(a) Steady-state fluorescence data for a small molecule labelled with a fluorescent dye were collected in solution in the absence or presence of a protein. The fluorescence quantum yield and lifetime of the dye are unchanged in both samples.
(a) 在没有蛋白质或有蛋白质的情况下，收集溶液中标记了荧光染料的小分子的稳态荧光数据。两种样品中染料的荧光量子产率和寿命均保持不变。

(i) Sketch the experimental setup used to collect the data in the table above and explain what is being measured.
(i) 绘制用于收集上表数据的实验装置草图，并解释测量的内容。
(ii) Explain how this experiment can detect binding of the small molecule to the protein.
(ii) 解释该实验如何检测小分子与蛋白质的结合。
(iii) Define all the terms in the equation above and use the data in the table to explain which sample is more likely to involve an interaction of the small molecule and protein.
(iii) 给上式中的所有术语下定义，并利用表格中的数据解释哪个样本更有可能涉及小 分子与蛋白质的相互作用。
(b) Explain, with the aid of a sketch, the random coil model of polymers. Your answer should explain why the random coil model can be applied to both flexible and semi-flexible polymers, and what assumptions are implicit in the model.
(b) 借助草图解释聚合物的无规线圈模型。答案应解释为什么无规线圈模型可适用于柔性和半柔性聚合物，以及该模型隐含了哪些假设。

© The equation above relates to the random coil model. Define the terms and, with the aid of a sketch, explain what they represent.
上式与随机线圈模型有关。请定义这些术语，并借助草图解释其含义。
(d) Very long double-stranded DNA (dsDNA) can be modelled as a random coil with $l=100\mathrm{nm}$$l=100\mathrm{nm}$l=100nml=100 \mathrm{~nm}, where $l$$l$ll has the same meaning as in the equation above. The dsDNA from the $\lambda$$\lambda$lambda\lambda-phage virus is 48,490 base pairs long and the average distance between neighbouring base pairs is 0.34 nm . Use this information to calculate $R_{rms}$$R_{rms}$R_(rms)R_{r m s} for $\lambda$$\lambda$lambda\lambda-phage DNA.
(d) 超长双链 DNA（dsDNA）可模拟为一个随机线圈，其中 $l=100\mathrm{nm}$$l=100\mathrm{nm}$l=100nml=100 \mathrm{~nm} ， $l$$l$ll 的含义与上式相同。来自 $\lambda$$\lambda$lambda\lambda -噬菌体病毒的 dsDNA 长度为 48 490 碱基对，相邻碱基对之间的平均距离为 0.34 nm。利用这些信息计算 $\lambda$$\lambda$lambda\lambda -phage DNA 的 $R_{rms}$$R_{rms}$R_(rms)R_{r m s} 。
(e) The persistence length of DNA is $\sim 50\mathrm{nm}$$\sim 50\mathrm{nm}$∼50nm\sim 50 \mathrm{~nm}. With the aid of a sketch, give a quantitative description of persistence length and explain whether dsDNA that is 200 base pairs long is best treated as a random coil or as a rigid rod.
(e) DNA 的持续长度为 $\sim 50\mathrm{nm}$$\sim 50\mathrm{nm}$∼50nm\sim 50 \mathrm{~nm} 。借助草图，给出持续长度的定量描述，并解释长度为 200 个碱基对的 dsDNA 最好被视为随机线圈还是刚性棒。

An unstructured polymer is end-labelled with a pair of fluorescent dyes that can be used as FRET labels. Data from single-molecule FRET measurements of immobilised polymer molecules are shown in the table below.
用一对可用作 FRET 标签的荧光染料对非结构化聚合物进行末端标记。固定聚合物分子的单分子 FRET 测量数据如下表所示。

(a) Explain what distance and occurrence in the table represent and explain briefly how they are obtained from the single-molecule FRET experiment.
(a) 解释表格中的距离和发生率代表什么，并简要说明如何从单分子 FRET 实验中获得它们。
(b) Using the data in the table:
(b) 利用表格中的数据：
(i) Calculate the root mean square separation of the polymer ends. Explain your approach.
(i) 计算聚合物末端的均方根分离度。解释你的方法。
(ii) Calculate the number of monomer units in the polymer, assuming the polymer can be treated as a random coil polymer with segment length of 0.5 nm .
(ii) 假设聚合物可视为段长为 0.5 纳米的无规线圈聚合物，计算聚合物中的单体单元数。
© If the sample contained an equal mixture of two polymers with root mean square separations differing by a factor of two, explain the advantage of single-molecule FRET over ensemble FRET measurements and sketch a graph of Distance vs Occurrence for this mixture.
如果样品中含有两种聚合物的等量混合物，且两种聚合物的均方根距离相差 2 倍，请解释单分子 FRET 比集合 FRET 测量的优势，并绘制该混合物的距离与发生率关系图。
(d) The graph below shows the electrospray mass spectrum for a biopolymer in deuterated water.
(d) 下图显示了生物聚合物在氘化水中的电喷雾质谱。

(i) Briefly explain the method of electrospray ionisation (ESI) and why this is useful for detecting biomolecules.
(i) 简要解释电喷雾离子化（ESI）方法，以及为什么这种方法有助于检测生物大 分子。
[2]
(ii) Using the information in the mass spectrum above, calculate the molecular weight of the biopolymer and identify each peak in the spectrum. Assume that the only source of positive ions is from the solvent.
(ii) 利用上述质谱信息，计算生物聚合物的分子量，并确定质谱中的每个峰值。假设正离子的唯一来源是溶剂。

(a) Static light-scattering data for a polymer in toluene using plane-polarised laser light at $\lambda =546\mathrm{nm}$$\lambda =546\mathrm{nm}$lambda=546nm\lambda=546 \mathrm{~nm} are shown in the table below. The distance from sample to detector was 30 cm , and the plane of polarisation of the incident light was orthogonal to the detection plane.
(a) 下表列出了使用 $\lambda =546\mathrm{nm}$$\lambda =546\mathrm{nm}$lambda=546nm\lambda=546 \mathrm{~nm} 平面偏振激光对甲苯中聚合物进行静态光散射的数据。样品到检测器的距离为 30 厘米，入射光的偏振面与检测面正交。

(i) Using the data and information above and the equations below, calculate with the aid of a graph the average molecular weight $\left({\overline{M}}_{\mathrm{w}}\right)$$\left({\overline{M}}_{\mathrm{w}}\right)$( bar(M)_(w))\left(\bar{M}_{\mathrm{w}}\right) and the radius of gyration $\left(R_{\mathrm{g}}\right)$$\left(R_{\mathrm{g}}\right)$(R_(g))\left(R_{\mathrm{g}}\right) of the polymer. The constant $K=3.60\times {10}^{-5}\mathrm{mol}{\mathrm{m}}^5{\mathrm{kg}}^{-2}$$K=3.60\times {10}^{-5}\mathrm{mol}{\mathrm{m}}^5{\mathrm{kg}}^{-2}$K=3.60 xx10^(-5)molm^(5)kg^(-2)K=3.60 \times 10^{-5} \mathrm{~mol} \mathrm{~m}^{5} \mathrm{~kg}^{-2} and the mass concentration $c_{\mathrm{p}}=900\mathrm{kg}{\mathrm{m}}^{-3}$$c_{\mathrm{p}}=900\mathrm{kg}{\mathrm{m}}^{-3}$c_(p)=900kgm^(-3)c_{\mathrm{p}}=900 \mathrm{~kg} \mathrm{~m}^{-3}.
(i) 利用上面的数据和信息以及下面的公式，借助图表计算出聚合物的平均分子量 $\left({\overline{M}}_{\mathrm{w}}\right)$$\left({\overline{M}}_{\mathrm{w}}\right)$( bar(M)_(w))\left(\bar{M}_{\mathrm{w}}\right) 和回转半径 $\left(R_{\mathrm{g}}\right)$$\left(R_{\mathrm{g}}\right)$(R_(g))\left(R_{\mathrm{g}}\right) 。常数 $K=3.60\times {10}^{-5}\mathrm{mol}{\mathrm{m}}^5{\mathrm{kg}}^{-2}$$K=3.60\times {10}^{-5}\mathrm{mol}{\mathrm{m}}^5{\mathrm{kg}}^{-2}$K=3.60 xx10^(-5)molm^(5)kg^(-2)K=3.60 \times 10^{-5} \mathrm{~mol} \mathrm{~m}^{5} \mathrm{~kg}^{-2} 和质量浓度 $c_{\mathrm{p}}=900\mathrm{kg}{\mathrm{m}}^{-3}$$c_{\mathrm{p}}=900\mathrm{kg}{\mathrm{m}}^{-3}$c_(p)=900kgm^(-3)c_{\mathrm{p}}=900 \mathrm{~kg} \mathrm{~m}^{-3} 。

(ii) The polymer has much higher solubility in methanol than in toluene. Explain, with justification, what will happen to the measured radius of gyration of the polymer as increasing amounts of methanol are added to a solution of the polymer in toluene. $N.B$$N.B$N.BN . B. assume methanol is completely miscible with toluene.
(ii) 该聚合物在甲醇中的溶解度远高于在甲苯中的溶解度。请解释聚合物在甲苯中的溶液中加入越来越多的甲醇后，测得的回转半径会发生什么变化，并说明理由。 $N.B$$N.B$N.BN . B .假设甲醇与甲苯完全混溶。
(b)
(i) Explain the design principles behind the formation of lipid-based colloidal nanostructures, including the structure of the lipids and the driving force for colloid formation.
(i) 解释脂基胶体纳米结构形成背后的设计原理，包括脂质的结构和胶体形成 的驱动力。
(ii) Assuming a particular lipid molecule spontaneously forms vesicles, explain and justify two changes you could make to its structure to promote the formation of spherical micelles.
(ii) 假设某一脂质分子会自发形成囊泡，请解释并说明为促进球形胶束的形成，可 对其结构进行的两种改变。
(iii) A crucial aspect of COVID-19 vaccines based on messenger RNA (mRNA) is the use of lipid-based colloids as drug delivery agents. Give three reasons why lipidbased colloids are suited to this role.
(iii) 以信使核糖核酸（mRNA）为基础的 COVID-19 疫苗的一个重要方面是使用脂 基胶体作为药物输送剂。请说明脂基胶体适合发挥这一作用的三个原因。

(a) The table below shows positive-mode electrospray ionisation data for a protein in aqueous solution. The adjacent peaks are related to each other by the gain or loss of a trivalent cation. The molecular weight of the protein is 8360.12 Daltons and there is only one type of trication ion present in solution.
(a) 下表列出了水溶液中蛋白质的正模式电喷雾离子化数据。相邻峰之间的关系是三价阳离子的增减。该蛋白质的分子量为 8360.12 道尔顿，溶液中只有一种三价离子。

(i) Write out the formula for the species formed during the electrospray ionisation process, assuming the protein is neutral in the absence of the trications.
(i) 假设蛋白质在没有三聚物的情况下呈中性，写出电喷雾离子化过程中形成的物 种的公式。
[2]
(ii) Write the formula for $m/z$$m/z$m//zm / z of two adjacent peaks in the electrospray mass spectrum.
(ii) 写出电喷雾质谱中两个相邻峰的 $m/z$$m/z$m//zm / z 公式。
(iii) Identify the trication and all four peaks in the mass spectrum.
(iii) 找出质谱中的三聚体和所有四个峰。
(b) The radius of gyration of a monodisperse sample of polyethene, which behaves as a freely jointed chain, was measured to be 3.2 nm .
(b) 测得聚乙烯单分散样品的回转半径为 3.2 nm，该样品表现为自由连接的链条。
(i) Calculate the end-to-end separation for this monodisperse polymer.
(i) 计算这种单分散聚合物的端对端分离度。
(ii) If the carbon-carbon bond length in polyethene is 153 pm , calculate the molecular weight of this monodisperse polymer.
(ii) 如果聚乙烯的碳-碳键长度为 153 pm，计算这种单分散聚合物的分子量。
(iii) Describe briefly how fluorescently labelled polyethene could be used to measure the end-to-end distribution of distances in polydisperse polyethene.
(iii) 简要说明如何使用荧光标记聚乙烯来测量多分散聚乙烯中端到端距离的分布。

(a) A flexible polymer, which behaves as a random coil with segment length of $5\text{Å}$$5\text{Å}$5"Å"5 \AA, is labelled at either end with a different fluorescent dye molecule. The dye molecules can act as a FRET pair with a Förster radius of $55\text{Å}$$55\text{Å}$55"Å"55 \AA. The average lifetime of the donor dye molecule is 2.20 ns in the doubly-labelled polymer. In an identical polymer that is labelled on only one end with a donor dye molecule, the lifetime of the donor is 4.10 ns .
(a) 一种柔性聚合物的两端标记有不同的荧光染料分子，这种聚合物表现为段长为 $5\text{Å}$$5\text{Å}$5"Å"5 \AA 的无规线圈。染料分子可作为 FRET 对，其 Förster 半径为 $55\text{Å}$$55\text{Å}$55"Å"55 \AA 。在双标记聚合物中，供体染料分子的平均寿命为 2.20 ns。在只在一端标记供体染料分子的相同聚合物中，供体的寿命为 4.10 ns。
(i) Explain, with the aid of a diagram, the photophysical mechanism that causes the reduction in the fluorescence lifetime of the donor molecule in the doubly-labelled polymer. How can this be used to measure the distance between the two dye molecules?
(i) 借助图表解释导致双标记聚合物中供体分子荧光寿命缩短的光物理机理。如何利用这一机制测量两个染料分子之间的距离？
(ii) Briefly discuss the assumptions made in treating a polymer as a random coil.
(ii) 简要讨论将聚合物视为无规线圈时所作的假设。
(iii) Using appropriate equations and a sketch, calculate the end-to-end separation of the polymer and the number of segments in the random coil polymer. Your answer should include a discussion of any assumptions in using FRET for the accurate measurement of distances.
(iii) 利用适当的方程式和草图，计算聚合物的端到端分离度和无规线圈聚合物的段数。答案应包括对使用 FRET 精确测量距离的假设的讨论。
(iv) Assuming the lifetimes given above are for the polymer in the bulk solid, discuss how the distance measurements could be affected by dissolving the polymer in solvent.
(iv) 假设上面给出的是聚合物在固体中的寿命，请讨论将聚合物溶解在溶剂中会如何 影响距离测量。
[2]
(b) A spherical nanoparticle is labelled with a single fluorescent dye molecule. The nanoparticle is transparent in the visible region of the spectrum; therefore, its absorption spectrum does not overlap with the absorption or emission of the fluorescent dye molecule. The table below gives the result of a steady-state fluorescence anisotropy experiment, whereby a solution of labelled nanoparticles is excited using linearly polarised light; the resultant dye molecule fluorescence is measured at two polarisations (parallel and perpendicular to the excitation light). The solution temperature is ${25}^{\circ }\mathrm{C}$${25}^{\circ }\mathrm{C}$25^(@)C25^{\circ} \mathrm{C}. The lifetime of the dye molecule was measured in a separate experiment to be 4.0 ns and the viscosity of the buffer at ${25}^{\circ }\mathrm{C}$${25}^{\circ }\mathrm{C}$25^(@)C25^{\circ} \mathrm{C} is $0.00104\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-1}$$0.00104\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-1}$0.00104kgm^(-1)s^(-1)0.00104 \mathrm{~kg} \mathrm{~m}^{-1} \mathrm{~s}^{-1}.
(b) 用单个荧光染料分子标记球形纳米粒子。纳米粒子在可见光谱区是透明的，因此其吸收光谱与荧光染料分子的吸收或发射光谱不重叠。下表列出了稳态荧光各向异性实验的结果：使用线性偏振光激发标记纳米粒子溶液；在两个偏振（平行于激发光和垂直于激发光）下测量染料分子的荧光。溶液温度为 ${25}^{\circ }\mathrm{C}$${25}^{\circ }\mathrm{C}$25^(@)C25^{\circ} \mathrm{C} 。在另一项实验中测得染料分子的寿命为 4.0 ns，缓冲液在 ${25}^{\circ }\mathrm{C}$${25}^{\circ }\mathrm{C}$25^(@)C25^{\circ} \mathrm{C} 时的粘度为 $0.00104\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-1}$$0.00104\mathrm{kg}{\mathrm{m}}^{-1}{\mathrm{s}}^{-1}$0.00104kgm^(-1)s^(-1)0.00104 \mathrm{~kg} \mathrm{~m}^{-1} \mathrm{~s}^{-1} 。

(i) Explain how fluorescence polarisation can provide information on the size of a molecule. Your answer should make reference to transition dipole moments.
(i) 解释荧光偏振如何提供分子大小的信息。答案中应提及过渡偶极矩。
[3]
(ii) Write an equation that relates steady-state anisotropy to the data in the Table.
(ii) 写出稳态各向异性与表中数据的关系式。
(iii) Define the terms in the Perrin equation (1) and the Debye-Stokes-Einstein equation (2) shown below.
(iii) 给下图所示的佩林方程 (1) 和德拜-斯托克斯-爱因斯坦方程 (2) 中的术语下个定义。

[2]
(iv) Use your answers to b (ii) and b (iii) to calculate the hydrodynamic volume of the nanoparticle, assuming that $r_0=0.375$$r_0=0.375$r_(0)=0.375r_{0}=0.375
(iv) 利用 b (ii) 和 b (iii) 的答案计算纳米粒子的流体力学体积，假设 $r_0=0.375$$r_0=0.375$r_(0)=0.375r_{0}=0.375

(a) Give a brief explanation of how electrospray ionisation (ESI) is used to produce macromolecular ions for mass spectrometry (MS).
(a) 简要说明电喷雾离子化（ESI）如何用于产生质谱（MS）分析中的大分子离子。
(b) The graph below shows a positive-mode electrospray ionisation mass spectrum for a protein in aqueous buffer. The peaks shown appear only when the buffer contains ${\mathrm{CaCl}}_2$${\mathrm{CaCl}}_2$CaCl_(2)\mathrm{CaCl}_{2}. Calculate the molecular weight of the protein and assign each of the four peaks, explaining your approach.
(b) 下图显示了水缓冲液中蛋白质的正模式电喷雾离子化质谱。只有当缓冲液中含有 ${\mathrm{CaCl}}_2$${\mathrm{CaCl}}_2$CaCl_(2)\mathrm{CaCl}_{2} 时才会出现所示峰值。请计算该蛋白质的分子量，并为四个峰分别赋值，同时解释你的方法。

© An ion moving through a magnetic field, $B$$B$BB, that is orthogonal to its velocity, $v$$v$vv, experiences a Lorentz force, $F_L$$F_L$F_(L)F_{L}, that is orthogonal to both $B$$B$BB and $v$$v$vv, and has a magnitude given by eq. 1 :
一个离子在与其速度 $v$$v$vv 正交的磁场 $B$$B$BB 中运动时，会受到一个洛伦兹力 $F_L$$F_L$F_(L)F_{L} 的作用，该力与 $B$$B$BB 和 $v$$v$vv 正交，其大小由公式 1 给出：

where $z$$z$zz is the ion’s charge number and $e$$e$ee is the elementary charge.
其中 $z$$z$zz 是离子的电荷数， $e$$e$ee 是基本电荷。

With the aid of a sketch, explain how a magnetic sector mass analyser makes use of the Lorentz force to separate ions. Your answer should make use of the equations (eq. 2 and eq. 3) for centripetal force ( $F_c$$F_c$F_(c)F_{c} ):
请借助简图解释磁扇区质量分析仪如何利用洛伦兹力分离离子。您的答案应利用向心力方程（ $F_c$$F_c$F_(c)F_{c} ）（公式 2 和公式 3）：

where $m$$m$mm is the mass of the ion, $r$$r$rr is the radius of curvature, and $V$$V$VV is the voltage across which the ion has been accelerated.
其中， $m$$m$mm 是离子的质量， $r$$r$rr 是曲率半径， $V$$V$VV 是离子被加速时的电压。
(d) Lyophobic colloidal sols are thermodynamically unstable with respect to the bulk material.
(d) 相对于主体材料而言，疏溶性胶体溶胶在热力学上是不稳定的。
(i) With the aid of a diagram, describe the electrical double layer in lyophobic colloidal dispersions.
(i) 借助图表，描述疏溶性胶体分散体中的电双层。
(ii) Describe how the electrical potential varies with distance from the solid surface and its role in colloid stabilisation.
(ii) 描述电势如何随距离固体表面的远近而变化，及其在胶体稳定中的作用。
(iii) Addition of ${\mathrm{AlCl}}_3$${\mathrm{AlCl}}_3$AlCl_(3)\mathrm{AlCl}_{3} to a clear dispersion of a lyophobic colloid (with particle size of $\sim 20\mathrm{nm}$$\sim 20\mathrm{nm}$∼20nm\sim 20 \mathrm{~nm} ) causes it to scatter light strongly. Explain this observation in terms of the DLVO theory of lyophobic dispersions.
(iii) 在疏溶胶体（粒度为 $\sim 20\mathrm{nm}$$\sim 20\mathrm{nm}$∼20nm\sim 20 \mathrm{~nm} ）的透明分散液中加入 ${\mathrm{AlCl}}_3$${\mathrm{AlCl}}_3$AlCl_(3)\mathrm{AlCl}_{3} 会使其产生强烈的光散射。请用疏溶性分散体的 DLVO 理论解释这一现象。