生物大分子介质中的反常扩散动力学理论★

doi:10.6023/A23040172

化学学报 ›› 2023, Vol. 81 ›› Issue (8): 967-978.DOI: 10.6023/A23040172 上一篇下一篇

所属专题：庆祝《化学学报》创刊90周年合辑

综述

生物大分子介质中的反常扩散动力学理论^★

魏文杰, 陈文龙, 戴晓彬, 燕立唐()

清华大学化学工程系北京 100084

投稿日期:2023-04-27 发布日期:2023-09-14

作者简介:

魏文杰, 清华大学化学工程系在读博士研究生. 2022年本科毕业于清华大学. 目前主要从事大分子体系中活性粒子的扩散动力学计算机模拟研究.

陈文龙, 清华大学化学工程系在读博士研究生. 2022年本科毕业于清华大学. 主要从事大分子网络中扩散动力学的计算机模拟研究.

戴晓彬, 清华大学化学工程系在读博士研究生. 2014年本科毕业于清华大学. 主要从事大分子的计算机理论计算与模拟研究, 包括聚合物纳米复合体系, 大分子网络体系等.

燕立唐, 清华大学化工系长聘教授. 主要研究方向为, 结合现代软凝聚态物理与传统高分子物理, 发展新的计算模型和解析理论, 应用于大分子组装、凝胶体系以及生命大分子体系的基础理论研究. 曾获德国洪堡学者基金, 国家基金委优秀青年基金和国家杰出青年科学基金项目资助.

^★庆祝《化学学报》创刊90周年.

† 共同第一作者

基金资助:
项目受国家重点基础研究发展规划(2022YFA1200061); 国家自然科学基金(22025302); 国家自然科学基金(21873053); 化学工程联合国家重点实验室(SKL-ChE-23T01)

Theory of Anomalous Diffusion Dynamics in Biomacromolecular Media^★

Wenjie Wei, Wenlong Chen, Xiaobin Dai, Li-Tang Yan()

Department of Chemical Engineering, Tsinghua University, Beijing 100084

Received:2023-04-27 Published:2023-09-14
Contact: *E-mail: ltyan@mail.tsinghua.edu.cn
About author:
^★Dedicated to the 90th anniversary of Acta Chimica Sinica.
† These authors contributed equally to this work.
Supported by:
State Key Development Program of Basic Research of China(2022YFA1200061); National Natural Science Foundation of China(22025302); National Natural Science Foundation of China(21873053); State Key Laboratory of Chemical Engineering(SKL-ChE-23T01)

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摘要/Abstract

生命体系中的扩散行为涉及营养摄取和药物递送等重要的生命过程. 深入了解粒子在生物大分子介质中的扩散行为将有助于理解相关生命现象以及发展新型医用材料. 生物大分子介质中的扩散行为往往是反常的, 不能简单地基于传统扩散常数方程进行描述. 这通常归因于生物介质中的拥挤环境与复杂相互作用使扩散产生了持续相关性, 进而导致中心极限定理不再适用. 从反常扩散的扩散系数、均方位移以及位移概率分布函数三个方面分析了反常扩散的机理与物理特征, 综述了近年来针对大分子介质中反常扩散的研究进展. 随后概述了反常扩散的物理模型与现有理论框架. 最后对生物大分子介质中反常扩散动力学理论的未来发展方向进行了展望.

关键词: 扩散, 反常扩散, 纳米粒子, 生物大分子介质, 动力学异质性

Diffusion behavior in life system involves important life processes such as nutrient uptake and drug delivery. A deeper understanding about diffusive behavior of particles in complex biomacromolecular media will facilitate the understanding of relevant life phenomena as well as the development of novel medical materials. The diffusion behavior in biomacromolecular media is often anomalous and cannot be described simply based on the conventional diffusion constant equation. This is usually attributed to the continuous correlation of diffusion caused by crowded environment and complex interactions in biological medium, which leads to the central limit theorem no longer applicable. The mechanism and physical characteristics of anomalous diffusion were analyzed from three aspects: diffusion coefficient, mean square displacement, and displacement probability distribution function. The recent progress of anomalous diffusion in biomacromolecular media was summarized. The physical model and existing theoretical framework of anomalous diffusion are then outlined. Finally, the future direction of anomalous diffusion dynamics in biomacromolecular media is discussed.

Key words: diffusion, anomalous diffusion, nanoparticle, biomacromolecular media, dynamics heterogeneity

引用此文

魏文杰, 陈文龙, 戴晓彬, 燕立唐. 生物大分子介质中的反常扩散动力学理论^★[J]. 化学学报, 2023, 81(8): 967-978.

Wenjie Wei, Wenlong Chen, Xiaobin Dai, Li-Tang Yan. Theory of Anomalous Diffusion Dynamics in Biomacromolecular Media^★[J]. Acta Chimica Sinica, 2023, 81(8): 967-978.

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图/表 8

图1. 生物大分子介质中常见的扩散现象. (a)被多核巨细胞内吞的聚苯乙烯微球[9]. (b)霍乱弧菌中RNA-蛋白质颗粒的扩散轨迹[14]. (c)大肠杆菌中RNA分子的扩散过程[12]. (d)小量子点聚集体在染色质中的扩散轨迹[17]. (e)腺病毒相关病毒感染HeLa细胞的扩散轨迹[10]

Figure 1. Common diffusion phenomena in biomacromolecular media. (a) Polystyrene microspheres endocytosed by multinucleated giant cells[9]. (b) Diffusion trajectory of RNA-protein particles in Vibrio cholerae[14]. (c) Diffusion process of RNA molecules in E. coli[12]. (d) Diffusion trajectory of small quantum dot aggregates in chromatin[17]. (e) Diffusion trajectory of adenovirus-associated virus-infected HeLa cells[10]

图2. (a)分散在聚苯乙烯中的油酸覆盖量子点的透射电镜显微镜(TEM)图. (b)由聚苯乙烯中量子点的实验测量扩散系数与由S-E关系计算出的理论扩散系数的比值随温度变化的函数. 假设体系黏度为不同的黏度值计算得到的S-E扩散系数: 纯聚合物黏度(True viscosity)、无缠结的纯聚合物黏度(Rouse viscosity), 共混物黏度(Blend viscosity)[36]. (c)在聚合物熔体中单个纳米粒子的示意图, 表明关联长度尺度和两个极端状态. 左图是一个“小”(2R<dT)粒子, 粒子不受缠结约束; 右图是一个“大”(2R>dT)粒子, 粒子被缠结网络捕获, 与周围聚合物的排斥强耦合. (d~f) S-E违反比作为纳米粒子直径与缠结网格孔径比的函数. 不同颜色线条代表不同的缠结度(从下到上): N/Ne=1(黑色), 2(红色), 4(蓝色), 8(粉红色)和16(绿色). (d)实曲线对应于未修正的SCGLE方法, 虚线对应于以前的纯约束-释放模型. (e)虚线对应考虑记忆函数对应的数值预因子的SCGLE计算结果, 实线对应不考虑数值预因子的结果. (f)黑色方块代表实验结果, 线条代表SCGLE理论结果. 实线使用数值预因子为3.6, 虚线不考虑数值预因子[37]

Figure 2. (a) Transmission electron microscope (TEM) micrographs of oleic acid-covered quantum dots dispersed in polystyrene. (b) The experimentally measured diffusion coefficient from a quantum dot in polystyrene as a function of the ratio of theoretical diffusion coefficient calculated from S-E relation: True viscosity, Rouse viscosity, Blend viscosity[36]. (c) Schematic representation of individual nanoparticles in polymer melts, indicating critical length scales and two extreme states. The left is a "small" (2R<dT) particle not constrained by entanglement; the right is a "large" (2R>dT) particle trapped by an entangled network, strongly coupled to the exclusion of the surrounding polymer. (d~f) S-E violation ratio as a function of the ratio of nanoparticle diameter versus entangled mesh size. Different color lines represent different levels of entanglement (from bottom to top): N/Ne=1 (black), 2 (red), 4 (blue), 8 (pink), and 16 (green). (d) The solid curves correspond to the uncorrected SCGLE method, and the dashed lines correspond to constraint-release model. (e) The dashed lines correspond to the SCGLE results considering the numerical prefactor memory function, and the solid lines correspond to the results without numerical prefactor. (f) Black squares represent experimental results and lines represent SCGLE results. The solid lines uses a numerical prefactor of 3.6, and the dashed lines ignore prefactor[37]

图3. (a)粒子在四官能度大分子网络中的示意图. (b)大分子网络的网格模型, 参数有: g, 亏格; n, 度; k, 官能度. (c)具有不同拓扑结构的网格模型. (d~f)粒子在大分子网络中三种扩散模式的轨迹: 布朗(d)、跳跃(e)与受限(f). (g)粒子在不同刚度的大分子网络中扩散的均方位移与非高斯参数. (h) g=6时粒子在网络中的典型扩散轨迹, d/ax分别为1.00, 1.65和1.90. (i)不同网格中粒子的均方位移[43-44]

Figure 3. (a) Schematic representation of particles in a four-functional macromolecular network. (b) The grid model of macromolecular network, the parameters are: g, genus; n, degree; k, functionality. (c) Mesh models with different topologies. (d~f) Trajectories of particles in three diffusion modes in a macromolecular network: Brownian (d), hopping (e) and trapped (f). (g) Mean square displacement (MSD) of particle diffusion in a macromolecules network of different stiffness and their non-Gaussian parameters. (h) Typical diffusion trajectory of particles in networks at g=6, d/ax of 1.00,1.65 and 1.90, respectively. (i) MSD of particles in different grids[43-44]

图4. (a)两种网格尺寸下跳跃等待时间随链刚度的变化, 其中实线为理论预测结果. (b)不同链刚度下跳跃过程的自由能位垒随约束参数的变化. (c)粒子在不同网格拓扑结构中所经历的自由能变化等值面ΔF. (d)不同粒子直径下自由能变ΔF(z)随位置z的变化. (e)不同拓扑结构的网格中粒子在相邻网格单元间经历的自由能垒Ub随受限参数d/ax的变化[44,46]

Figure 4. (a) The change of the waiting time with the chain stiffness for two grid sizes, where the solid line is the theoretical prediction result. (b) The change of the free energy barrier of hopping process at different chain stiffness. (c) Free energy (ΔF) isosurface experienced by particles in different grid topologies. (d) Changes of the free energy variation ΔF(z) with position z for different particle diameters. (e) The change of the free energy barrier Ub experienced by particles between adjacent grid cells in a grid of different topologies with the constrained parameter d/ax[44,46]

图5. (a)在细胞膜内的氧化石墨烯示意图. (b)在大肠杆菌包围环境中扩散的Janus粒子. (c)带不同电荷的粒子在细胞膜表面扩散示意图. (d)超扩散轨迹中持续段(红)和振荡段(蓝)的分段均方位移. (e)氧化石墨烯在细胞膜内的超扩散轨迹示意图. (f)不同相互作用能下的跳跃长度分布. (g)轨迹的相邻持续段之间的角度的统计分布, 上: 正常扩散, 下: 超扩散[49?-51]

Figure 5. (a) A Schematic representation of the graphene oxide (GO) within the cell membrane. (b) Janus particles that diffuse in the environment surrounded by E. coli. (c) Schematic representation of particles with different charges spreading on the cell membrane surface. (d) The segment MSD of the persistence part (red) and oscillation part (blue) in the super diffusion trajectory. (e) Schematic representation of the super diffusion trajectory of GO within the cell membrane. (f) Hopping length distribution under different interaction energies. (g) Statistical distribution of angles between adjacent persistent segments of the trajectory, top: normal diffusion, bottom: super diffusion[49?-51]

图6. (a)氧化石墨烯诱导形成的半孔示意图. (b)孔隙和氧化石墨烯面积比和扩散指数随相互作用能Ka的变化, 红色和蓝色曲线分别描绘了最可能的孔隙面积和平均孔隙面积, 背景的四种颜色分别对应四种孔隙状态. (c)氧化石墨烯不同时刻的运动示意图, Ka=25.29 kBT/nm2, t=22160τ, 22240τ, 22480τ, 22800τ和23040τ(上)及Ka=34.74 kBT/nm2, t=22320τ, 22360τ, 22400τ, 22440τ和22480τ (下). (d) Janus粒子四周的细菌密度分布, R=6.97 μm, c0=0.05 mmol/L(左)以及c0=1.0 mmol/L(右). (e)含有表面电荷β=0.8(左)、0(中)和－0.8(右)的纳米粒子的脂质双层膜的波动. (f)均匀带电粒子与细胞膜接触点到膜平面的距离l随电荷量|β|的变化[49?-51]

Figure 6. (a) Schematic diagram of pores induced by GO. (b) The pore and GO area ratio and diffusion index vary with the interaction energy Ka, the red and blue curves depict the most likely pore area and the mean pore area, respectively, and the four colors of the background correspond to the four pore states. (c) Schematic representation of the GO motion at different times, Ka=25.29 kBT/nm2, t=22160τ, 22240τ, 22480τ, 22800τ, 23040τ (top) and Ka=34.74 kBT/nm2, t=22320τ, 22360τ, 22400τ, 22440τ, 22480τ (bottom). (d) Distributions of bacterial density around the particle with R=6.97 μm and c0=0.05 mmol/L (left), c0=1.0 mmol/L (right). (e) Fluctuations of lipid bilayer membranes containing nanoparticles with surface charge β=0.8 (left), 0 (middle), and －0.8 (right). (f) The changes of the distance l between the contact points of uniformly charged particles to the cell membrane and the membrane plane with charge |β|[49?-51]

图7. (a)在缓慢松弛环境中, 扩散距离r的物体在一定时间t内的位移分布可以用非高斯概率分布函数Gs(r,t)来描述, 该函数可以分解为一组基本扩散高斯过程(白曲线)[64]. (b)推测的在中心极限定理要求的高斯行为出现时间τclt, 菲克扩散出现的时间τFick, 环境的平均弛豫时间<τenv>及其波动范围之间的关系. (c)胶体球沿着半径接近的线性磷脂双层管扩散示意图, 以及相应布朗的均方位移与非高斯的位移概率密度分布函数[53]. (d)胶体球在缠结纤维型肌动蛋白网格中扩散的示意图, 以及相应布朗的均方位移与反常位移概率密度分布函数. (e)粗棒在聚合物网络中扩散的示意图, 不同棒长粒子的均方位移, 其中棒长与网格尺寸比为整数倍的粒子长时间呈现布朗行为, 以及对应棒长下非高斯的概率密度分布函数[65]

Figure 7. (a) In slow relaxation environment, displacement distribution of an object with a diffusion distance r at a certain time t can be described by the non-Gaussian probability distribution function Gs(r,t), which can be decomposed into a set of basic diffusion Gaussian processes (white curves)[64]. (b) The relationship between appearance time of Gaussian behavior τclt, Fick diffusion τFick, average relaxation time of environment <τenv> and its fluctuation range. (c) Schematic representation of colloidal beads spreading along linear phospholipid bilayers with close radius, and the corresponding Brownian MSD and non-Gaussian DPDF[53]. (d) Schematic representation of the diffusion of colloidal beads in an entangled fiber-type actin grid, and the corresponding Brownian MSD versus abnormal DPDF. (e) Schematic representation of coarse rod diffusion in polymer network, MSD of different rod length particles. When the rod length to grid size is an integer multiple, the particle presents Brownian behavior, and the non-Gaussian DPDF under the corresponding rod length[65]

图8. (a)脂质体在纤维肌动蛋白丝向列相溶液中扩散的对数均方位移. 方向平行于肌动蛋白丝的结果(开圆和青色线), 方向垂直于肌动蛋白丝的结果(填充圆和橙色线), 没有肌动蛋白的水中脂质体的结果(虚线), 以及从(b)中所示的位移概率分布的尾部推断出的假设的结果(灰色符号). (b)相应体系下的位移概率分布, 符号与(a)中相同. (c)体系中脂质体扩散的扩散系数的概率分布P(D), 通过脂质体位移的非高斯概率分布计算的, 对于垂直于肌动蛋白丝(黄色)和平行(青色)的运动的结果. 其中垂直线表示平均扩散系数. (d)为(c)结果绘制于对数坐标的情况. 其中垂直线区分了“慢”尖峰和“快”宽峰, 这表明了间歇性作用于脂质体的独立扩散过程[64]

Figure 8. (a) Log mean square displacement of liposome diffusion in a nematic solution of F-actin filaments. Direction parallel to the actin filament results (open circles and cyan lines), direction perpendicular to the actin filament results (filled circles and orange lines), results of liposomes in water without actin (dashed lines), and the hypothesis inferred from the tail of the displacement probability distribution shown in (b) (gray symbol). (b) Displacement probability distribution under the corresponding system, with the same symbol as in (a). (c) Probability distribution P(D) of the diffusion coefficient of liposome diffusion in the system, calculated from a non-Gaussian probability distribution of liposome displacement, for motions perpendicular to actin filaments (yellow) and parallel (cyan). The vertical line represents the average diffusion coefficient. (d) For (c) results plotted in logarithmic coordinates. Where the vertical lines distinguish the "slow" sharp and "fast" broad peaks, which indicates an independent diffusion process acting intermittently on the liposomes[64]

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生物大分子介质中的反常扩散动力学理论^★

Theory of Anomalous Diffusion Dynamics in Biomacromolecular Media^★

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生物大分子介质中的反常扩散动力学理论★

Theory of Anomalous Diffusion Dynamics in Biomacromolecular Media★

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生物大分子介质中的反常扩散动力学理论^★

Theory of Anomalous Diffusion Dynamics in Biomacromolecular Media^★