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.

Proteins are vital biological macromolecules that execute biological functions and form the core of synthetic biological systems. The history of de novo protein has evolved from initial successes in subordinate structural design to more intricate protein creation, challenging the complexities of natural proteins. Recent strides in protein design have leveraged computational methods to craft proteins for functions beyond their natural capabilities. Molecular dynamics (MD) simulations have emerged as a crucial tool for comprehending the structural and dynamic properties of de novo-designed proteins. In this study, we examined the pivotal role of MD simulations in elucidating the sampling methods, force field, water models, stability, and dynamics of de novo-designed proteins, highlighting their potential applications in diverse fields. The synergy between computational modeling and experimental validation continued to play a crucial role in the creation of novel proteins tailored for specific functions and applications.

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.

The aim of this review is to summarize the progress made in the determination of the protonation constants of biologically active ligands: endo- and exogenous L-amino acids and their derivatives in aqueous and mixed solutions using different experimental techniques. The knowledge of the protonation constants of the aforementioned ligands is crucial for the determination of the equilibrium constants of complex formation and thus for the understanding of complex biological reactions such as transamination, racemization, and decarboxylation. Thus, the protonation constants of ligands are a measure of their ability to form complexes with metal ions. This knowledge not only helps to understand fundamental biochemical processes, but also has practical applications in areas such as drug design, where ligands are often targeted for therapeutic purposes. The activity of the ligands tends to increase after complexation and their order is consistent with the values of the stepwise dissociation constants of the complexes formed. Understanding the properties of ligands by determining their protonation constants in different environments and their interactions with surrounding molecules is crucial to unraveling the complexity of biological systems.

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.

Soon after its introduction in 1987, polymerase chain reaction (PCR) has become a technique widely employed in diagnostic medical devices and forensic science with the intention of amplifying genetic information. PCR prescribes that each of its cycles must include a heating subprocess at 95 °C or more (denominated DNA denaturation and provided for allowing a claimed orderly separation of the two complementary nucleotides strands), which can produce significant damage to DNA, caused by high-speed collisions with surrounding molecules. Since such disruption should be prevented in order to reliably employ PCR, a study of the mechanics of such loss of structural integrity is herein presented, preceded by a review of the fundamental literature which has elucidated the effects of molecular agitation on DNA fragmentation. The main conclusion of this retrospective survey is that the body of examined theoretical and experimental evidence consistently and redundantly confirms scarce resilience and significant loss of structural integrity when DNA is heated at temperatures above 90 °C, even for 1 minute. Such conclusion contradicts the claimed paradigm of PCR fidelity and raises the concern that, at least for long sequences, if PCR can amplify some information, such amplified information may be unreliable for diagnostic or forensic applications, since it originates from sequences of nucleotides subjected to random fragmentation and reaggregation. Such a low-reliability scenario should be preventively considered in the various fields where DNA amplification methodologies are employed which provide for high-temperature heating under conditions equal to or similar to those prescribed by the PCR protocols reviewed in this study.

Molecular motors are machines essential for life since they convert chemical energy into mechanical work. However, the precise mechanism by which nucleotide binding, catalysis, or release of products is coupled to the work performed by the molecular motor is still not entirely clear. This is due, in part, to a lack of understanding of the role of force in the mechanical–structural processes involved in enzyme catalysis. From a mechanical perspective, one promising hypothesis is the Haldane–Pauling hypothesis which considers the idea that part of the enzymatic catalysis is strain-induced. It suggests that enzymes cannot be efficient catalysts if they are fully complementary to the substrates. Instead, they must exert strain on the substrate upon binding, using enzyme-substrate energy interaction (binding energy) to accelerate the reaction rate. A novel idea suggests that during catalysis, significant strain energy is built up, which is then released by a local unfolding/refolding event known as ‘cracking’. Recent evidence has also shown that in catalytic reactions involving conformational changes, part of the heat released results in a center-of-mass acceleration of the enzyme, raising the possibility that the heat released by the reaction itself could affect the enzyme’s integrity. Thus, it has been suggested that this released heat could promote or be linked to the cracking seen in proteins such as adenylate kinase (AK). We propose that the energy released as a consequence of ligand binding/catalysis is associated with the local unfolding/refolding events (cracking), and that this energy is capable of driving the mechanical work.

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.

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.

Elastin function is to endow vertebrate tissues with elasticity so that they can adapt to local mechanical constraints. The hydrophobicity and insolubility of the mature elastin polymer have hampered studies of its molecular organisation and structure-elasticity relationships. Nevertheless, a growing number of studies from a broad range of disciplines have provided invaluable insights, and several structural models of elastin have been proposed. However, many questions remain regarding how the primary sequence of elastin (and the soluble precursor tropoelastin) governs the molecular structure, its organisation into a polymeric network, and the mechanical properties of the resulting material. The elasticity of elastin is known to be largely entropic in origin, a property that is understood to arise from both its disordered molecular structure and its hydrophobic character. Despite a high degree of hydrophobicity, elastin does not form compact, water-excluding domains and remains highly disordered. However, elastin contains both stable and labile secondary structure elements. Current models of elastin structure and function are drawn from data collected on tropoelastin and on elastin-like peptides (ELPs) but at the tissue level, elasticity is only achieved after polymerisation of the mature elastin. In tissues, the reticulation of tropoelastin chains in water defines the polymer elastin that bears elasticity. Similarly, ELPs require polymerisation to become elastic. There is considerable interest in elastin especially in the biomaterials and cosmetic fields where ELPs are widely used. This review aims to provide an up-to-date survey of/perspective on current knowledge about the interplay between elastin structure, solvation, and entropic elasticity.

Zoonoses are infectious agents that are transmissible between animals and humans. Up to 60% of known infectious diseases and 75% of emergent diseases are zoonotic. Genomic variation between homeostatic populations provides a novel window into the effect of environmental pathogens on allelic distributions within the populations. Genodynamics is a biophysical approach utilizing developed metrics on biallelic single-nucleotide polymorphisms (SNPs) that can be used to quantify the adaptive influences due to pathogens. A genomic free energy that is minimized when overall population health is optimized describes the influence of environmental agents upon genomic variation. A double-blind exploration of over 100 thousand SNPs searching for smooth functional dependencies upon four zoonotic pathogens carried by four possible hosts amidst populations that live in their ancestral environments has been conducted. Exemplars that infectious agents can have significant adaptive influence on human populations are presented. One discussed SNP is likely associated with both adaptive and innate immune regulation. The adaptive response of another SNP suggests an intriguing connection between zoonoses and human cancers. The adaptive forces of the presented pathogens upon the human genome have been quantified.

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.