Why nanorods assemble

In a recent paper in Phys. Rev. E, Brandeis postdoc Yasheng Yang and Assistant Professor of Physics Michael Hagan developed a theory to describe the assembly behavior of colloidal rods (i.e. nanorods) in the presence of inert polymer (which induces attractions between the nanorods). The nanorods assemble into several kinds of structures, including colloidal membranes, which  are two dimensional membrane-like structures composed of a one rod-length thick monolayer of aligned rods.  The theory shows that colloidal membranes are stabilized against stacking on top of each other by an entropic force arising from protrusions of rods from the membranes and that there is a critical aspect ratio (rod length/rod diameter) below which membranes are never stable. Understanding the forces that stabilize colloidal membranes is of practical importance since these structures could enable the manufacture of inexpensive and easily scalable optoelectronic devices. This work was part of a collaboration with the experimental lab of Zvonimir Dogic at Brandeis, where colloidal membranes are developed and studied.

Yang YS, Hagan MF. Theoretical calculation of the phase behavior of colloidal membranes. Phys Rev E. 2011;84(5).

Microtubules and Molecular Motors Do The Wave

Most people are familiar with audiences in crowded arenas performing “the wave,” raising their hands in sync to produce a pattern that propagates around the whole stadium.  This self-organized motion appears seemingly out of nowhere.  It is not produced by any external control, but is rather emerges from thousands of individuals interacting only with their neighbors.  A similar principle of self-organization might also be relevant on length scales that are billion times smaller.  On this scale, nanometer-sized proteins interact with each other to produce dynamical structures and patterns that are essential for life—and some of these processes are reminiscent of waves in crowded stadiums.  For example, thousands of nano-sized molecular motors located within a single eukaryotic flagellum or cilium coordinate their activity to produce wave-like beating patterns.  Furthermore, dense arrays of cilia spontaneously synchronize their beating to produce metachronal waves.

Proper functioning of cilia is essential for health; for example, cilia determine the correct polarity and location of our organs during development.  Defective cilia can cause a serious condition called situs inversus, in which the positions of the heart and lungs are mirrored from the normal state.  In another example, thousands of cilia in our lungs function to clear airways of microscopic debris such as dust or smoke by organizing their beating into coordinated, wave-like patterns.  Despite the importance of ciliar function, the exact mechanisms that lead to spontaneous wave-like patterns within isolated cilia, as well as in dense ciliary fields, is not well understood.

In a paper published in the journal Science this week, an interdisciplinary team consisting of physics graduate student Timothy Sanchez and biochemistry graduate student David Welch working with biophysicist Zvonimir Dogic and biologist Daniela Nicastro present a striking finding: the first example of a simple microscopic system that self-organizes to produce cilia-like beating patterns.  Their experimental system consists of three main components: 1) microtubule filaments; 2) motor proteins called kinesin, which consume chemical fuel to move along microtubules; and (3) a bundling agent that induces assembly of filaments into bundles.  Sanchez et al. found that under a certain set of conditions, these very simple components are able to self-organize into active bundles that spontaneously beat in a periodic manner.  One large spontaneously beating bundle is featured below:

In addition to observing the beating of isolated bundles, the researchers were also able to assemble a dense field of bundles that spontaneously synchronized their beating patterns into traveling waves.  An example of this higher-level organization is shown here:

The significance of these observations is several-fold. First, due to the importance of ciliar function for health, there is great interest in elucidating the mechanism that controls the beating patterns of isolated cilia as well as dense ciliary fields.  However, the complexity of these structures presents a major challenge.  Each eukaryotic flagellum and cilium contains more than 600 different proteins.  For this reason, most previous studies of cilia and flagella have employed a top-down approach; they have attempted to elucidate the beating mechanism by deconstructing the fully functioning organelles through the systematic elimination ­­­of constituent proteins. In this study, the researchers utilize an alternative bottom-up approach and demonstrate for the first time that it is possible to construct artificial cilia-like structures from a “minimal system,” comprised of only three components.  These observations suggest that emergent properties, spontaneously arising when microscopic molecular motors interact with each other, might play a role in formation of ciliary beating patterns.

Second, self-organizing processes in general have recently become the focus of considerable interest in the physics community.  These processes range in scale from microscopic cellular functions and swarms of bacteria to macroscopic phenomena such as flocking of birds and manmade traffic jams. Theoretical models indicate that these vastly different phenomena can be described using similar theoretical formalisms.  However, controllable experiments with flocks of birds or crowds at football stadiums are virtually impossible to conduct.  The experiments described by Sanchez et al. could serve as a model system to test a broad range of theoretical predictions. Third, the reproduction of such an essential biological functionality in a simple in vitro system will be of great interest to the fields of cellular and evolutionary biology. Finally, these findings open the door for the development of one of the major goals of nanotechnology: to design motile nano-scale objects.

These encouraging results are only the first from this very new model system.  The Dogic lab is currently planning refinements to the system to study these topics in greater depth.

UPDATE: Today, this publication was additionally featured on NPR Science Friday as the video pick of the week:

 

Summer course on building a microscope from simple components

This past June the MRSEC Center offered a condensed summer course based on the popular graduate course QB120: Quantitative Biology Instrumentation Laboratory.

Professor Dogic

The course was taught by Zvonimir Dogic of the Physics Department (pictured).   Prof. Dogic has extensive experience with several forms of microscopy and his Lab features several home-built or heavily modified optical setups.

The course is designed to offer students hands on experience with building their own optical setups from basic components as well as learning how to optimally acquire imaging data from commercial microscopes.  The focus was on understanding the physics behind microscope function and leveraging that knowledge towards improving data acquisition in the lab.

Initially, students used basic lenses, apertures, an objective, a camera and a light source to build the simplest possible light microscope.  This initial setup was quickly extended to include Köhler illumination, a core principle in microscopy which allows even illumination of the sample as well as access to the conjugate image plane for image filtering.

The next project required students to build a fluorescence microscope, a highly relevant and ubiquitous technique in biological imaging.  To image a slide with fluorescently labeled beads students used a dichroic mirror to separate excitation light at one wavelength from emission light at another wavelength.  A schematic diagram, a photo of this setup with the light path superimposed and actual data acquired with one of these microscopes can be seen in the video below.

Next, a more advanced technique in microscopy, total internal reflection microscopy (TIRF), was introduced and an imaging setup using this technique was built.  TIRF microscopes excel at imaging small molecules that are immobilized in a small area.  A laser beam was pointed to shine through a prism at an angle sufficient to cause total internal reflection and the resulting evanescent wave caused fluorescent excitation of the sample.  The video below shows a schematic and imaging data of a TIRF microscope built by students.

Finally, students used commercial microscopes to understand the principles behind phase contrast and difference interference contrast microscopy, both techniques well suited for imaging samples that are nearly transparent.

Overall the Course provided an excellent introduction to the physical principles behind microscope function.  I highly recommend it to anyone interested in using microscopes in their research!

Trimethoprim decorated beads for magnetically manipulating mammalian cells

Brandeis grad students Yue Pan (Chemistry) and Marcus Long (Biochemistry), together with postdoc Hsin-Chieh Lin and Professors Lizbeth Hedstrom and Bing Xu, have extended their previous work on 6 nm diameter magnetic nanobeads (comparable in size to a globular protein). They’ve shown that when decorated with the ligand trimethoprim, the nanobeads can be used to selectively bind to target E coli DHFR fusion proteins, and in addition can be used to manipulate live cells with a magnetic force. This work entitled “Cell Compatible Trimethoprim (TMP)-Decorated Iron Oxide Nanoparticles Bind Dihydrofolate Reductase (DHFR) for Magnetically Modulating Focal Adhesion of Mammalian Cells” is now online in the Journal of the American Chemical Society (JACS).

These small, magnetic beads are the first example of solid supported trimethoprim and have numerous advantages over larger traditional beads, including rapid purification, and ultra low non-specific binding. It is, however, their ability to affect live cells that is most important. In the paper they first show that Cos-1 and HeLa cells can be incubated with the beads for over 5 days with little cell death. These cells can subsequently be manipulated by transfection. Finally when exposed to a magnetic force, the focal adhesion of bead-treated Cos-1 cells can be manipulated.

See also: recommendation at Faculty of 1000

Collective behaviors in active matter

Active matter is describes systems whose constituent elements consume energy and are thus out-of-equilibrium. Examples include flocks or herds of animals, collections of cells, and components of the cellular cytoskeleton. When these objects interact with each other, collective behavior can emerge that is unlike anything possible with an equilibrium system. The types of behaviors and the factors that control them however, remain incompletely understood. In a recent paper in Physical Review Letters, “Excitable patterns in active nematics“, Giomi and coworkers develop a continuum theoretical description motivated by recent experiments from the Dogic group at Brandeis in which microtubules (filamentous cytoskeletal molecules) and clusters of kinesin (a molecular motor) exhibit dramatic spatiotemporal fluctuations in density and alignment. Specifically, they consider a hydrodynamic description for density, flow, and nematic alignment. In contrast to previous theories of this type, the degree of nematic alignment is allowed to vary in space and time.  Remarkably, the theory predicts that the interplay between non-uniform nematic order, activity and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media and biological examples such as the cardiac cycle. At even higher activity the dynamics is chaotic and leads to large-scale swirling patterns which resemble those seen in recent experiments. An example of the flow pattern is shown below left, and the nematic order parameter, which describes the degree of alignment of the filaments, as shown for the same configuration below right. These predictions can be tested in future experiments on systems of microtubules and motor proteins.

The system behavior for an active nematic at high activity. (left) The velocity field (arrows) is superimposed on a plot of the concentration of active nematogens (green=large concentration, red=small concentration). (right) A plot of the nematic order parameter, S,  (blue=large S, brown=small S) is superimposed on a plot of the nematic director (arrows). The flow under high activity is characterized by large vortices that span lengths of the order of the system size and the director field is organized in grains.

 

Prolonging assembly through dissociation

Microtubules are semiflexible polymers that serve as structural components inside the eukaryotic cell and are involved in many cellular processes such as mitosis, cytokinesis, and vesicular transport. In order to perform these functions, microtubules continually rearrange through a process known as dynamic instability, in which they switch from a phase of slow elongation to rapid shortening (catastrophe), and from rapid shortening to growth (rescue). The basic self-assembly mechanism underlying this process, assembly mediated by nucleotide phosphate activity, is omnipresent in biological systems.  A recent paper, Prolonging assembly through dissociation: A self-assembly paradigm in microtubules ,  published in the May 3 issue of Physical Review E,  presents a new paradigm for such self-assembly in which increasing depolymerization rate can enhance assembly.  Such a scenario can occur only out of equilibrium. Brandeis Physics postdoc Sumedha, working with Chakraborty and Hagan, carried out theoretical analysis of a stochastic hydrolysis model to demonstrate the effect and predict features of growth fluctuations, which should be measurable in experiments that probe microtubule dynamics at the nanoscale.

Model for microtuble dynamics. All activity is assumed to occur at the right end of the microtubule (denoted as ">")

The essential features of the model that leads to the counterintuitive result of depolymerization helping assembly are (a) stochastic hydrolysis that allows GTP to transform into GDP  in any part of the microtubule, and (b) a much higher rate of GTP attachment if the end of the microtubule has a GTP-bound tubulin dimer, compared to a GDP-bound tubulin dimer.    Process (a) leads to islands of GTP-bound tubulins to be buried deep in the microtubule.   Depolymerization from the end reveals these islands and enhances assembly because of the biased attachment rate (b).  The simplicity of the model lent itself to analytical results for various aspects of the growth statistics in particular parameter regimes.   Simulations of the model supported these analytical results, and extended them to regimes where it was not possible to solve the model analytically.  The statistics of the growth fluctuations in this stochastic hydrolysis model are very different from “cap models” which do not have GTP remnants buried inside a growing microtubule.   Testing the predictions in experiments could, therefore, lead to a better understanding of the processes underlying dynamical instability in-vivo and in-vitro.   An interesting question to explore is whether the bias in the attachment rates is different under different conditions of microtubule growth.

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