It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field of heterogeneous anomalous transport (HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction–diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

中文翻译：

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细胞和分子生物学中的异质异常运输


众所周知，细胞和分子生物学中的多种现象都涉及异常运输，例如异常运输。细胞和分子运动的统计数据是分数的，不符合简单扩散或弹道运输的原型。最近的研究表明，异常传输在许多情况下在时间和空间上都是异质的。因此，单一的反常指数和单一的广义扩散系数无法令人满意地描述细胞和分子生物学中的许多关键现象。我们重点考虑异质异常输运（HAT）领域的进展：实验技术（单分子方法、显微镜、图像分析、荧光相关光谱、非弹性中子散射和核磁共振）、数据分析的理论工具（稳健的统计方法）例如首次通过概率、生存分析、不同种类的均方位移等）、基于模拟的解析理论和生成理论模型。特别强调基于机器学习和神经网络的高通量分析技术。此外，我们还考虑了微流变学和复杂流体的非均质粘弹性背景下的异常传输。反应扩散系统波前的 HAT 也被考虑，因为它在形态发生和信号传导中发挥着重要作用。此外，我们还提供了细胞生物学的具体例子，包括胚胎细胞、白细胞、癌细胞、细菌细胞、细菌生物膜和真核微生物。分子生物学的案例研究包括 DNA、膜、内体运输、内质网、粘蛋白、球状蛋白和淀粉样蛋白。