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Most granular packings possess shear moduli (G) that increase with the applied external pressure, and bulk moduli (B) that increase or remain constant with pressure. This paper presents “tessellated” granular metamaterials for which both Gand the ratio G/Bdecrease with increasing pressure. The granular metamaterials are made from flexible tessellations forming a ring of closed cells, each containing a small number of solid particles. For under-constrained tessellations, the dominant contributions to Gand Bare the particle–particle and particle–cell interactions. With specific particle configurations in the cells, we limit the number of possible particle rearrangements to achieve decreasing Gas we increase the pressure difference between the inside and outside of the tessellation, leading to G/B≪1at large pressures. We further study tessellated granular metamaterials with cells containing a single particle and many particles to determine the variables that control the mechanical response of particle-filled tessellations as a function of pressure.

The spongy mesophyll is a complex, porous tissue found in plant leaves that enables carbon capture and provides mechanical stability. Unlike many other biological tissues, which remain confluent throughout development, the spongy mesophyll must develop from an initially confluent tissue into a tortuous network of cells with a large proportion of intercellular airspace. How the airspace in the spongy mesophyll develops while the tissue remains mechanically stable is unknown. Here, we use computer simulations of deformable polygons to develop a purely mechanical model for the development of the spongy mesophyll tissue. By stipulating that cell wall growth and remodelling occurs only near void space, our computational model is able to recapitulate spongy mesophyll development observed in Arabidopsis thalianaleaves. We find that robust generation of pore space in the spongy mesophyll requires a balance of cell growth, adhesion, stiffness and tissue pressure to ensure cell networks become porous yet maintain mechanical stability. The success of this mechanical model of morphogenesis suggests that simple physical principles can coordinate and drive the development of complex plant tissues like the spongy mesophyll.

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ϕand ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.

Intrinsically disordered proteins (IDPs) are increasingly recognized for their important roles in a range of biological contexts, both in normal physiological function and in a variety of devastating human diseases. However, their structural characterization by traditional biophysical methods, for the purposes of understanding their function and dysfunction, has proved challenging. Here, we investigate the model IDPs α-Synuclein (αS) and tau, that are involved in major neurodegenerative conditions including Parkinson’s and Alzheimer’s diseases, using excluded volume Monte Carlo simulations constrained by pairwise distance distributions from single-molecule fluorescence measurements. Using this, to our knowledge, novel approach we find that a relatively small number of intermolecular distance constraints are sufficient to accurately determine the dimensions and polymer conformational statistics of αS and tau in solution. Moreover, this method can detect local changes in αS and tau conformations that correlate with enhanced aggregation. Constrained Monte Carlo simulations produce ensembles that are in excellent agreement both with experimental measurements on αS and tau and with all-atom, explicit solvent molecular dynamics simulations of αS, with much lower configurational sampling requirements and computational expense.

The energy functions used to predict protein structures typically include both molecular-mechanics and knowledge-based terms. In contrast, our approach is to develop robust physics- and geometry-based methods. Here, we investigate to what extent simple hard-sphere models can be used to predict side-chain conformations. The distributions of the side-chain dihedral angle χ1of Val and Thr in proteins of known structure show distinctive features: Val side chains predominantly adopt χ1= 180°, whereas Thr side chains typically adopt χ1= 60° and 300° (i.e., χ1= ±60° or g− and g+configurations). Several hypotheses have been proposed to explain these differences, including interresidue steric clashes and hydrogen-bonding interactions. In contrast, we show that the observed side-chain dihedral angle distributions for both Val and Thr can be explained using only localsteric interactions in a dipeptide mimetic. Our results emphasize the power of simple physical approaches and their importance for future advances in protein engineering and design.

We describe the self-assembly of nonspherical particles into crystals with novel structure and optical properties combining a partial photonic band gap with birefringence that can be modulated by an external field or quenched by solvent evaporation. Specifically, we study symmetric optical-scale polymer dumbbells with an aspect ratio of 1.58. Hard particles with this geometry have been predicted to crystallize in equilibrium at high concentrations. However, unlike spherical particles, which readily crystallize in the bulk, previous experiments have shown that these dumbbells crystallize only under strong confinement. Here, we demonstrate the use of an external electric field to align and assemble the dumbbells to make a birefringent suspension with structural color. When the electric field is turned off, the dumbbells rapidly lose their orientational order and the color and birefringence quickly go away. In this way, dumbbells combine the structural color of photonic crystals with the field addressability of liquid crystals. In addition, we find that if the solvent is removed in the presence of an electric field, the particles self-assemble into a novel, dense crystalline packing hundreds of particles thick. Analysis of the crystal structure indicates that the dumbbells have a packing fraction of 0.7862, higher than the densest known packings of spheres and ellipsoids. We perform numerical experiments to more generally demonstrate the importance of controlling the orientation of anisotropic particles during a concentration quench to achieve long-range order.

A theoretical framework is developed to study the dynamics of protein folding. The key insight is that the search for the native protein conformation is influenced by the rate rat which external parameters, such as temperature, chemical denaturant, or pH, are adjusted to induce folding. A theory based on this insight predicts that 1), proteins with complex energy landscapes can fold reliably to their native state; 2), reliable folding can occur as an equilibrium or out-of-equilibrium process; and 3), reliable folding only occurs when the rate ris below a limiting value, which can be calculated from measurements of the free energy. We test these predictions against numerical simulations of model proteins with a single energy scale.