Biological Physics

The study of the morphology of living system is an area of active research that dates back to the seminal work “On Growth and Form” by D’Arcy Wentworth Thompson in 1917, which laid the foundation of applying concepts from mathematics and physics to understand the beautiful and complex forms observed in nature. My research focuses on understanding the morphology of biological system under different situations, most of which involve non-equilibrium processes, such as growth, change in external environmental conditions such as noise, applied stresses, humidity, etc. Most of the research in my group focuses on the study of individual organisms and we are starting to foray into the realm of the collective. We are interested in questions such as “What is their shape?”, “How are they formed?”, “What are emergent states?”. Through the study of different biological systems, we hope to extract general principles that can elucidate biological pattern and organization. Some notable projects by my group are listed below.

Farisan Dary, Haiyi Liang, and Ee Hou Yong,
"Helical stability of double-stranded semiflexible chains with interstrand interactions,"
forthcoming

Abstract: The mechanical and structural properties of dsDNA have been successfully described by models with varying levels of complexity and coarse-graining schemes. However, the interplay between base-stacking interactions in dsDNA and its intrinsic twist is rarely discussed despite their importance in preserving the double-helix structure of dsDNA. Here we investigate the delicate balance required for the strength of base-pairing interactions and the twisting energy to preserve the double-helix structure in a model made up of two semiflexible chains. We found that the model exhibits several distinct morphological phases: flat, random coil, double-helix, and the unwound double-helix. We calculate the Gauss linking number to characterize transitions between these phases.

Ee Hou Yong and L. Mahadevan,
"Lyapunov-Schmidt bifurcation analysis of a supported compressible elastic beam,"
submitted to Nonlinearity, preprint on arXiv

Abstract: The archetypal instability of a structure is associated with the eponymous Euler beam, modeled as an inextensible curve which exhibits a supercritical bifurcation at a critical compressive load. In contrast, a soft compressible beam is capable of a subcritical instability, a problem that is far less studied, even though it is increasingly relevant in the context of soft materials and structures. Here, we study the stability of a soft extensible elastic beam on an elastic foundation under the action of a compressive axial force, using the Lyapunov-Schmidt reduction method which we corroborate with numerical calculations. Our calculated bifurcation diagram differs from those associated with the classical Euler-Bernoulli beam, and shows two critical loads, p± cr(n), for each buckling mode n. The beam undergoes a supercritical pitchfork bifurcation at p+(n) for all n and slenderness. Due to the elastic foundation, the lower order modes at p−(n) exhibit subcritical pitchfork bifurcations, and perhaps surprisingly, the first supercritical pitchfork bifurcation point occurs at a higher critical load. The presence of the foundation makes it harder to buckle the elastic beam, but when it does so, it tends to buckle into a more undulated shape. Overall, we find that an elastic support can lead to a myraid of buckled shapes for the classical elastica and one can tune the substrate stiffness to control desired buckled modes—an experimentally testable prediction.

Donn Liew, Zi Way Lim, and Ee Hou Yong,
"Machine learning-based prediction of DNA G-quadruplex folding topology with G4ShapePredictor,"
Scientific Reports 14(1), 24238, 2024.

Abstract: Deoxyribonucleic acid (DNA) is able to form non-canonical four-stranded helical structures with diverse folding patterns known as G-quadruplexes (G4s). G4 topologies are classified based on their relative strand orientation following the 5’ to 3’ phosphate backbone polarity. Broadly, G4 topologies are either parallel (4+0), antiparallel (2+2), or hybrid (3+1). G4s play crucial roles in biological processes such as DNA repair, DNA replication, transcription and have thus emerged as biological targets in drug design. While computational models have been developed to predict G4 formation, there is currently no existing model capable of predicting G4 folding topology based on its nucleic acid sequence. Therefore, we introduce G4ShapePredictor (G4SP), an application featuring a collection of multi-classification machine learning models that is trained on a custom G4 dataset combining entries from existing literature and in-house circular dichroism experiments. G4ShapePredictor is designed to accurately predict G4 folding topologies in potassium (K+) buffer based on its primary sequence and is able to incorporate a threshold optimization strategy allowing users to maximise precision. Furthermore, We have identified three topological sequence motifs that suggest specific G4 folding topologies of (4+0), (2+2) or (3+1) when utilising the decision-making mechanisms of G4ShapePredictor.

Javad Deylami, Shu Sin Chng, and Ee Hou Yong,
“Elucidating Antibiotic Permeation through the Escherichia coli Outer Membrane: Insights from Molecular Dynamics,”
Journal of Chemical Information and Modeling, 64(21), 8310, 2024.

Research covered in Nature Index article

Abstract: Antibiotic resistance represents a critical public health threat, with an increasing number of Gram-negative pathogens demonstrating resistance to a broad range of clinical drugs. A primary challenge in enhancing antibiotic efficacy is overcoming the robust barrier presented by the bacterial outer membrane. Our research tackles a longstanding question: What is the rate of antibiotic permeation across the outer membrane (OM) of Gram-negative bacteria? Utilizing molecular dynamics (MD) simulations, a pivotal technique for elucidating the permeation mechanisms and physicochemical properties of solutes across membrane systems, this study assesses the passive permeability pro- files of four commercially available antibiotics—gentamicin, novobiocin, rifampin, and tetracycline. These assessments are conducted through an asymmetric model of the Escherichia coli (E. coli) OM, employing the inhomogeneous solubility-diffusion model (ISDM). Our examination of the interactions between these drugs and their environ- mental context during OM permeation reveals that extended hydrogen bond formation and drug-cation interactions significantly hinder the energetics of passive permeation, notably affecting novobiocin. Our MD simulations corroborate well with experimental data, and reveal new implications of solvation on drug permeability, overall advanc- ing the possible use of computational prediction of membrane permeability in future antibiotic discovery.

Ee Hou Yong, Farisan Dary, Luca Giomi, and L. Mahadevan,
“Reply to van der Heijden and Starostin: On the persistent helicity of fluctuating ribbons,”
Proceedings of the National Academy of Sciences of the United States of America, 121 (28), e2303436121, 2024.

Nuoya Zhang and Ee Hou Yong,
“Dynamics, statistics, and task allocation of foraging ants,”
Physical Review E 108, 054306, 2023.

Abstract: Ant foraging is one of the most fascinating examples of cooperative behavior observed in nature. It is well studied from an entomology viewpoint, but there is currently a lack of mathematical synthesis of this phenomenon. We address this by constructing an ant foraging model that incorporates simple behavioral rules within three task groups of the ant colony during foraging (foragers, transporters, and followers), pheromone trails, and memory effects. The motion of an ant is modeled as a discrete correlated random walk, with a characteristic zigzag path that is congruent with experimental data. We simulate the foraging cycle, which consists of ants searching for food, transporting food, and depositing chemical trails to recruit and orient more ants (en masse) to the food source. This allows us to gain insights into the basic mechanism of the cooperative interactions between ants and the dynamical division of labor within an ant colony during foraging to achieve optimal efficiency. We observe a disorder-order phase transition from the start to the end of a foraging process, signaling collective motion at the population level. Finally, we present a set of time delay ODEs that corroborates with numerical simulations.

Ee Hou Yong, Farisan Dary, Luca Giomi, and L. Mahadevan,

"Statistics and topology of fluctuating ribbons,"

Proceedings of the National Academy of Sciences of the United States of America, 119 (32), e2122907119, 2022.

Abstract: Ribbons are a class of slender structures whose length, width, and thickness are widely separated from each other. This scale separation gives a ribbon unusual mechanical properties in athermal macroscopic settings, for example, it can bend without twisting, but cannot twist without bending. Given the ubiquity of ribbon-like biopolymers in biology and chemistry, here we study the statistical mechanics of microscopic inextensible, fluctuating ribbons loaded by forces and torques. We show that these ribbons exhibit a range of topologically and geometrically complex morphologies exemplified by three phases—a twist-dominated helical phase (HT), a writhe-dominated helical phase (HW), and an entangled phase—that arise as the applied torque and force are varied. Furthermore, the transition from HW to HT phases is characterized by the spontaneous breaking of parity symmetry and the disappearance of perversions (that correspond to chirality-reversing localized defects). This leads to a universal response curve of a topological quantity, the link, as a function of the applied torque that is similar to magnetization curves in second-order phase transitions.

Mary Caswell Stoddard, Ee Hou Yong, Derya Akkaynak, Catherine Sheard, Joseph A. Tobias, and L. Mahadevan,
"Form, Function and Evolution of Avian Egg Shape,"
Science 356, 1249-1254, 2017.

Cover issue of vol. 356. Review Article on paper

Abstract: Avian egg shape is generally explained as an adaptation to life history, yet we currently lack a global synthesis of how egg-shape differences arise and evolve. Here, we apply morphometric, mechanistic, and macroevolutionary analyses to the egg shapes of 1400 bird species. We characterize egg-shape diversity in terms of two biologically relevant variables, asymmetry and ellipticity, allowing us to quantify the observed morphologies in a two-dimensional morphospace. We then propose a simple mechanical model that explains the observed egg-shape diversity based on geometric and material properties of the egg membrane. Finally, using phylogenetic models, we show that egg shape correlates with flight ability on broad taxonomic scales, suggesting that adaptations for flight may have been critical drivers of egg-shape variation in birds.

Ee Hou Yong, David R. Nelson, and L. Mahadevan,
"Elastic Platonic Shells,"
Physical Review Letters 111(17), 177801, 2013.

Cover of Physical Review Letters vol. 111, issue 17

Abstract: On microscopic scales, the crystallinity of flexible tethered or cross linked membranes determines their mechanical response. We show that by controlling the type, number and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical Platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading-unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.

Ozgur Sahin, Ee Hou Yong, Adam Driks and L. Mahadevan,
"Physical basis for the adaptive flexibility of bacillus spore coats,"
Journal of the Royal Society Interface 9, 3156-3160, 2012.

Abstract: Bacillus spores are highly resistant dormant cells formed in response to starvation. The spore is surrounded by a structurally complex protein shell, the coat, which pro- tects the genetic material. In spite of its dormancy, once nutrient is available (or an appropriate physical stimulus is provided) the spore is able to resume metabolic activity and return to vegetative growth, a process requiring the coat to be shed. Spores dynamically expand and contract in response to humidity, demanding that the coat be flexible. Despite the coat’s critical bio- logical functions, essentially nothing is known about the design principles that allow the coat to be tough but also flexible and, when metabolic activity resumes, to be efficiently shed. Here, we investigated the hypoth- esis that these apparently incompatible characteristics derive from an adaptive mechanical response of the coat. We generated a mechanical model predicting the emergence and dynamics of the folding patterns uniformly seen in Bacillus spore coats. According to this model, spores carefully harness mechanical instabilities to fold into a wrinkled pattern during sporulation. Owing to the inherent nonlinearity in their formation, these wrinkles persist during dormancy and allow the spore to accommodate changes in volume without compromising structural and biochemical integrity. This characteristic of the spore and its coat may inspire design of adaptive materials.