Self-referring DNA and protein: a remark on physical and geometrical aspects

Royal Society 2016 Philosophical transactions. Series A, Mathematical Vol.374 No.2063

<P>All known life forms are based upon a hierarchy of interwoven feedback loops, operating over a cascade of space, time and energy scales. Among the most basic loops are those connecting DNA and proteins. For example, in genetic networks, DNA genes are expressed as proteins, which may bind near the same genes and thereby control their own expression. In this molecular type of self-reference, information is mapped from the DNA sequence to the protein and back to DNA. There is a variety of dynamic DNA-protein self-reference loops, and the purpose of this remark is to discuss certain geometrical and physical aspects related to the back and forth mapping between DNA and proteins. The mappings are examined as dimensional reductions and expansions between high-and low-dimensional manifolds in molecular spaces. The discussion raises basic questions regarding the nature of DNA and proteins as self-referring matter, which are examined in a simple toy model.</P>

Comment on “Ribosome utilizes the minimum free energy changes to achieve the highest decoding rate and fidelity”

Savir, Yonatan,Tlusty, Tsvi American Physical Society 2016 Physical Review E Vol.93 No.5

Strain analysis of protein structures and low dimensionality of mechanical allosteric couplings

Mitchell, Michael R.,Tlusty, Tsvi,Leibler, Stanislas National Academy of Sciences 2016 PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF Vol.113 No.40

<P>In many proteins, especially allosteric proteins that communicate regulatory states from allosteric to active sites, structural deformations are functionally important. To understand these deformations, dynamical experiments are ideal but challenging. Using static structural information, although more limited than dynamical analysis, is much more accessible. Underused for protein analysis, strain is the natural quantity for studying local deformations. We calculate strain tensor fields for proteins deformed by ligands or thermal fluctuations using crystal and NMR structure ensembles. Strains-primarily shears-show deformations around binding sites. These deformations can be induced solely by ligand binding at distant allosteric sites. Shears reveal quasi-2D paths of mechanical coupling between allosteric and active sites that may constitute a widespread mechanism of allostery. We argue that strain-particularly shear-is the most appropriate quantity for analysis of local protein deformations. This analysis can reveal mechanical and biological properties of many proteins.</P>

Enhanced Diffusion and Oligomeric Enzyme Dissociation

Jee, Ah-Young,Chen, Kuo,Tlusty, Tsvi,Zhao, Jiang,Granick, Steve American Chemical Society 2019 JOURNAL OF THE AMERICAN CHEMICAL SOCIETY - Vol.141 No.51

<P>The concept that catalytic enzymes can act as molecular machines transducing chemical activity into motion has conceptual and experimental support, but experimental support has involved oligomeric enzymes, often studied under conditions where the substrate concentration is higher than biologically relevant and accordingly exceeds <I>k</I><SUB>M</SUB>, the Michaelis constant. Urease, a hexamer of subunits, has been considered to be the gold standard demonstrating enhanced diffusion. Here we show that urease and certain other oligomeric enzymes dissociate above <I>k</I><SUB>M</SUB> into their subunits that diffuse more rapidly, thus providing a simple physical mechanism that contributes to enhanced diffusion in this regime of concentrations. Mindful that this conclusion may be controversial, our findings are supported by four independent analytical techniques: static light scattering, dynamic light scattering (DLS), size-exclusion chromatography (SEC), and fluorescence correlation spectroscopy (FCS). Data for urease are emphasized and the conclusion is validated for hexokinase, acetylcholinesterase, and aldolase. For hexokinase and aldolase no enhanced diffusion is observed except under conditions when these oligomeric enzymes dissociate. At substrate concentration regimes below <I>k</I><SUB>M</SUB> at which acetylcholinesterase and urease do not dissociate, our finding showing up to 10% enhancement of the diffusion coefficient is consistent with various theoretical scenarios in the literature.</P> [FIG OMISSION]</BR>

Lossless Brownian Information Engine

Paneru, Govind,Lee, Dong Yun,Tlusty, Tsvi,Pak, Hyuk Kyu American Physical Society 2018 Physical Review Letters Vol.120 No.2

<P>We report on a lossless information engine that converts nearly all available information from an errorfree feedback protocol into mechanical work. Combining high-precision detection at a resolution of 1 nm with ultrafast feedback control, the engine is tuned to extract the maximum work from information on the position of a Brownian particle. We show that the work produced by the engine achieves a bound set by a generalized second law of thermodynamics, demonstrating for the first time the sharpness of this bound. We validate a generalized Jarzynski equality for error-free feedback-controlled information engines.</P>

Green function of correlated genes in a minimal mechanical model of protein evolution

Dutta, Sandipan,Eckmann, Jean-Pierre,Libchaber, Albert,Tlusty, Tsvi National Academy of Sciences 2018 PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF Vol.115 No.20

<▼1><P><B>Significance</B></P><P>Many protein functions involve large-scale motion of their amino acids, while alignment of their sequences shows long-range correlations. This has motivated search for physical links between genetic and phenotypic collective behaviors. The major challenge is the complex nature of protein: nonrandom heteropolymers made of 20 species of amino acids that fold into a strongly coupled network. In light of this complexity, simplified models are useful. Our model describes protein in terms of the Green function, which directly links the gene to force propagation and collective dynamics in the protein. This allows for derivation of basic determinants of evolution, such as fitness landscape and epistasis, which are often hard to calculate.</P></▼1><▼2><P>The function of proteins arises from cooperative interactions and rearrangements of their amino acids, which exhibit large-scale dynamical modes. Long-range correlations have also been revealed in protein sequences, and this has motivated the search for physical links between the observed genetic and dynamic cooperativity. We outline here a simplified theory of protein, which relates sequence correlations to physical interactions and to the emergence of mechanical function. Our protein is modeled as a strongly coupled amino acid network with interactions and motions that are captured by the mechanical propagator, the Green function. The propagator describes how the gene determines the connectivity of the amino acids and thereby, the transmission of forces. Mutations introduce localized perturbations to the propagator that scatter the force field. The emergence of function is manifested by a topological transition when a band of such perturbations divides the protein into subdomains. We find that epistasis—the interaction among mutations in the gene—is related to the nonlinearity of the Green function, which can be interpreted as a sum over multiple scattering paths. We apply this mechanical framework to simulations of protein evolution and observe long-range epistasis, which facilitates collective functional modes.</P></▼2>

Catalytic enzymes are active matter

Jee, Ah-Young,Cho, Yoon-Kyoung,Granick, Steve,Tlusty, Tsvi National Academy of Sciences 2018 PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF Vol.115 No.46

<▼1><P><B>Significance</B></P><P>Catalysis and mobility of reactants in fluid are normally thought to be decoupled. Violating this classical paradigm, this paper presents the catalyst laws of motion. Comparing experimental data to the theory presented here, we conclude that part of the free energy released by chemical reaction is channeled into driving catalysts to execute wormlike trajectories by piconewton forces performing work of a few <I>k</I><SUB><I>B</I></SUB><I>T</I> against fluid viscosity, where the rotational diffusion rate dictates the trajectory persistence length. This active motion agitates the fluid medium and produces antichemotaxis, the migration of catalyst down the gradient of the reactant concentration. Alternative explanations of enhanced catalyst mobility are examined critically.</P></▼1><▼2><P>Using a microscopic theory to analyze experiments, we demonstrate that enzymes are active matter. Superresolution fluorescence measurements—performed across four orders of magnitude of substrate concentration, with emphasis on the biologically relevant regime around or below the Michaelis–Menten constant—show that catalysis boosts the motion of enzymes to be superdiffusive for a few microseconds, enhancing their effective diffusivity over longer timescales. Occurring at the catalytic turnover rate, these fast ballistic leaps maintain direction over a duration limited by rotational diffusion, driving enzymes to execute wormlike trajectories by piconewton forces performing work of a few <I>k</I><SUB><I>B</I></SUB><I>T</I> against viscosity. The boosts are more frequent at high substrate concentrations, biasing the trajectories toward substrate-poor regions, thus exhibiting antichemotaxis, demonstrated here experimentally over a wide range of aqueous concentrations. Alternative noncatalytic, passive mechanisms that predict chemotaxis, cross-diffusion, and phoresis, are critically analyzed. We examine the physical interpretation of our findings, speculate on the underlying mechanism, and discuss the avenues they open with biological and technological implications. These findings violate the classical paradigm that chemical reaction and motility are distinct processes, and suggest reaction–motion coupling as a general principle of catalysis.</P></▼2>

Enzyme leaps fuel antichemotaxis

Jee, Ah-Young,Dutta, Sandipan,Cho, Yoon-Kyoung,Tlusty, Tsvi,Granick, Steve National Academy of Sciences 2018 PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF Vol.115 No.1

<▼1><P><B>Significance</B></P><P>Challenging the traditional view that enzyme kinetics are only a matter of catalyzing chemical reactions, there is mounting evidence that the enzyme catalysis enhances enzyme mobility. This is significant to programming spatio-temporal patterns of molecular response to chemical stimulus, which is common to living matter as well as to significant chemical technology. This paper shows that the enhanced diffusivity of enzymes is a “run-and-tumble” process analogous to that performed by swimming microorganisms, executed in this situation by molecules that lack the decision-making machinery of microorganisms. The result is that enzymes display “antichemotaxis” when they turn over substrate; they migrate in the direction of lesser reactant concentration.</P></▼1><▼2><P>There is mounting evidence that enzyme diffusivity is enhanced when the enzyme is catalytically active. Here, using superresolution microscopy [stimulated emission-depletion fluorescence correlation spectroscopy (STED-FCS)], we show that active enzymes migrate spontaneously in the direction of lower substrate concentration (“antichemotaxis”) by a process analogous to the run-and-tumble foraging strategy of swimming microorganisms and our theory quantifies the mechanism. The two enzymes studied, urease and acetylcholinesterase, display two families of transit times through subdiffraction-sized focus spots, a diffusive mode and a ballistic mode, and the latter transit time is close to the inverse rate of catalytic turnover. This biochemical information-processing algorithm may be useful to design synthetic self-propelled swimmers and nanoparticles relevant to active materials. Executed by molecules lacking the decision-making circuitry of microorganisms, antichemotaxis by this run-and-tumble process offers the biological function to homogenize product concentration, which could be significant in situations when the reactant concentration varies from spot to spot.</P></▼2>

Two-dimensional flow of driven particles: a microfluidic pathway to the non-equilibrium frontier

Beatus, Tsevi,Shani, Itamar,Bar-Ziv, Roy H.,Tlusty, Tsvi The Royal Society of Chemistry 2017 Chemical Society reviews Vol.46 No.18

<P>We discuss the basic physics of the flow of micron-scale droplets in 2D geometry. Our focus is on the use of droplet ensembles to look into fundamental questions of non-equilibrium systems, such as the emergence of dynamic patterns and irreversibility. We review recent research in these directions, which demonstrate that 2D microfluidics is uniquely set to study complex out-of-equilibrium phenomena thanks to the simplicity of the underlying Stokes flow and the accessibility of lab-on-chip technology.</P>