 2 or Side Chain 5](1)</Checkpoint>

Based on the above pairing relationships, calculate the $x_{i j}=a_{i} \times b_{j}$ values for each pair:

$x_{1,1}=1/ 1=1.00$

$x_{2,4}=2/4=0.50$

$x_{3,2}=3/2=1.50$

$x_{3,5}=3/5=0.60$

$x_{4,3}=4/3=1.33$

<Checkpoint>[$x_{1,1}=1,x_{2,4}=0.5,x_{3,2}=1.5,x_{3,5}=0.6,x_{4,3}=1.33$](1)</Checkpoint>

Calculate the sum of $x_{i,j}$: 

 $z = \sum x_{i,j} = 4.93$, so select option **C**.

<Checkpoint>[$z= 4.93$, choose C ](1)</Checkpoint>
将药物分子片段与侧链基团进行如下匹配：

药物分子 1 & 2：增加脂溶性，通常通过引入非极性的烃基链或酯化掩盖极性基团（如-OH或-COOH）来实现。

<Checkpoint>[增加脂溶性需要掩盖极性基团](0.5)</Checkpoint>

侧链 1 (丁酰基) 和侧链 4 (乙基) 都是非极性基团，能有效增加脂溶性，侧链 1 (丁酰基) 可以酰基化羟基成酯，而侧链 4 (乙基) 可以酯化羧基成酯。

<Checkpoint>[侧链 1 (丁酰基) 和侧链 4 (乙基) 会增加脂溶性](0.5)</Checkpoint>

药物分子 2 的 $R$ 基连接在一个羧基上（$\mathrm{-COOH}$）。将其转化为乙酯（接上侧链 4）是药物化学中非常经典的提高脂溶性和口服生物利用度的方法。因此，2号分子-4号侧链是合理的匹配。

<Checkpoint>[2号分子匹配4号侧链](1)</Checkpoint>

药物分子 1 的R基连接在一个羟基上（-OH）。将其酯化（接上侧链 1）同样可以有效掩盖极性，增加脂溶性。因此，1号分子-1号侧链是合理的匹配。

<Checkpoint>[1号分子匹配1号侧链](1)</Checkpoint>

药物分子 3：增加水溶性，对于一个非常庞大且脂溶性强的分子（紫杉醇类似物），需要引入强极性、可电离或带电荷的基团来显著增加其水溶性。

侧链 2 (含羧基)、侧链 3 (葡萄糖) 和侧链 5 (季铵盐) 都是极性或带电荷的基团，会增加水溶性。根据题目中的信息“每个侧链基团对应且只对应一个药物分子片段，一个药物分子片段可能对应多个侧链基团”，这三个中至少有一个需要对应药物分子 4，先考虑药物分子 4.

药物分子 4：提高作用部位特异性。提高药物对特定组织或细胞（如肿瘤细胞）的靶向性。一种常用策略是利用这些细胞表面高表达的转运体，例如葡萄糖转运体（GLUTs）。侧链 3 是一个葡萄糖基团。将药物与葡萄糖连接，可以使其被高表达GLUTs的细胞优先摄取，从而实现靶向递送。

<Checkpoint>[侧链 3 (葡萄糖) 可使药物被高表达GLUTs的细胞优先摄取](1)</Checkpoint>

因此，4号分子-3号侧链是实现该目标的标准策略。

<Checkpoint>[4号分子匹配3号侧链](1)</Checkpoint>

因此，增加药物分子 3 的水溶性可以引入侧链 2 或 5。

<Checkpoint>[3号分子匹配2号侧链或5号侧链](1)</Checkpoint>

根据以上配对关系，计算每对的 $x_{i j}=a_{i}/b_{j}$ 值:

$x_{1,1}=1/ 1=1.00$

$x_{2,4}=2/4=0.50$

$x_{3,2}=3/2=1.50$

$x_{3,5}=3/5=0.60$

$x_{4,3}=4/3=1.33$

<Checkpoint>[$x_{1,1}=1,x_{2,4}=0.5,x_{3,2}=1.5,x_{3,5}=0.6,x_{4,3}=1.33$](1)</Checkpoint>

计算 $x_{i,j}$ 的加和: 

 $z = \sum x_{i,j} = 4.93$，故选择选项 **C**。

<Checkpoint>[$z= 4.93$，选择C ](1)</Checkpoint>