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Allosteric Biomaterials: Mechanism and Design
Allosteric Biomaterials: Mechanism and Design
Collaborators: R. Ravasio, C. Brito, M. Wyart
An essential type of regulations in life is enabled through the allosteric pathways in allosteric proteins, whose catalytic activity or binding affinity depends on the appearance and concentration of certain chemicals. The well-known example is hemoglobin, to the four heme groups on which the bindings of oxygen molecules are cooperative: the binding of one makes the binding of another to the same protein easier. Effectively, the protein mediates a long-range interaction of binding molecules by transmitting mechanical signals. However, the physical mechanism of the interaction is still a mystery. We model the proteins as elastic materials, and use the in-silico evolution or learning method to solve the inverse elasticity problem: searching for the elastic structures optimizing the given allosteric function. Based on the resulted functioning structures, we build a theoretical framework for realizing allosteric pathway in an elastic medium and predict a scaling relation between the energy of the optimal allosteric response and the protein size, verified with more than 30 allosteric proteins various in size over 20 folds. Our theory provides a direction on identifying allosteric pathway of a protein based its structure and on designing proteins as specific molecular drugs.
An essential type of regulations in life is enabled through the allosteric pathways in allosteric proteins, whose catalytic activity or binding affinity depends on the appearance and concentration of certain chemicals. The well-known example is hemoglobin, to the four heme groups on which the bindings of oxygen molecules are cooperative: the binding of one makes the binding of another to the same protein easier. Effectively, the protein mediates a long-range interaction of binding molecules by transmitting mechanical signals. However, the physical mechanism of the interaction is still a mystery. We model the proteins as elastic materials, and use the in-silico evolution or learning method to solve the inverse elasticity problem: searching for the elastic structures optimizing the given allosteric function. Based on the resulted functioning structures, we build a theoretical framework for realizing allosteric pathway in an elastic medium and predict a scaling relation between the energy of the optimal allosteric response and the protein size, verified with more than 30 allosteric proteins various in size over 20 folds. Our theory provides a direction on identifying allosteric pathway of a protein based its structure and on designing proteins as specific molecular drugs.
Model of allosteric protein. Binding of the ligand at the allosteric site changes the shape at the active site to fit with the target shape of the substrate.
Illustration of the elastic network model that accomplishes the allosteric task.
Prediction on the scaling relations between the energy of allosteric response and the protein size, together with the actual energy data obtained from crystallized structures for 34 allosteric proteins.
The idea of cooperative energy and allostery.
The allosteric response of Human Mitochondrial NAD(P)-dependent Malic Enzyme (1QR6). Black arrows show the conformational change of the allosteric pathway, the red balls are alpha-carbons under strong shear strain.
Rigidity of Epithelial Tissue
Rigidity of Epithelial Tissue
Collaborators: D. Bi
The rigidity of epithelial tissue is essential to development and physiology. It has been shown that a rigidity transition could happen in epithelial tissue without changing the cell density but primarily by controlling the cortical tension at the cell junctions. However, it's puzzling why this transition occurs and what physics controls the rigidity. In addition, rosettes, where more than three cells meet, always appear in developments and pathogenic changes. How are they involved in the global rigidity of the tissue? We study these questions using the vertex model, with polygonal cells framed by vertices, including rosettes, vertices connecting more than four other vertices. By creating rosettes, the whole system can also be driven to a solid phase with finite elastic modulus. Most importantly, we provide a theoretical framework on the origin of this rigidity, which is a result of incompatibility of the preferred cell shapes and the system constraints. These constraints are nontrivial ones, emergent from the cell-cell edge tensions.
The rigidity of epithelial tissue is essential to development and physiology. It has been shown that a rigidity transition could happen in epithelial tissue without changing the cell density but primarily by controlling the cortical tension at the cell junctions. However, it's puzzling why this transition occurs and what physics controls the rigidity. In addition, rosettes, where more than three cells meet, always appear in developments and pathogenic changes. How are they involved in the global rigidity of the tissue? We study these questions using the vertex model, with polygonal cells framed by vertices, including rosettes, vertices connecting more than four other vertices. By creating rosettes, the whole system can also be driven to a solid phase with finite elastic modulus. Most importantly, we provide a theoretical framework on the origin of this rigidity, which is a result of incompatibility of the preferred cell shapes and the system constraints. These constraints are nontrivial ones, emergent from the cell-cell edge tensions.
Fluidization transition in confluent epithelial tissue (bronchial epithelial). Left: normal tissue; Right: from asthma patient under pressure. (Park Group, Harvard School of Public Health).
Phase diagram of the confluent tissue rigidity. Red dots are where the tissue is fluid, and green dots are where is solid. A tissue can be driven to be solid by lowering p0, the preferred shape index, optimal perimeter normalized by the square root of area, or by increasing Z, the average coordination number of the vertices, number of cells sharing the corner.
Rosettes in confluent epithelial tissue. Top: bronchial epithelial tissue (Park Group, Harvard School of Public Health); Bottom: Drosophila Germ-band extension (Kasza et.al. PNAS 2014).
Extinction and Speciation in Rapidly Evolving Pathogens
Extinction and Speciation in Rapidly Evolving Pathogens
Collaborators: R. Neher, B. Shraiman
Rapidly evolving pathogens, including the case of the common flu - influenza A/H3N2 virus - can persist in a state of continuous evolution, accumulating antigenic novelty fast enough to evade the adaptive immunity of the host population, yet without continuous accumulation of genetic diversity. Cross-immunity imposed general selection for the most antigenically advanced strains balances the influx of diversity due to mutation. This continuous adaptation in large rapidly mutating populations is well understood in terms of traveling wave theories of population genetics. We make an explicit mapping of a Susceptible-Infected-Recovered epidemic model onto the traveling wave theory under conditions of long-range cross-immunity. We then investigate the stability of the traveling wave focusing on the rate of extinction and the rate of "speciation". We find the states of persisting low diversities in fast mutating populations are transient, but in a certain range of evolutionary parameters it can exist for the time long compared to the typical circulating time of a particular strain. The long-term behavior of phylogenetics is ruled by a dynamic transition in the phase diagram.
Rapidly evolving pathogens, including the case of the common flu - influenza A/H3N2 virus - can persist in a state of continuous evolution, accumulating antigenic novelty fast enough to evade the adaptive immunity of the host population, yet without continuous accumulation of genetic diversity. Cross-immunity imposed general selection for the most antigenically advanced strains balances the influx of diversity due to mutation. This continuous adaptation in large rapidly mutating populations is well understood in terms of traveling wave theories of population genetics. We make an explicit mapping of a Susceptible-Infected-Recovered epidemic model onto the traveling wave theory under conditions of long-range cross-immunity. We then investigate the stability of the traveling wave focusing on the rate of extinction and the rate of "speciation". We find the states of persisting low diversities in fast mutating populations are transient, but in a certain range of evolutionary parameters it can exist for the time long compared to the typical circulating time of a particular strain. The long-term behavior of phylogenetics is ruled by a dynamic transition in the phase diagram.
Phylogenetic trees of Influenza A and B. Single backbone of Influenza A/H3N2 in contrast to two circulating lineages of Influenza B.
Extinction and speciation time scales depend on parameters.
Traveling wave under the selection of host immunity.
Phase diagram of the phylogenetics of the mutating virus.
Geometric Defects and Germ-Band Extension in Drosophila Embryo
Geometric Defects and Germ-Band Extension in Drosophila Embryo
Collaborators: S. Streichan, S. Shadkhoo, M. Bowick, B. Shraiman
Morphogenesis in multicellular organisms is realized through collective dynamics of cells. For example, in Drosophila melanogaster, initially homogeneous cells in the germ-band segregates into 14 parasegments after the germ-band extension and retraction. Specifically, the parasegments are separated by furrows, formed by additional cells intercalated along the germ-band extension direction. S. Streichan and coworkers has shown the predictability of tissue dynamics as usual elasto-viscous materials in the extension on a coarse-grained level. However, it would be extremely useful to improve the resolution to the single cell scale to learn the cell fate. The elasticity and thus the mechanical response of tissue are revealed to depend on the geometric defects, which have different than six number of neighbors when embedded in a two dimensional manifold. To unveil the connection between the geometry of cells and the roles of individual cells, we develop an image analysis pipeline to detect this hexagonal order and the cell orientations. We find patches of six-fold order with well-defined cell directions separated by the lines of defects. We are curious to see how the defects and the orientations of the patches are related to the later shape forming and mechanics like intercalations.
Morphogenesis in multicellular organisms is realized through collective dynamics of cells. For example, in Drosophila melanogaster, initially homogeneous cells in the germ-band segregates into 14 parasegments after the germ-band extension and retraction. Specifically, the parasegments are separated by furrows, formed by additional cells intercalated along the germ-band extension direction. S. Streichan and coworkers has shown the predictability of tissue dynamics as usual elasto-viscous materials in the extension on a coarse-grained level. However, it would be extremely useful to improve the resolution to the single cell scale to learn the cell fate. The elasticity and thus the mechanical response of tissue are revealed to depend on the geometric defects, which have different than six number of neighbors when embedded in a two dimensional manifold. To unveil the connection between the geometry of cells and the roles of individual cells, we develop an image analysis pipeline to detect this hexagonal order and the cell orientations. We find patches of six-fold order with well-defined cell directions separated by the lines of defects. We are curious to see how the defects and the orientations of the patches are related to the later shape forming and mechanics like intercalations.
Germ-band extension in the Drosophila embryo. Besides in the ventral furrow, cells stay on the surface of the embryo during the extension. Tissue is elongated along the extension direction through intercalation (C. Guillot, T. Lecuit, Science 2013).
Hexagonal order for cells on the Drosophila embryo after the 13th cell cycle just before the gastrulation, ventral view.
Hexagonal order for cells on the Drosophila embryo unfold projection.
Cylinder map (equirectangular) projection of the embryo surface. Signals from histone labelled mCherry Fluorescent proteins correspond to nuclei (Streichan Group).
Orientations for cells on the Drosophila embryo after the 13th cell cycle just before the gastrulation, ventral view.
Orientations for cells on the Drosophila embryo unfold projection.
Mutations and Regulations of Mitochondrial DNA in Budding Yeast
Mutations and Regulations of Mitochondrial DNA in Budding Yeast
Collaborators: K. Kuns, E. Hamilton, C. Osman, B. Shraiman
Mitochondria, producing a massive amount of ATP through aerobic respiration, are of the most important organelles in eukaryote cells. Loss or dysfunction of them can be deadly to most cells and causes severe diseases in vertebrates like Alzheimer's and many syndromes during the childhood. However, the fact that the mitochondria possess and pass on their own mitochondrial DNA implies that unlike to other organelles, the relation between cell and mitochondria is more like the one between the host and the virus if the cells have little control over the replication of the mitochondrial DNA. So it's important to understand the intracellular regulations on the mitochondrial DNA. We have initiated the problem in Saccharomyces cerevisiae, the budding yeast, which could survive without functioning mitochondria. The difference of ATP production efficiency in aerobic and anaerobic respirations ends up into two phenotypes of yeast colonies when grown on certain media. We sequence DNA in Grand and Petite colonies to detect the mutations in mitochondrial DNA that induce the dysfunction of mitochondria. We find evidence that the homologous recombinations associated with GC clusters potentially cause the loss of the trunk of coding genes in yeast mitochondrial DNA.
Mitochondria, producing a massive amount of ATP through aerobic respiration, are of the most important organelles in eukaryote cells. Loss or dysfunction of them can be deadly to most cells and causes severe diseases in vertebrates like Alzheimer's and many syndromes during the childhood. However, the fact that the mitochondria possess and pass on their own mitochondrial DNA implies that unlike to other organelles, the relation between cell and mitochondria is more like the one between the host and the virus if the cells have little control over the replication of the mitochondrial DNA. So it's important to understand the intracellular regulations on the mitochondrial DNA. We have initiated the problem in Saccharomyces cerevisiae, the budding yeast, which could survive without functioning mitochondria. The difference of ATP production efficiency in aerobic and anaerobic respirations ends up into two phenotypes of yeast colonies when grown on certain media. We sequence DNA in Grand and Petite colonies to detect the mutations in mitochondrial DNA that induce the dysfunction of mitochondria. We find evidence that the homologous recombinations associated with GC clusters potentially cause the loss of the trunk of coding genes in yeast mitochondrial DNA.
Mitochondria are the power plants in eukaryote cells. They carry on their own genes on Mitochondrial DNA.
Coverage of mitochondrial DNA averaged over the coverage of nuclear DNA of different colonies. Cells in petite colonies possess either no mtDNA (barcode10) or noncoding pieces (barcode9). Cells in grand colonies (barcode5-8) possess on average more mitochondria per cell than in the whole culture (barcode1-4).
Grand and Petite phenotypes of budding yeast cells, colonized on YPDG plates.
Cumulative distribution of yeast cell colony sizes. Different colors are cells cultured in different media at different stages.
Rigidity Transition and Glass
Collaborators: G. During, M. Wyart
Super-cooled liquids are characterized by their fragility: the slowing down of the dynamics under cooling is more sudden and the jump of specific heat at the glass transition is generally larger in fragile liquids than in strong ones. Despite the importance of this quantity in classifying liquids, explaining what aspects of the microscopic structure control fragility remains a challenge.
Surprisingly, experiments indicate that the linear elasticity of the glass -- a purely local property of the free energy landscape -- is a good predictor of fragility. In particular, materials presenting a large excess of soft elastic modes, the so-called boson peak, are strong. This is also the case for network liquids near the rigidity percolation, known to affect elasticity. Here we introduce a model of the glass transition based on the assumption that particles can organize locally into distinct configurations, which are coupled spatially via elasticity. The model captures the mentioned observations connecting elasticity and fragility. We find that materials presenting an abundance of soft elastic modes have little elastic frustration: energy is insensitive to most directions in phase space, leading to a small jump of specific heat. In this framework strong liquids turn out to lie the closest to a critical point associated with a rigidity or jamming transition, and their thermodynamic properties are related to the problem of number partitioning and to Hopfield nets in the limit of small memory.
We study the evolution of structural disorder under cooling in supercooled liquids, focusing on covalent networks. We introduce a model for the energy of networks that incorporates weak non-covalent interactions. We show that at low-temperature, these interactions considerably affect the network topology near the rigidity transition that occurs as the coordination increases. As a result, this transition becomes mean-field and does not present a line of critical points previously argued for, the "rigidity window". Vibrational modes are then not fractons, but instead are similar to the anomalous modes observed in packings of particles near jamming. These results suggest an alternative interpretation for the intermediate phase observed in chalcogenides.
Modeling covalent glass by elastic network model. Top: Covalent glasses from polymer-like to highly-connected networks, red rods are covalent bonds, blue dashed lines are van der Waals forces. Bottom: Elastic networks below, at and above the rigidity transition (Maxwell counting) for strong network connected by the red springs, stiffness of blue springs are significantly smaller.
Rigidity transition scenarios by increasing the network connectivity. (a) Rigidity percolation in random connected networks, configurational entropy optimized. (b) Mean-field jamming transition in self-organized homogeneous networks, elastic energy optimized. (c) Percolation of the rigid subnet in rigid-floppy separated networks, vibrational entropy optimized. (d) Intermediate phase in networks undergoing heterogeneous-homogeneous transitions near the Maxwell point, free energy (elastic energy+vibrational entropy) optimized.
Avalanches and Marginal Stability in Spin Glasses
Collaborators: M. Muller, M. Wyart
Marginal stability is the notion that stability is achieved, but only barely so. This property constrains the ensemble of configurations explored at low temperature in a variety of systems, including spin, electron, and structural glasses. A key feature of marginal states is a (saturated) pseudogap in the distribution of soft excitations. We examine how such pseudogaps appear dynamically by studying the Sherrington-Kirkpatrick (SK) spin glass. After revisiting and correcting the multi-spin-flip criterion for local stability, we show that stationarity along the hysteresis loop requires soft spins to be frustrated among each other, with a correlation diverging as C(λ) ∼ 1/λ, where λ is the stability of the more stable spin. We explain how this arises spontaneously in a marginal system and develop an analogy between the spin dynamics in the SK model and random walks in two dimensions. We discuss analogous frustrations among soft excitations in short range glasses and how to detect them experimentally. We also show how these findings apply to hard sphere packings.
Erosion Transition
Collaborators: P. Aussillous, E. Guazzelli, M. Wyart
Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we study, experimentally, the collective dynamics of the moving particles, using a setup where the system spontaneously evolves toward the erosion onset. We find that the spatial organization of the erosion flux is heterogeneous in space and occurs along channels of local flux σ whose distribution displays scaling near threshold and follows P(σ)≈J/σ, where J is the mean erosion flux. Channels are strongly correlated in the direction of forcing but not in the transverse direction. We show that these results quantitatively agree with a model where the dynamics is governed by the competition of disorder (which channels mobile particles) and particle interactions (which reduces channeling). These observations support that, for laminar flows, erosion is a dynamical phase transition that shares similarity with the plastic depinning transition occurring in dirty superconductors. The methodology we introduce here could be applied to probe these systems as well.
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