Biomembranes, which are primarily composed of lipid bilayers, are not merely passive barriers, but dynamic, complex materials whose shapes are governed by the principles of soft-matter physics. This review examines the shape problem in biomembranes from the perspectives of materials science and liquid-crystal theory. We apply the Helfrich elastic model to the biomembrane shape in an electromagnetic field, and we extend the Helfrich free energy to multilayer systems, drawing parallels between the focal-conic structures of smectic liquid crystals and the geometries of fullerenes, carbon nanotubes, and the icosahedral virus. The review concludes by highlighting the unifying power of continuum elastic theories in describing a wide range of membrane morphologies across biological and synthetic systems.

The F1-ATPase and V1-ATPase are rotary biomotors. Alignment of their amino acid sequences, which originate from bovine heart mitochondria (1BMF) and Enterococcus hirae (3VR6), respectively, demonstrates that the segment forming the ATP catalytic pocket is highly conserved. Single-molecule experiments, however, have revealed subtle differences in efficiency between the F1 and V1 motors. Here, we perform both atomistic and coarse-grained molecular dynamics simulations to investigate the mechanochemical coupling and coordination in F1 and V1 ATPase. Our results show that the correlation between conformational changes in F1 is stronger than that in V1, indicating that the mechanochemical coupling in F1 is tighter than in V1. Moreover, the unidirectional rotation of F1 is more processive than that of V1, which accounts for the higher efficiency observed in F1 and explains the occasional backward steps detected in single-molecule experiments on V1.

Colloidal crystals permeated by mobile ions exhibit a coupling between electrostatic and elastic degrees of freedom that renormalizes the effective screening length and induces wave-vector-dependent elastic softening. Building on a recently proposed continuum model [Commun. Theor. Phys. 77, 055602 (2025)], we perform a rigorous Gaussian fluctuation analysis to elucidate the stability limits of the homogeneous phase. By integrating out the electrostatic fluctuations, we derive the effective elastic modulus Γ(q) as a function of wave vector q. We show that the long-wavelength modulus Γ(0) remains identically equal to the bare modulus βK, protected by perfect ionic screening. In contrast, the short-wavelength modulus Γ(q→∞) = βK(1-ξ) softens as the electrostatic-elastic coupling ξ≡ 2βn_0 v_0^2 K increases, vanishing at a critical value ξ=1. For ξ>1, the fluctuation spectrum exhibits a negative eigenvalue for all wave vectors q > q_c = κ_0/√(ξ-1), signaling an ultraviolet instability of the uniform phase. In a real colloidal crystal, this divergence is regulated by the discrete lattice cutoff q_max/a, confining the physical instability to a finite band q_c < q < q_max. The macroscopic limit q→ 0 remains unconditionally stable for all ξ. The transition at ξ=1 thus marks the onset of short-wavelength mechanical failure, while macroscopic elastic stiffness remains intact. Our analysis clarifies the proper physical interpretation of the minimal coupling model and provides a consistent picture of how non-DLVO interactions can drive local structural collapse in charged colloidal crystals.

Biological membranes are the quintessential functional interface of life, where lipid bilayer mechanics, compositional heterogeneity, and dynamic protein interactions converge to govern cellular physiology [...]

Charged colloidal crystals exhibit a subtle interplay between electrostatic screening and elastic deformation. When an isotropic electrostatic volumetric softening acts on an anisotropic elastic background, the longitudinal acoustic response softens preferentially along specific crystallographic axes. This article provides a self-contained derivation of the long-wavelength acoustic stability condition for cubic crystals subject to a generic electrostatic-elastic coupling. Starting from an effective static elastic tensor renormalized by a scalar coupling constant λg, we obtain an explicit condition for the onset of a long-wavelength acoustic instability: the direction k̂ that first loses strong ellipticity is determined by the inverse Christoffel matrix evaluated along that direction. Closed-form expressions for the critical coupling λgc are given for the [100], [110], and [111] high-symmetry directions. We further provide a microscopic derivation of λg from the Poisson-Boltzmann theory in a spherical Wigner-Seitz cell, linking the phenomenological constant to experimentally accessible parameters, such as salt concentration, particle charge, and volume fraction. The analysis reveals that the most fragile direction can be identified without full lattice-dynamical calculations, and the associated unstable strain patterns are discussed. We also compare these acoustic thresholds with the Born stability condition for homogeneous volume change and show that, for a Born-stable reference cubic crystal, the volume mode becomes unstable before any directional acoustic mode, provided that homogeneous dilation is admissible. Numerical illustrations using representative modulus values reported for soft colloidal assemblies illustrate how the criterion can be applied to predict directional softening trends. The present framework serves as a diagnostic tool for interpreting directional anomalies in static compressibility or low-frequency acoustic softening.

Helfrich's liquid crystal membrane theory successfully establishes a quantitative framework for describing biomembrane morphology by combining surface differential geometry with membrane elasticity mechanics, laying the foundation for the physics of biomembranes. The Zhong-Can-Helfrich equation provides a central mathematical tool for this theory, enabling the analytical solution of complex biological shapes such as the biconcave disk of red blood cells and promoting theoretical predictions and experimental validations of various membrane structures, including toroidal vesicles. This review article focuses on analytical solutions of the Zhong-Can-Helfrich shape equation for fluid membranes. We also review applications of this equation to membranes with open boundaries and to multisphere solutions of the equation relevant to myelin formation in red blood cells. At the end of this paper, the membrane shape of red blood cells in a vessel is studied for slow blood velocity, and it is found that conical red blood cells can exist in flowing blood.

Cell membranes contain a variety of biomolecules, especially various kinds of lipids and proteins, which constantly change with fluidity and environmental stimuli. Though Helfrich curvature elastic energy has successfully explained many phenomena for single-component membranes, a new theoretical framework for multicomponent membranes is still a challenge. In this work, we propose a generalized Helfrich free-energy functional describe equilibrium shapes and phase behaviors related to membrane heterogeneity with via curvature-component coupling in a unified framework. For multicomponent membranes, a new but important Laplace-Beltrami operator is derived from the variational calculation on the integral of Gaussian curvature and applied to explain the spontaneous nanotube formation of an asymmetric glycolipid vesicle. Therefore, our general mathematical framework shows a predictive capabilities beyond the existing multicomponent membrane models. The set of new curvature-component coupling EL equations have been derived for global vesicle shapes associated with the composition redistribution of multicomponent membranes for the first time and specified into several typical geometric shape equations. The equilibrium radii of isotonic vesicles for both spherical and cylindrical geometries are calculated. The analytical solution for isotonic vesicles reveals that membrane stability requires distinct elastic moduli among components (kA≠kB, k¯A≠k¯B), which is consistent with experimental observations of coexisting lipid domains. Furthermore, we elucidate the biophysical implications of the derived shape equations, linking them to experimentally observed membrane remodeling processes. Our new free-energy framework provides a baseline for more detailed microscopic membrane models.

A mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloidal crystals is subject to an electrostatic-elastic coupling,which we study on the continuum level by introducing a minimal coupling between electrostatic and displacement fields.We derive linearized,Debye-Hückel-like mean-field equations that can be analytically solved,incorporating the minimal coupling between electrostatic and displacement fields leading to an additional effective attractive interaction between mobile charges that depends in general on the strength of the coupling between the electrostatic and displacement fields.By analyzing the Gaussian fluctuations around the mean-field solution we also identify and quantify the region of its stability in terms of the electrostatic-elastic screening length.This detailed continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges provides a baseline to investigate the electrostatic-elastic coupling for microscopic models in colloid science and materials science.

In this work, we construct a multiple solutions theory based on a membrane shape equation. The membrane shape of a vesicle or a red blood cell is determined using the Zhongcan–Helfrich shape equation. These spherical solutions, which have an identical radius rs but different center positions, can be described by the same equation: ϕ−ρ/rs=0. A degeneracy for the spherical solutions exists, leading to multisphere solutions with the same radius. Therefore, there can be multiple solutions for the sphere equilibrium shape equation, and these need to satisfy a quadratic equation. The quadratic equation has a maximum of two roots. We also find that the multiple solutions should be in a line to undergo rotational symmetry. We use the quadratic equation to compute the sphere radius, together with a membrane surface constraint condition, to obtain the number of small spheres. We ensure matching with the energy constraint condition to determine the stability of the full solutions. The method is then extended into the myelin formation of red blood cells. Our numerical calculations show excellent agreement with the experimental results and enable the comprehensive investigation of cell fission and fusion phenomena. Additionally, we have predicted the existence of the bifurcation phenomenon in membrane growth and proposed a control strategy.

Electrostatic-elastic coupling in colloidal crystals, composed of a mobile Coulomb gas permeating a fixed background crystalline lattice of charged colloids, is studied on the continuum level in order to analyze the lattice-mediated interactions between mobile charges. The linearized, Debye-Huckel-like mean-field equations incorporating a minimal coupling between electrostatic and displacement fields imply an additional effective attractive interaction between mobile charges. For small screening lengths, the interactions between like mobile charges exhibit colloid-lattice-mediated effective interaction, ranging from weak to strong attraction, while for large screening lengths the lattice-mediated interaction is purely repulsive. Continuum theory incorporating the standard lattice elasticity and electrostatics of mobile charges, augmented by the minimal electrostatic-elastic coupling terms, can serve as a baseline for more detailed microscopic models. Copyright (c) 2024 EPLA All rights, including for text and data mining, AI training, and similar technologies, are reserved.

We have extended the Helfrich's spontaneous curvature model of the equilibrium vesicle by adding the interaction between magnetic field and the constituent molecules to supply an explaination in principle of the emerging manipulated deformation of a magnetic vesicles such as the reversibly deformation of artificial stomatocyte. The small deformation can be measured by birefringence. Here, we present the derivations of formulas in detailed to reveal the perturbation of deformation psi under two cases. New features, for example, a 'phase transition' of shape will occur with increasing of B from B(1)(*)B1* for Delta chi < 0, in which the major axis of ellipse was rotated by 90 degrees, have been revealed. It is worthy for experimenter to demonstrate the 'phase transition'. The significance of imaginary relation (B-1(*) < B < B-2*) is also waiting to be uncovered.

ATP synthase (FoF1-ATPase) is the model rotary molecular motor with three sites of ATP syntheses/hydrolyses in the “stator” of F1. The coupling between chemical progress and mechanical one is tight, and both progresses are reversible. Thus, the mechanochemical reversibility of FoF1-ATPase may resemble that of a heat engine. Single-molecule experiment has demonstrated that the efficiency of rotary motor is nearly 100%. However, it is impossible for a heat engine to achieve such high efficiency. On the other hand, kinesin is the model linear biomotor with only two sites of ATP hydrolyses located in the two heads, respectively, while its efficiency is just [Formula: see text]. Myosin V is another processive linear motor with nearly [Formula: see text] efficiency as well. However, the chemical progress of processive linear motors with two heads is irreversible. That is, if they walk backward in hand over hand along with a track by an external force, the energy molecule ATP is not synthesized, but consumed yet. This chemical irreversibility excludes the possibility that kinesin/myosin V can be treated energetically as a heat engine. The most intriguing fact is why the efficiency of a processive linear motor with two sites is just [Formula: see text] of that of a processive rotary motor with three sites.

We develop a minimal phenomenological model to describe the auxetic response recently observed in liquid crystal elastomers, and further determine by theoretical calculation the critical condition required for the auxetic response to occur.

Looking Beyond the Frontiers of Science, pp. 67-86 (2022) No AccessBiological Liquid Crystal Research and K.K. Phua's Visionary SupportZhong-can OuyangZhong-can OuyangInstitute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, Chinahttps://doi.org/10.1142/9789811263699_0013Cited by:0 PreviousNext AboutSectionsPDF/EPUB ToolsAdd to favoritesDownload CitationsTrack CitationsRecommend to Library ShareShare onFacebookTwitterLinked InRedditEmail Abstract: In 2021, there were two major events in the Chinese scientific community: Chinese scholars all over the world held celebrations for the centennial birthday of Dr. C.N. Yang and for the 95-year birthday of Dr. T. D. Lee, both being the first Chinese Nobel laureates (in 1957) and world-renowned physicists. During these events, I was invited to write two commemorative articles, Dr. Yang's support for the interdisciplinary science of physics and biology in China (published officially by the Institute of Advanced Research, Tsinghua University, 2021-10-20), and Dr. Lee and statistical mechanics (published in Modern Physics (in Chinese), 2021, 33(5): 40–50). These two events were heavily reported in media. Another great event, however, was rarely reported but also definitely worth remembering: the 40th anniversary of World Scientific Publishing Company (WSPC), the largest academic publishing company in the Asia Pacific region, which was founded by Prof. K.K. Phua. Since the establishment of WSPC, Prof. Phua has worked closely with top publishing houses and famous scholars in China for a long time, and is committed to introducing the academic achievements of Chinese scholars to the world. Therefore, he was the only Chinese who received recognition from 15 winners from 14 countries at the ceremony of the 15th China Book Special Contribution Award (Beijing, September 14, 2021). As the beneficiary of his great contributions, I would like to take this opportunity that celebrates Phua's 80th birthday to express my deepest respect for him… FiguresReferencesRelatedDetails Looking Beyond the Frontiers of ScienceMetrics History PDF download

软物质是广泛存在于自然界并与我们日常生活息息相关的物质体系,泛指处于固体和理想流体之间的复杂凝聚态物质,主要共同点是其基本单元之间的相互作用比较弱(约为室温热能量级),熵效应显著,且易形成有序结构.自20世纪90年代以来,在大批新型实验技术和理论方法的推动下,软物质物理学得以快速发展.基础研究方面,已经提炼出具有复杂相互作用的软物质系统的一些共性,在复杂有序结构的观测、结构形成的热力学和动力学机制等方面已取得重要的实验和理论进展.应用方面,平板显示、智能软材料、高性能新材料/新器件(如高强度碳纤维、复合材料、软性可穿戴太阳能电池等)、环保问题(如雾霾控制、水资源保护)、环保智能型建筑材料的开发以及生物医药相关研究领域的创新等,都与软物质研究直接相关.

The fidelity of DNA transcription catalyzed by RNA polymerase (RNAP) has long been an important issue in biology. Experiments have revealed that RNAP can incorporate matched nucleotides selectively and proofread the incorporated mismatched nucleotides. However, systematic theoretical researches on RNAP fidelity are still lacking. In the last decade, several theories on RNA transcription have been proposed, but they only handled highly simplified models without considering the high-order neighbor effects and the oligonucleotides cleavage both of which are critical for the overall fidelity. In this paper, we regard RNA transcription as a binary copolymerization process and calculate the transcription fidelity by the steady-state copolymerization theory recently proposed by us for DNA replication. With this theory, the more realistic models considering higher-order neighbor effects, oligonucleotides cleavage, multi-step incorporation and multi-step cleavage can be rigorously handled.

The high fidelity of DNA polymerase (DNAP) is critical for the faithful replication of DNA. There are several quantitative approaches to measure DNAP fidelity. Directly counting the error frequency in the replication products gives the true fidelity but it turns out very hard to implement in practice. Two biochemical kinetic approaches, the steady-state assay and the transient-state assay, were then suggested and widely adopted. In these assays, the error frequency is indirectly estimated by using kinetic theories combined with the measured apparent kinetic rates. However, whether it is equivalent to the true fidelity has never been clarified theoretically, and in particular there are different strategies using these assays to quantify the proofreading efficiency of DNAP but often lead to inconsistent results. In this paper, we make a comprehensive examination on the theoretical foundation of the two kinetic assays, based on the theory of DNAP fidelity recently proposed by us. Our studies show that while the conventional kinetic assays are generally valid to quantify the discrimination efficiency of DNAP, they are valid to quantify the proofreading efficiency of DNAP only when the kinetic parameters satisfy some constraints which will be given explicitly in this paper.These results may inspire more carefully-designed experiments to quantify DNAP fidelity.

DNA replication is a high-fidelity information-copying processes which is realized by DNA polymerase (DNAP). The high fidelity was explained on the basis of the well-known kinetic-proofreading mechanism (KPR), under which the so-called fidelity-speed trade-off was studied theoretically. However, numerous biochemical experiments have shown that the high fidelity of DNA replication is achieved due to the initial discrimination of polymerase domain of DNAP, as well as the proofreading of the exonuclease domain of DNAP. This exonuclease-proofreading mechanism (EPR) is totally different from KPR. So the trade-off issues are worth being re-examined under EPR. In this paper, we use the first-passage method recently proposed by us to discuss the possible trade-offs in DNA replication under EPR. We show that there could be no fidelity-speed trade-off under EPR, i.e., the fidelity and the speed can be simultaneously enhanced by EPR in a large range of kinetic parameters. This provides a new perspective to understand the experimental data of the exonuclease activity of T7 DNAP and T4 DNAP. We also show that there exists the fidelity-proofreading cost trade-off, i.e., the fidelity is enhanced at the cost of increasing the futile hydrolysis of dNTP. A possible way to avoid this trade-off is to regulate the rate of DNAP translocation: slowing down the forward translocation (in the presence of the terminal mismatch) can enhance the fidelity without changing the speed and the proofreading cost. Our theoretical analysis offers deeper insights on the kinetics-function relation of DNAP. PACS numbers: 82.39.-k, 87.15.Rn, 87.16.A-

A unified model is constructed to study the recently observed DNA entropic elasticity, cooperative extensibility, and supercoiling property. With the introduction of a new structural parameter (the folding angle ϕ), bending deformations of sugar-phosphate backbones, steric effects of nucleotide basepairs, and short-range basestacking interactions are considered. The comprehensive agreement of theoretical results with experimental observations on both torsionally relaxed and negatively supercoiled DNAs strongly indicates that, basestacking interactions, although short-ranged in nature, dominate the elasticity of DNA and hence are of vital biological significance.

值李政道先生九十五华诞之际,《现代物理知识》杂志邀请笔者介绍李先生在统计力学方面的贡献.作为李先生一手倡导并建立的国内博士后制度的首批受益人,笔者深感荣幸.李先生是20世纪后半叶国际高能物理学界备受尊崇的领袖之一,他在宇称不守恒等方面的伟大研究成就已载入物理学史册,不仅被学界、也为一般读者所熟知.对李先生在物理学其他方向的贡献,国内大众媒体或一般科普读物上则少有提及或语焉不详.笔者愿借此机会,对李先生在统计力学方面的开创性成果及历史意义做稍微详细一点的科普介绍.统计力学是研究宏观系统的学问,迥异于粒子物理学研究的微观世界.纵观20世纪物理学史,能在相去如此悬殊的学术方向上都作出令人仰望的成就的,李先生是少有的几位物理学大师之一.