Helices are one of the most frequently encountered symmetries in biological assemblies. Helical symmetry has been exploited in electron microscopic studies as a limited number of filament images, in principle, can provide all the information needed to do a three-dimensional reconstruction of a polymer. Over the past 25 years, three-dimensional reconstructions of helical polymers from cryo-EM images have shifted completely from Fourier–Bessel methods to single-particle approaches. The single-particle approaches have allowed people to surmount the problem that very few biological polymers are crystalline in order, and despite the flexibility and heterogeneity present in most of these polymers, reaching a resolution where accurate atomic models can be built has now become the standard. While determining the correct helical symmetry may be very simple for something like F-actin, for many other polymers, particularly those formed from small peptides, it can be much more challenging. This review discusses why symmetry determination can be problematic, and why trial-and-error methods are still the best approach. Studies of many macromolecular assemblies, such as icosahedral capsids, have usually found that not imposing symmetry leads to a great reduction in resolution while at the same time revealing possibly interesting asymmetric features. We show that for certain helical assemblies asymmetric reconstructions can sometimes lead to greatly improved resolution. Further, in the case of supercoiled flagellar filaments from bacteria and archaea, we show that the imposition of helical symmetry can not only be wrong, but is not necessary, and obscures the mechanisms whereby these filaments supercoil.

Graph theory, a branch of mathematics that focuses on the study of graphs (networks of nodes and edges), provides a robust framework for analysing the structural and functional properties of biomolecules. By leveraging molecular dynamics (MD) simulations, atoms or groups of atoms can be represented as nodes, while their dynamic interactions are depicted as edges. This network-based approach facilitates the characterization of properties such as connectivity, centrality, and modularity, which are essential for understanding the behaviour of molecular systems. This review details the application and development of graph theory-based models in studying biomolecular systems. We introduce key concepts in graph theory and demonstrate their practical applications, illustrating how innovative graph theory approaches can be employed to design biomolecular systems with enhanced functionality. Specifically, we explore the integration of graph theoretical methods with MD simulations to gain deeper insights into complex biological phenomena, such as allosteric regulation, conformational dynamics, and catalytic functions. Ultimately, graph theory has proven to be a powerful tool in the field of molecular dynamics, offering valuable insights into the structural properties, dynamics, and interactions of molecular systems. This review establishes a foundation for using graph theory in molecular design and engineering, highlighting its potential to transform the field and drive advancements in the understanding and manipulation of biomolecular systems.

Fluorescence correlation spectroscopy (FCS) is a well-known and established non-invasive method for quantification of physical parameters that preside over molecular mechanisms and dynamics. It combines maximum sensitivity and statistical confidence for the analysis of speed, size, and number of fluorescent molecules and interactions with surrounding molecules by time-averaging fluctuation analysis in a well-defined volume element. The narrow compass of this study is to acquaint the basic principle of diffusion and the FCS method in general regarding variable magnitudes and standardization adjustment. In this review, we give a theoretical introduction, examples of experimental applications, and utensils in solution systems with future perspectives.

Single-molecule techniques to analyze proteins and other biomolecules involving labels and tethers have allowed for new understanding of the underlying biophysics; however, the impact of perturbation from the labels and tethers has recently been shown to be significant in several cases. New approaches are emerging to measure single proteins through light scattering without the need for labels and ideally without tethers. Here, the approaches of interference scattering, plasmonic scattering, microcavity sensing, nanoaperture optical tweezing, and variants are described and compared. The application of these approaches to sizing, oligomerization, interactions, conformational dynamics, diffusion, and vibrational mode analysis is described. With early commercial successes, these approaches are poised to have an impact in the field of single-molecule biophysics.

The parallel and synergistic developments of atomic resolution structural information, new spectroscopic methods, their underpinning formalism, and the application of sophisticated theoretical methods have led to a step function change in our understanding of photosynthetic light harvesting, the process by which photosynthetic organisms collect solar energy and supply it to their reaction centers to initiate the chemistry of photosynthesis. The new spectroscopic methods, in particular multidimensional spectroscopies, have enabled a transition from recording rates of processes to focusing on mechanism. We discuss two ultrafast spectroscopies – two-dimensional electronic spectroscopy and two-dimensional electronic-vibrational spectroscopy – and illustrate their development through the lens of photosynthetic light harvesting. Both spectroscopies provide enhanced spectral resolution and, in different ways, reveal pathways of energy flow and coherent oscillations which relate to the quantum mechanical mixing of, for example, electronic excitations (excitons) and nuclear motions. The new types of information present in these spectra provoked the application of sophisticated quantum dynamical theories to describe the temporal evolution of the spectra and provide new questions for experimental investigation. While multidimensional spectroscopies have applications in many other areas of science, we feel that the investigation of photosynthetic light harvesting has had the largest influence on the development of spectroscopic and theoretical methods for the study of quantum dynamics in biology, hence the focus of this review. We conclude with key questions for the next decade of this review.

Structure-switching aptamers have become ubiquitous in several applications, notably in analytical devices such as biosensors, due to their ease of supporting strong signaling. Aside from their ability to bind specifically with their respective target, this class of aptamers also undergoes a conformational rearrangement upon target recognition. While several well-studied and early-developed aptamers (e.g., cocaine, ATP, and thrombin) have been found to have this structure-switching property, the vast majority do not. As a result, it is common to try to engineer aptamers into switches. This proves challenging in part because of the difficulty in obtaining structural and functional information about aptamers. In response, we review various readily available biophysical characterization tools that are capable of assessing structure switching of aptamers. In doing so, we delve into the fundamentals of these different techniques and detail how they have been utilized in characterizing structure-switching aptamers. While each of these biophysical techniques alone has utility, their real power to demonstrate the occurrence of structural change with ligand binding is when multiple techniques are used. We hope that through a deeper understanding of these techniques, researchers will be better able to acquire biophysical information about their aptamer–ligand systems and accelerate the translation of aptamers into biosensors.

Solving the mechanism of a chemical reaction requires determining the structures of all the ground states on the pathway and the elusive transition states linking them. 2024 is the centenary of Brønsted’s landmark paper that introduced the β-value and structure-activity studies as the only experimental means to infer the structures of transition states. It involves making systematic small changes in the covalent structure of the reactants and analysing changes in activation and equilibrium-free energies. Protein engineering was introduced for an analogous procedure, Φ-value analysis, to analyse the noncovalent interactions in proteins central to biological chemistry. The methodology was developed first by analysing noncovalent interactions in transition states in enzyme catalysis. The mature procedure was then applied to study transition states in the pathway of protein folding – ‘part (b) of the protein folding problem’. This review describes the development of Φ-value analysis of transition states and compares and contrasts the interpretation of β- and Φ-values and their limitations. Φ-analysis afforded the first description of transition states in protein folding at the level of individual residues. It revealed the nucleation-condensation folding mechanism of protein domains with the transition state as an expanded, distorted native structure, containing little fully formed secondary structure but many weak tertiary interactions. A spectrum of transition states with various degrees of structural polarisation was then uncovered that spanned from nucleation-condensation to the framework mechanism of fully formed secondary structure. Φ-analysis revealed how movement of the expanded transition state on an energy landscape accommodates the transition from framework to nucleation-condensation mechanisms with a malleability of structure as a unifying feature of folding mechanisms. Such movement follows the rubric of analysis of classical covalent chemical mechanisms that began with Brønsted. Φ-values are used to benchmark computer simulation, and Φ and simulation combine to describe folding pathways at atomic resolution.

Cell segregation caused by collective cell migration (CCM) is crucial for morphogenesis, functional development of tissue parts, and is an important aspect in other diseases such as cancer and its metastasis process. Efficiency of the cell segregation depends on the interplay between: (1) biochemical processes such as cell signaling and gene expression and (2) physical interactions between cells. Despite extensive research devoted to study the segregation of various co-cultured systems, we still do not understand the role of physical interactions in cell segregation. Cumulative effects of these physical interactions appear in the form of physical parameters such as: (1) tissue surface tension, (2) viscoelasticity caused by CCM, and (3) solid stress accumulated in multicellular systems. These parameters primarily depend on the interplay between the state of cell–cell adhesion contacts and cell contractility. The role of these physical parameters on the segregation efficiency is discussed on model systems such as co-cultured breast cell spheroids consisting of two subpopulations that are in contact. This review study aims to: (1) summarize biological aspects related to cell segregation, mechanical properties of cell collectives, effects along the biointerface between cell subpopulations and (2) describe from a biophysical/mathematical perspective the same biological aspects summarized before. So that overall it can illustrate the complexity of the biological systems that translate into very complex biophysical/mathematical equations. Moreover, by presenting in parallel these two seemingly different parts (biology vs. equations), this review aims to emphasize the need for experiments to estimate the variety of parameters entering the resulting complex biophysical/mathematical models.

Optogenetics, the use of microbial rhodopsins to make the electrical activity of targeted neurons controllable by light, has swept through neuroscience, enabling thousands of scientists to study how specific neuron types contribute to behaviors and pathologies, and how they might serve as novel therapeutic targets. By activating a set of neurons, one can probe what functions they can initiate or sustain, and by silencing a set of neurons, one can probe the functions they are necessary for. We here review the biophysics of these molecules, asking why they became so useful in neuroscience for the study of brain circuitry. We review the history of the field, including early thinking, early experiments, applications of optogenetics, pre-optogenetics targeted neural control tools, and the history of discovering and characterizing microbial rhodopsins. We then review the biophysical attributes of rhodopsins that make them so useful to neuroscience – their classes and structure, their photocycles, their photocurrent magnitudes and kinetics, their action spectra, and their ion selectivity. Our hope is to convey to the reader how specific biophysical properties of these molecules made them especially useful to neuroscientists for a difficult problem – the control of high-speed electrical activity, with great precision and ease, in the brain.

Although viral protein structure and replication mechanisms have been explored extensively with X-ray crystallography, cryo-electron microscopy, and population imaging studies, these methods are often not able to distinguish dynamic conformational changes in real time. Single-molecule fluorescence resonance energy transfer (smFRET) offers unique insights into interactions and states that may be missed in ensemble studies, such as nucleic acid or protein structure, and conformational transitions during folding, receptor–ligand interactions, and fusion. We discuss the application of smFRET to the study of viral protein conformational dynamics, with a particular focus on viral glycoprotein dynamics, viral helicases, proteins involved in HIV reverse transcription, and the influenza RNA polymerase. smFRET experiments have played a crucial role in deciphering conformational changes in these processes, emphasising the importance of smFRET as a tool to help elucidate the life cycle of viral pathogens and identify key anti-viral targets.

Ferric heme b (= ferric protoporphyrin IX = hemin) is an important prosthetic group of different types of enzymes, including the intensively investigated and widely applied horseradish peroxidase (HRP). In HRP, hemin is present in monomeric form in a hydrophobic pocket containing among other amino acid side chains the two imidazoyl groups of His170 and His42. Both amino acids are important for the peroxidase activity of HRP as an axial ligand of hemin (proximal His170) and as an acid/base catalyst (distal His42). A key feature of the peroxidase mechanism of HRP is the initial formation of compound I under heterolytic cleavage of added hydrogen peroxide as a terminal oxidant. Investigations of free hemin dispersed in aqueous solution showed that different types of hemin dimers can form, depending on the experimental conditions, possibly resulting in hemin crystallization. Although it has been recognized already in the 1970s that hemin aggregation can be prevented in aqueous solution by using micelle-forming amphiphiles, it remains a challenge to prepare hemin-containing micellar and vesicular systems with peroxidase-like activities. Such systems are of interest as cheap HRP-mimicking catalysts for analytical and synthetic applications. Some of the key concepts on which research in this fascinating and interdisciplinary field is based are summarized, along with major accomplishments and possible directions for further improvement. A systematic analysis of the physico-chemical properties of hemin in aqueous micellar solutions and vesicular dispersions must be combined with a reliable evaluation of its catalytic activity. Future studies should show how well the molecular complexity around hemin in HRP can be mimicked by using micelles or vesicles. Because of the importance of heme b in virtually all biological systems and the fact that porphyrins and hemes can be obtained under potentially prebiotic conditions, ideas exist about the possible role of heme-containing micellar and vesicular systems in prebiotic times.

The cardiac sarcomere is a cellular structure in the heart that enables muscle cells to contract. Dozens of proteins belong to the cardiac sarcomere, which work in tandem to generate force and adapt to demands on cardiac output. Intriguingly, the majority of these proteins have significant intrinsic disorder that contributes to their functions, yet the biophysics of these intrinsically disordered regions (IDRs) have been characterized in limited detail. In this review, we first enumerate these myofilament-associated proteins with intrinsic disorder (MAPIDs) and recent biophysical studies to characterize their IDRs. We secondly summarize the biophysics governing IDR properties and the state-of-the-art in computational tools toward MAPID identification and characterization of their conformation ensembles. We conclude with an overview of future computational approaches toward broadening the understanding of intrinsic disorder in the cardiac sarcomere.

Nanofluidic structures have over the last two decades emerged as a powerful platform for detailed analysis of DNA on the kilobase pair length scale. When DNA is confined to a nanochannel, the combination of excluded volume and DNA stiffness leads to the DNA being stretched to near its full contour length. Importantly, this stretching takes place at equilibrium, without any chemical modifications to the DNA. As a result, any DNA can be analyzed, such as DNA extracted from cells or circular DNA, and it is straight-forward to study reactions on the ends of linear DNA. In this comprehensive review, we first give a thorough description of the current understanding of the polymer physics of DNA and how that leads to stretching in nanochannels. We then describe how the versatility of nanofabrication can be used to design devices specifically tailored for the problem at hand, either by controlling the degree of confinement or enabling facile exchange of reagents to measure DNA–protein reaction kinetics. The remainder of the review focuses on two important applications of confining DNA in nanochannels. The first is optical DNA mapping, which provides the genomic sequence of intact DNA molecules in excess of 100 kilobase pairs in size, with kilobase pair resolution, through labeling strategies that are suitable for fluorescence microscopy. In this section, we highlight solutions to the technical aspects of genomic mapping, including the use of enzyme-based labeling and affinity-based labeling to produce the genomic maps, rather than recent applications in human genetics. The second is DNA–protein interactions, and several recent examples of such studies on DNA compaction, filamentous protein complexes, and reactions with DNA ends are presented. Taken together, these two applications demonstrate the power of DNA confinement and nanofluidics in genomics, molecular biology, and biophysics.

The advent of single-molecule force spectroscopy represents the introduction of forces, torques, and displacements as controlled variables in biochemistry. These methods afford the direct manipulation of individual molecules to interrogate the forces that hold together their structure, the forces and torques that these molecules generate in the course of their biochemical reactions, and the use of force, torque, and displacement as tools to investigate the mechanisms of these reactions. Because of their microscopic nature, the signals detected in these experiments are often dominated by fluctuations, which, in turn, play an important role in the mechanisms that underlie the operation of the molecular machines of the cell. Their direct observation and quantification in single-molecule experiments provide a unique window to investigate those mechanisms, as well as a convenient way to investigate fundamental new fluctuation theorems of statistical mechanics that bridge the equilibrium and non-equilibrium realms of this discipline. In this review we have concentrated on the developments that occurred in our laboratory on the characterization of biopolymers and of molecular machines of the central dogma. Accordingly, some important areas like the study of cytoskeletal motors have not been included. While we adopt at times an anecdotal perspective with the hope of conveying the personal circumstances in which these developments took place, we have made every effort, nonetheless, to include the most important developments that were taking place at the same time in other laboratories.

Biophysical studies have a very high impact on the understanding of internalization, molecular mechanisms, interactions, and localization of CPPs and CPP/cargo conjugates in live cells or in vivo. Biophysical studies are often first carried out in test-tube set-ups or in vitro, leading to the complicated in vivo systems. This review describes recent studies of CPP internalization, mechanisms, and localization. The multiple methods in these studies reveal different novel and important aspects and define the rules for CPP mechanisms, hopefully leading to their improved applicability to novel and safe therapies.