Hongyuan Jiang

Cellular pressure and volume regulation and implications for cell mechanics

In eukaryotic cells, small changes in cell volume can serve as important signals for cell proliferation, death, and migration. Volume and shape regulation also directly impacts the mechanics of cells and tissues. Here, we develop a mathematical model of cellular volume and pressure regulation, incorporating essential elements such as water permeation, mechanosensitive channels, active ion pumps, and active stresses in the cortex. The model can fully explain recent experimental data, and it predicts cellular volume and pressure for several models of cell cortical mechanics. Moreover, we show that when cells are subjected to an externally applied load, such as in an atomic force microscopy indentation experiment, active regulation of volume and pressure leads to a complex cellular response. Instead of the passive mechanics of the cortex, the observed cell stiffness depends on several factors working together. This provides a mathematical explanation of rate-dependent response of cells under force.

Mechanical control of bacterial cell shape.

In bacteria, cytoskeletal filament bundles such as MreB control the cell morphology and determine whether the cell takes on a spherical or a rod-like shape. Here we use a theoretical model to describe the interplay of cell wall growth, mechanics, and cytoskeletal filaments in shaping the bacterial cell. We predict that growing cells without MreB exhibit an instability that favors rounded cells. MreB can mechanically reinforce the cell wall and prevent the onset of instability. We propose that the overall bacterial shape is determined by a dynamic turnover of cell wall material that is controlled by mechanical stresses in the wall. The model affirms that morphological transformations with and without MreB are reversible, and quantitatively describes the growth of irregular shapes and cells undergoing division. The theory also suggests a unique coupling between mechanics and chemistry that can control organismal shapes in general.

Bending Nanowire Growth in Solution by Mechanical Disturbance

The effect of mechanical disturbance on one-dimensional nanocrystal growth in solution phase is investigated by controlled growth of Au nanowires with and without stirring. While a static growth leads to straight, single-crystal Au nanowires, the mechanic disturbance by stirring tends to bend the nanowire growth, yielding nanowire kinks abundant in various types of crystal defects including dislocations, twin boundaries, and grain boundaries. Mechanical modeling and analysis is introduced to elucidate the nanowire growth mechanisms in these two conditions. The provided fundamental understanding of crystal defect formation at nanoscale could be applied to guide the development of advanced nanomaterials with shape control and unique mechanical properties.

Physics of Bacterial Morphogenesis

SUMMARY Bacterial cells utilize three-dimensional (3D) protein assemblies to perform important cellular functions such as growth, division, chemoreception, and motility. These assemblies are composed of mechanoproteins that can mechanically deform and exert force. Sometimes, small-nucleotide hydrolysis is coupled to mechanical deformations. In this review, we describe the general principle for an understanding of the coupling of mechanics with chemistry in mechanochemical systems. We apply this principle to understand bacterial cell shape and morphogenesis and how mechanical forces can influence peptidoglycan cell wall growth. We review a model that can potentially reconcile the growth dynamics of the cell wall with the role of cytoskeletal proteins such as MreB and crescentin. We also review the application of mechanochemical principles to understand the assembly and constriction of the FtsZ ring. A number of potential mechanisms are proposed, and important questions are discussed.

Vesicle shape, molecular tilt, and the suppression of necks

Can the presence of molecular-tilt order significantly affect the shapes of lipid bilayer membranes, particularly membrane shapes with narrow necks? Motivated by the propensity for tilt order and the common occurrence of narrow necks in the intermediate stages of biological processes such as endocytosis and vesicle trafficking, we examine how tilt order inhibits the formation of necks in the equilibrium shapes of vesicles. For vesicles with a spherical topology, point defects in the molecular order with a total strength of +2 are required. We study axisymmetric shapes and suppose that there is a unit-strength defect at each pole of the vesicle. The model is further simplified by the assumption of tilt isotropy: invariance of the energy with respect to rotations of the molecules about the local membrane normal. This isotropy condition leads to a minimal coupling of tilt order and curvature, giving a high energetic cost to regions with Gaussian curvature and tilt order. Minimizing the elastic free energy with constraints of fixed area and fixed enclosed volume determines the allowed shapes. Using numerical calculations, we find several branches of solutions and identify them with the branches previously known for fluid membranes. We find that tilt order changes the relative energy of the branches, suppressing thin necks by making them costly, leading to elongated prolate vesicles as a generic family of tilt-ordered membrane shapes.

Growth of curved and helical bacterial cells

A combination of cell wall growth and cytoskeletal protein action gives rise to the observed bacterial cell shape. Aside from the common rod-like and spherical shapes, bacterial cells can also adopt curved or helical geometries. To understand how curvature in bacteria is developed or maintained, we examine how Caulobacter crescentus obtains its crescent-like shape. Caulobacter cells with or without the cytoskeletal bundle crescentin, an intermediate filament-like protein, exhibit two distinct growth modes, curvature maintenance that preserves the radius of curvature and curvature relaxation that straightens the cell (Fig. 1). Using a proposed mechanochemical model, we show that bending and twisting of the crescentin bundle can influence the stress distribution in the cell wall, and lead to the growth of curved cells. In contrast, after crescentin bundle is disrupted, originally curved cells will slowly relax towards a straight rod over time. The model is able to quantitatively capture experimentally observed curvature dynamics. Furthermore, we show that the shape anisotropy of the cross-section of a curved cell is never greater than 4%, even in the presence of crescentin.

High efficiency fabrication of complex microtube arrays by scanning focused femtosecond laser Bessel beam for trapping/releasing biological cells

In this paper, we present a focused femtosecond laser Bessel beam scanning technique for the rapid fabrication of large-area 3D complex microtube arrays. The femtosecond laser beam is converted into several Bessel beams by two-dimensional phase modulation using a spatial light modulator. By scanning the focused Bessel beam along a designed route, microtubes with variable size and flexible geometry are rapidly fabricated by two-photon polymerization. The fabrication time is reduced by two orders of magnitude in comparison with conventional point-to-point scanning. Moreover, we construct an effective microoperating system for single cell manipulation using microtube arrays, and demonstrate its use in the capture, transfer, and release of embryonic fibroblast mouse cells as well as human breast cancer cells. The new fabrication strategy provides a novel method for the rapid fabrication of functional devices using a flexibly tailored laser beam.

Bond formation of surface-tethered receptor-ligand pairs in relative separation

We theoretically and numerically investigate the interplay between diffusion of a surface-bound receptor and its reaction with an opposing ligand. Special attention has been paid to the mechanical regulation of bond association by varying the initial gap distance and relative separation speed between the protein-bearing surfaces. Such diffusion-reaction coupling effects can cause the apparent on-rate or reciprocal of the average waiting time for bond formation, to be not constant, but instead a function sensitive to the system parameters that affect the transport of proteins. The results provide a quantitative understanding of how significantly the transport mechanism can affect overall binding behavior of molecular interactions and call for a paradigm shift in modeling receptor-ligand bond association when the protein-bearing surfaces are in relative separation.

Shape and Dynamics of Adhesive Cells: Mechanical Response of Open Systems

Cell adhesion is an essential biological process. However, previous theoretical and experimental studies ignore a key variable, the changes of cellular volume and pressure, during the dynamic adhesion process. Here, we treat cells as open systems and propose a theoretical framework to investigate how the exchange of water and ions with the environment affects the shape and dynamics of cells adhered between two adhesive surfaces. We show that adherent cells can be either stable (convex or concave) or unstable (spontaneous rupture or collapse) depending on the adhesion energy density, the cell size, the separation of two adhesive surfaces, and the stiffness of the flexible surface. Strikingly, we find that the unstable states vanish when cellular volume and pressure are constant. We further show that the detachments of convex and concave cells are very different. The mechanical response of adherent cells is mainly determined by the competition between the loading rate and the regulation of the cellular volume and pressure. Finally, we show that as an open system the detachment of adherent cells is also significantly influenced by the loading history. Thus, our findings reveal a major difference between living cells and nonliving materials.

The shape of telephone cord blisters

Formation of telephone cord blisters as a result of buckling delamination is widely observed in many compressed film-substrate systems. Here we report a universal morphological feature of such blisters characterized by their sequential sectional profiles exhibiting a butterfly shape using atomic force microscopy. Two kinds of buckle morphologies, light and heavy telephone cord blisters, are observed and differentiated by measurable geometrical parameters. Based on the Föppl-von Kármán plate theory, the observed three-dimensional features of the telephone cord blister are predicted by the proposed approximate analytical model and simulation. The latter further replicates growth and coalescence of the telephone cord into complex buckling delamination patterns observed in the experiment.