The Science Behind the Image Contest Winners: Bovine Knees Are Beautiful

This year’s winning entry in the BPS Art of Sciences Image Contest was submitted by Chiara Peres, a postdoctoral student at the Istituto Italiano di Tecnologia in Genoa.  The image shows collagen fibers in a radial section of an ex vivo bovine knee meniscus, which based on the votes, was a crowd pleaser among the BPS Meeting attendees.  Peres took some time to provide some information about the image and the science it represents.

Peres-Chiara-1st-placeTo produce this image, I used a custom made microscope for Second Harmonic Generation (SHG) Microscopy, a label free technique that exploits a second order nonlinear coherent optical process to image macromolecules with non-centrosymmetric structure, like collagen fibers. The picture is a mosaic of false colored images given by the overlay of the Backward and Forward SHG signal from the not-stained collagen fibers. In particular the image shows the big long branches of radial “tie” collagen fibers which pack together circumferential fibers, perpendicularly aligned with respect to the plane of the image.

I submitted this image because I love the hierarchical structure of the collagen and the harmonious branched, natural organization of the collagen fibers in this section of the meniscus that makes it to look like a big tree in a forest. I love also the fact that this image is “natural” and staining independent, being an image taken with a label-free technique, just collecting and false coloring the endogenous Second Harmonic Generation signal and the Two-Photon autofluorescence of the collagen, without any modification of the sample.

I also like this image because it is a good example of my research activity: I am working to improve and develop new microscopy techniques for biological applications. In particular I am using SHG microscopy as an imaging tool for morphological characterization. This image gives us an easy and immediate means to visualize at a glance the hierarchical structure, organization and orientation of collagen fibers in different areas of the bovine meniscus, the final aim of this study.

When others look at the image, I hope that this image reminds them of an expressionist painting of a forest, as if they were looking at a “micro Van Gogh” being, at the same time, an important method of tissue imaging which connects structures at the micro-scale to macroscopic properties.

Supporting Scientific Information

The cartilage meniscus regeneration after an injury is rarely successful, because the soft scaffolds used lack the mechanical properties to withstand immediate loading. For this reason a strong effort is being done in tissue engineering area to design and to develop a new scaffold that mimics the original tissue, selecting an appropriate material and paying close attention at its mechanical and structural properties. We are studying ex vivo bovine meniscus to realize a proper model for a meniscus scaffold. Our work provides insights on the link between microscopic organization of collagen in different areas of meniscus and its biomechanical macroscopic functions. These results offer, for example, precious guidance for tissue engineers to evaluate the good outcome of the artificial tissues.

In addition to tissue engineering applications, our work can be useful for medical applications. In fact collagen is essential for the biomechanical integrity and the physical properties of various biological tissues and organs. In this context SHG microscopy can be used for ex-vivo imaging of different kinds of collagenous tissues that have a crucial structural and mechanical role in organism. Not only collagen, but also the myosin presents in muscle sarcomeres is another biological macromolecules which generates second harmonic. So SHG microscopy can be used to visualize the organization of these macromolecules in tissue, giving a powerful tool to monitor tissue development and pathology diagnosis.

To learn more about this research, visit my website or LinkedIn profile.

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The Science Behind the Image Contest Winners: Influenza A Virus and Mammalian Plasma Membrane Models

We are starting off the week taking a look at the science and scientist behind the scenes of the influenza A virus model that won second place in the Society’s 2015 Image contest.  The image was created by Heidi Koldsø, a postdoctoral researcher in Mark Sansom’s group in the Department of Biochemistry at Oxford University. Koldsø moved to Oxford from Denmark three years ago on an independent fellowship from the Alfred Benzon foundation.  Her research is mainly focused on understanding in details how membrane proteins, which are the largest pharmaceutical target, interact with their surrounding environment. She notes that understanding of not only the membrane proteins but also the lipids surrounding them is of the utmost importance – for example understanding how antimicrobial peptides target bacterial membranes and not human ones. Also, as illustrated in this image, if it is possible to understand how a virus interacts with the cell membrane, scientists can hopefully come up with solutions for better antiviral pharmaceuticals.


The images of the molecular models that captured the attention (and votes) of the 2015 BPS annual meeting attendees were constructed using the molecular visualization program Visual Molecular Dynamics (VMD). Ambient occlusion shading and rendering techniques were applied to the images within VMD. The image depicts an influenza A virus model in close proximity to a coarse grained mammalian plasma membrane model. Due to the large number of particles within these models we used a powerful workstation with lots of memory and a recent graphics card to create the image.

I chose this particular image to submit to the contest because it encapsulates both the achievements we have already made and those that are to come and it was a natural choice as an image that represents the science we study, the hard work we put into it and the potential real world applications it has. Both the project on the outer envelope of the influenza A virus and the large scale cell membranes are very ambitious and time consuming projects and are the result of a lot of hard work from a number of people. This image is the culmination of those two separate endeavours but also the beginning of the next.

When looking at the image, I hope it inspires the viewer to appreciate the current advances in computational modelling and how far we have come in our efforts to probe very real and relevant problems. The image is not only a pretty representation of a simulation as being able to visualize systems at these length scales provide us with unique insight to how these elements might look in vivo. The image does not only give a first glimpse of the molecular details of virus interactions with the membrane but also hopefully provides scientists and the general public with something that they can relate to and will hopefully promote intelligent discussion.

Supporting Scientific Information

The image is a product of the combined efforts of two large ongoing projects in the Sansom research lab at Department of Biochemistry, University of Oxford. The specific research from which the structures are taken involves performing coarse grained molecular dynamics simulations that we run on super-computing resources.

During the last couple of years I have been working on methods to construct complex asymmetric membrane models that allows us to move towards more ‘in vivo’ like systems. Our initial results on studies of complex membranes and the correlation between membrane nano-domains and curvature was published last year (Koldsø et al. PLoS Comput Biol (2014) 10(10): e1003911. doi:10.1371/journal.pcbi.1003911). We have recently started to move toward studying ‘in vivo’ like plasma membrane models at experimental length scales, meaning we are running simulations of systems >100 nm in dimensions and composed or millions of particles.

A complete model of the outer envelope of influenza A virus has recently been revealed, this project was initiated by a previous Postdoc in the Sansom lab,. Daniel Parton (currently working with John Chodera at MSKCC in New York) and has been continued by Tyler Reddy during the last 3 years in Oxford. This Influenza A virion model was recently published in Structure (Reddy et al. (2015) Structure, 23, 584-597).

The image is a result of combining these two projects on the influenza A virus and large scale mammalian cell membranes. We are exploiting the large deformations and curvatures that we observe in the mammalian plasma membrane model to accommodate the virus. This system is extremely complex and large (> 10 M particles) and Tyler and I are currently in the process of equilibrating and optimizing this model. Computational studies of the influenza A virus in close proximity to the cell membrane will potentially provide us with valuable information regarding how viruses enters the human cell during infection.

More information about my research and publications can be found on my website  and the website of my collaborator, Tyler Reddy.

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Technique Reveals a Novel Cell Migration Model


The cover image of Biophysical Journal (Volume 108, Issue 7) shows two chemoattractant-loaded microsource beads, which are being used to induce directed Jurkat cell migration.  The image of the cell was obtained using SEM.  The microsource beads, denoted by the two larger blue spheres, are fabricated using a solvent evaporation-spontaneous emulsion technique loaded with SDF-1α chemoattractant.  The beads can be trapped and manipulated by optical tweezers, represented by the two beams of light, so that the chemoattractant molecules are released to form a concentration gradient that stimulates cell migration.  The released molecules are denoted as a mass of small blue dots.  Cell migration is involved in many fundamental biological phenomena, such as cancer, tissue repair, embryonic morphogenesis, and neural development.  Cell migration is often driven by chemotaxis, where cells follow a gradient toward or away from a source of a specific chemical.  For example, bacteria find food by swimming toward the highest concentration of food molecules, or inversely flee from poisons.

The technique represented by this cover image provides a powerful new tool to probe the mechanisms of chemotactic cell migration.  In the associated study, this tool was used to reveal a novel cell migration model, which illustrates the relationship among the concentration gradient, the protrusion force, and the cell velocity.  The theoretical prediction and the experimental results show that the motility of the cell increases when the gradient initially changes, indicating that the cell is sensitive to the initial external stimulation.  However, both the cell velocity and protrusion force gradually stabilize when the gradient was higher than a certain value.  This finding is novel and important for us to better understand cell migration.

There are still many outstanding questions about chemotaxis and cell migration.  The approach shown here provides an effective tool to study cell migration in a controllable, observable, and flexible way.  The data available from this approach are also relevant to the development of migration-based biomedical applications, such as targeted therapy, stem cell therapy, and tissue engineering.  Further information on our research can be found at:

– Hao Yang, Xue Gou, Yong Wang, Tarek M Fahmy, Anskar Y-H Leung, Jian Lu and Dong Sun

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The Science Behind the Image Contest Winners: MinD, Spirals, and Turing Patterns

Each year the Biophysical Society hosts an image contest in conjunction with the Annual Meeting. And each year we are blown away by the beauty, the variety, and the scientific advancements encaptured by the submitted images.

Annual meeting attendees vote for their favorite images and the top three vote getters are recognized with prizes, as well as in the Society newsletter. To follow-up this year, we will be featuring the winners here on the BPS blog, so that readers can learn more about the images and the research behind them.  Today, we start off with the third place winner, Anthony G. Vecchiarelli, a research fellow in the laboratory of Kiyoshi Mizuuchi at the National Institutes of Health, where he uses microfluidics and single-molecule microscopy to reconstitute and visualize self-organizing systems involved in intracellular organization. Vecchiarelli notes that “Collectively, these studies have fundamentally changed our understanding of intracellular spatial organization and unveiled a new mode of transport that uses protein patterns on biological surfaces for the positioning of DNA, organelles, and the cell-division apparatus.”

Min-Spiral---3rd-place_2My submission to the 2015 BPS image contest shows one of the many stunning and dynamic patterns that this minimal system can achieve when reconstituted in our flowcell. At a wave front, MinD binds the membrane. Towards the rear of the wave, MinE accumulates up to a threshold density that results in the precipitous release of both proteins. Once MinE also releases the bilayer, MinD initiates another wave. As shown in our image, this interplay can form spirals, which are consistent with Turing patterns based on reaction-diffusion principles.

Similar spirals were first reconstituted on flat bilayers by Martin Loose while in the Schwille group (Loose et al., 2008). Together, the Schwille and Mizuuchi labs have used this technique to provide significant advances in understanding the patterning mechanism (Loose et al., 2008; Ivanov et al., 2010; Vecchiarelli et al., 2014). It is an exciting time to study this unique positioning mechanism as a growing diversity of intracellular cargos have been shown to use related systems for their subcellular organization (Vecchiarelli et al., 2012). We anticipate that surface-mediated bio-molecular patterning will become an emerging theme throughout all kingdoms of life.

I submitted this image to the BPS Image contest because I love how it emphasizes what can be achieved with proteins when released from the confines of the cell. In vivo, MinD and MinE form a pole-to-pole oscillator. But on an expansive flat bilayer, their biochemical potential for pattern formation is unleashed. MinD and MinE can form a variety of patterns including the spirals shown in my image. Dissecting how these patterns form outside of the cell is unraveling the oscillatory mechanism used inside the cell.

“What I cannot create, I do not understand.”  This quote by Richard Feynman is the essence of synthetic biology. To say that we fully understand a cell, we must first build one from the bottom up. We are approaching a time where it is feasible to experimentally challenge the concept of a protocell. The MinCDE system, and related positioning systems, will be key to such an endeavor because they are composed of a minimal number of components that self-organize to position essential cargos, such as the cell division apparatus. But first we must define the systems and develop a full biochemical understanding of the components, which can be achieved via cell-free reconstitution experiments presented in the image. I hope this image gets others just as excited and motivated as I am about studying this fascinating pattern-mediated positioning system, which may turn out to be the norm as opposed to the exception in all cells.

This image shown is a Turing pattern. Alan Turing was first to describe a mathematical model called “reaction-diffusion” that explains how the concentration of one or more substances distributed in space changes after a local reaction and subsequent diffusion. Alan is mainly known for conceiving of a machine that we now call a computer, and for breaking the German Enigma code, which played a pivotal role in ending WWII. But he always had a fascination with patterns in nature and his one and only Biology paper that describes reaction-diffusion is also his most cited. Turing was not applauded for these extraordinary efforts. Rather, because Alan Turing was gay at a time it was illegal, he was sentenced to chemical castration, labeled a security risk, and lost his job as perhaps one of the best code breakers that ever lived. The resultant depression led to suicide. I hope this image reminds viewers of Alan’s ongoing contributions to science.

Supporting Scientific Information

The intricate subcellular organization of a eukaryotic cell is mainly communicated by actin filaments, microtubules, and motor proteins that drive along these cables. Recent improvements in microscopy have recently shown that bacteria also display complex intracellular organization. The view of bacterial cells as simply sacks of enzymes is obsolete. But instead of using cables and motors for moving the ‘innards’ of a bacteria cell, dynamic protein patterns on biological surfaces, such as the inner membrane, are emerging as the critical driving forces for positioning a wide variety of cargos such as the bacterial chromosome, plasmids, organelles, and even the cell division apparatus.

In E. coli, the MinCDE system self-organizes into a cell-pole-to-cell-pole oscillator that positions the divisome at mid-cell so that daughter cells are equal in size. The MinD protein is an ATPase that binds the membrane in its ATP-bound form and recruits the cell division inhibitor MinC. MinE stimulates the ATP-hydrolysis activity of MinD, which releases MinD from the membrane. The perpetual chase of MinD by MinE creates the pole-to-pole oscillator, which maintains a low level of the division inhibitor at mid-cell where divisome assembly and cell division is allowed to take place. How Min proteins interact with the membrane surface to generate the in vivo oscillations is a subject of intense study.

The number of factors involved in subcellular organization makes it difficult to study individual systems under controlled conditions in vivo. We in Dr. Kiyoshi Mizuuchi’s group developed a cell-free technique to visualize and study spatial organization mechanisms.  The MinD protein was fused to Green Fluorescent Protein and the MinE protein was labeled with an Alexa dye. The two proteins were mixed in a buffer containing ATP and infused into a flowcell that had its surfaces coated with a flat lipid bilayer, which acts as a biomimetic of the inner membrane. The dynamics of MinD and MinE were then visualized by total internal reflection fluorescence microscopy (TIRFM), a technique that specifically resolves surface-associated processes.


Loose M, Fischer-Friedrich E, Ries J, Kruse K, Schwille P. 2008. Spatial Regulators for Bacterial Cell Division Self-Organize into Surface Waves in vitro. Science 320: 789
Ivanov V, Mizuuchi K. Multiple modes of interconverting dynamic pattern formation by bacterial cell division proteins. 2010. Proc Natl Acad Sci USA 107: 8071
Vecchiarelli AG, Li M, Mizuuchi M, Mizuuchi K. 2014. Differential affinities of MinD and MinE to anionic phospholipid influence Min patterning dynamics in vitro. Mol Microbiol 93: 453
Vecchiarelli AG, Mizuuchi K, Funnell BE. 2012. Surfing biological surfaces: exploiting the nucleoid for partition and transport in bacteria. Mol Microbiol 86:513
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A Bright Future: Using Bioluminescence as a Reporter of Mechanosensitivity












The cover of Biophysical Journal (Volume 108, Issue 6) shows autofluorescence of a cell of the bioluminescent dinoflagellate Pyrocystis lunula. In this laser scanning confocal microscope image, blue is the fluorescence of luciferin, the substrate molecule for the bioluminescence reaction that originates from vesicles called scintillons, while red is chlorophyll fluorescence originating from the plastids. Dinoflagellate bioluminescence, which in nature functions in predator defense, here serves as a rapid whole-cell reporter of mechanosensitivity. Bioluminescence emission is mediated by a poorly understood but complex signaling pathway that involves activity at the plasma membrane, release of calcium from intracellular stores, depolarization of the vacuolar membrane, and acidification of the scintillons to activate the oxidation of luciferin. With a delay from mechanical stimulation to response of only 15-20 ms, dinoflagellate bioluminescence is one of the fastest known mechanosensitive cell systems. Thus dinoflagellate bioluminescence serves as an extremely rapid, whole cell noninvasive reporter of mechanosensitivity.

In our study, we used atomic force microscopy and a spherical probe to stimulate individual cells and to examine the relationship between cell mechanical properties and mechanosensitivity as assessed by intrinsic bioluminescence. The dinoflagellate flash, in this species lasting about 400 ms, is an all-or-nothing phenomenon that served as an indicator of cell response. By varying the parameters of the applied stimulation, we were able to determine a threshold force and velocity that was necessary to stimulate the cell. We observed that cells did not respond to a low indentation velocity. To explain this phenomenon we carried out stress relaxation experiments to measure the viscoeleastic properties of the cell. We formulated a simple viscoelastic model involving dashpots and springs to explain the velocity-dependent responses in terms of mechanosensor activation. At high rates of stimulation, stress accumulates in the cell membrane leading to a conformational change in mechanosensors, while at low stimulation rates the energy is dissipated due to relaxation. We are excited to develop our studies using dinoflagellate bioluminescence as a tool to investigate cellular mechanisms of rapid mechanosensing.

In nature, dinoflagellate bioluminescence is responsible for spectacular nighttime light displays when stimulated by mechanical stress associated with swimming animals, boat wakes, and breaking waves. In the laboratory, dinoflagellate bioluminescence is demonstrating its value to the physical sciences as a flow visualization tool for regions of increased mechanical stress, especially in applications not amenable to conventional measurement methods, such as shear stress within bioreactors, in breaking waves, above a rippled seabed, and associated with a moving dolphin.

Our use of dinoflagellate bioluminescence as a flow visualization tool was inspired by Leonardo da Vinci, who more than 500 years ago used grass seeds as particles to visualize flow patterns. Bioluminescence is a beautiful expression of nature, and it has been inspiring to collaborate with artists to express that beauty in photographs and video, for example Dinoflagellate bioluminescence also serves as a tool in education and public outreach, that, along with its artistic value, is valuable in bringing science to the public. For more information about our research and dinoflagellate bioluminescence, visit

– Benoit Tesson, Michael Latz

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Pi, Pie, Knotted Structures, and Biophysics

Biophysicists have always found themselves closely connected to many allied disciplines and conducting research that blurs the lines between these disciplines. With March 14 officially marking the celebration of Pi, the Biophysical Society thought it was a good time to shed some light on the amazing discoveries mathematics research (and Pi!) has contributed to the field of biophysics.

The Society was fortunate to co-sponsor a meeting on the significance of knotted structures for functions of proteins and nucleic acids that included among the speakers many mathematicians.  We have asked three speakers from that meeting to share some thoughts on their work, their career trajectory, and of course, Pi, with us in honor of Pi day.

 Stu Whittington
University of Toronto

Stuart (Stu) Whittington’s interest in Biophysics was sparked when he realized that circular DNA molecules from bacteria could be knotted and that these knots could interfere with cellular processes such as replication. He says that he is “definitely not a biologist — indeed I never took a biology course in high school or in university.” His main research interests are in rigorous statistical mechanics, especially of models of polymers, and he likes models with a combinatorial (so that he can count instead of integrating) or topological flavor. Whittington first became interested in knotting in ring polymers when he heard De Witt Sumners talk about it in about 1986. Whittingon and Sumners have been working together on random knotting and linking ever since. They have proved some results about the inevitability of knotting in long flexible objects (like hose pipes and DNA molecules) and also about the inevitability of writhe. These ideas are easily understood by the general public (who hasn’t found random knots in an extension cord?) and are a useful way to engage the average person about the utility of mathematics in biophysics, as well as in chemistry and physics.

Chris Soteros
University of Saskatchewan

Chris Soteros focuses on lattice models of polymers and biopolymers.  She uses combinatorics, probability, and asymptotic analysis to study the models as well as exact enumeration and Monte Carlo computer simulation methods. In addition, analyzing the computer simulation data involves statistical methods. By using these mathematical approaches, Soteros and her colleagues can identify the minimal ingredients needed to incorporate into a model in order to observe trends similar to those obtained in polymer and biopolymer experiments.  Sometimes it is possible to prove results about the models.  This can lead to new insights into the experimental results or can significantly strengthen the evidence for what was previously conjectured.

Soteros, who identifies herself as a mathematician, got her start in biophysical research in 1988 when she was a postdoc working with Stuart Whittington.  At that time she had the opportunity to study a mathematical problem that was motivated by a DNA topology question. This work was in collaboration with De Witt Sumners and resulted in a paper:  C.E. Soteros, D.W. Sumners and S.G. Whittington, 1992. Entanglement Complexity of Graphs in Z3. Math. Proc. Camb. Phil. Soc., 111, 75-91.  Soteros has been studying related problems every since then.

One challenge Soteros finds in working at this interface is learning enough terminology from another discipline, such as molecular biology, to read journal articles in that discipline. It can also be a challenge to keep on top of the latest advances in more than one discipline.  On the other hand, these barriers are greatly reduced when one collaborates with others who have complementary expertise and who are open to bridging the communication gap.  Soteros feels fortunate to have been involved in many such collaborations.

Soteros is especially grateful for having many opportunities to learn from others at interdisciplinary conferences involving molecular biologists, physicists, chemists, mathematicians, and computer scientists. The September 2014 Biophysical Society’s thematic meeting, “Significance of Knotted Structures for Functions of Proteins and Nucleic Acids’’ Conference in Warsaw, Poland was a prime example.

From the perspective of other researchers, Soteros thinks her work is interesting when she and her colleagues prove or find strong evidence for hypotheses that were previously only conjectures, or when they propose a novel hypothesis or conjecture.  She offers an example, “We were able to prove for a model of polymers confined to a tube, that knotting is inevitable for very large polymers, regardless of whether they are stretched or compressed (M. Atapour, C. Soteros and S. Whittington, 2009. Stretched polygons in a lattice tube. J. Phys. A:  Math. Theor., vol. 42, 322002 (9pp)).

From the perspective of the public, Soteros’ work demonstrates that fairly simple mathematical models can be used to gain insights into DNA experiments. More broadly, improved understanding of enzyme action on DNA through collaborative efforts involving mathematicians, physicists and molecular biologists is expected to lead to improved cancer treatments.

As for Pi, Soteros does use it in her work.  She says, “Some simple examples come immediately to mind. We studied how knot reduction in a model of topoisomerase action on DNA depends on the opening angle at the strand-passage site (M. L. Szafron and C. E. Soteros, 2011. The effect of juxtaposition angle on knot reduction in a lattice polygon model of strand passage. Fast Track Communication, J. of Phys. A: Math. Theor., Vol. 44 (322001), (11 pp)).   In the calculations, the angles were calculated in radians where 2Pi radians corresponds to 360 degrees.  Also, in the statistical analysis of our computer simulation data, we use the central limit theorem; this uses the standard Normal (or Gaussian) distribution that has density function function 1/√2π e^(-〖x〗^2/2).  Also, we use polygons on the simple-cubic lattice to model polymer and biopolymer configurations.  The bond angles on this lattice are all either Pi/2 or Pi.”

Soteros looks forward to celebrating Pi day with some PIE!

Note:  Soteros wanted BPS blog readers  to be aware of two upcoming meetings focused on the type of research she has described in this post: May 18-29, 2015 Graduate Summer School in Applied Combinatorics  and June 1-4, 2015 The Canadian Discrete and Algorithmic Mathematics Conference (CanaDAM)


A planar projection of a 3-dimensional 5100-edge simple-cubic lattice polygon sampled from computer simulations for the paper Cheston M., McGregor K., Soteros C., and Szafron M., 2014. New evidence on the asymptotics of knotted lattice polygons via local strand-passage models. J. Stat. Mech.: Theor. Exp., 2014(2): P02014. It is a polygon with knot-type 5_1 where the “knotted part’’ is in the bright green part of the polygon at the right of the image. This is a randomly chosen 5_1 lattice polygon that illustrates what we expect to occur most often for large polygons, namely that the “knotted part” is relatively localized within the polygon. The image was created by M. Szafron using Rob Scharein’s KnotPlot software and the colour of an edge indicates its depth in the direction perpendicular to the plane of the image.

Eric Rawdon
University of St. Thomas

Eric Rawdon studies the knotting and tangling that occurs in physical systems, e.g. with DNA, proteins, or subatomic glueballs. He says he has always been drawn to computers, and gravitates towards problems that have some computational aspect. Most recently, he and his colleagues have been studying knotting in proteins, trying to understand which proteins are knotted, how they are knotted, and why they are knotted.

From Rawdon’s perspective as a trained mathematician, he thinks the things that biologists are able to do in the lab are amazing.  He notes, “I am too clumsy or impatient to deal with such messy experiments.  So I try to understand certain knotting behavior in physical systems by stripping away less relevant details.  For example, proteins are chains of amino acids.  If you analyze proteins at the atomic level, it is a mess (or at least that is how it looks to me), there are atoms and bonds everywhere. So we simplify the situation and model the protein as a chain of line segments. This is a coarse model and gives you a sort of long distance view of how the system is behaving.”

Like Soteros, Rawdon got his start in biophysical research early in his career.  His PhD advisor, Jon Simon (retired mathematician, University of Iowa), seemed to be drawn to mathematical problems in the sciences.  At conferences, Simon introduced Rawdon to many different people working in many different fields.  Rawdon never expected to do “applied” mathematics, but the biologists, chemists, and physicists brought such interesting questions to the table that he couldn’t help himself.  Early in his career he started working with Ken Millett (mathematician, University of California Santa Barbara). Like Simon, Millett had done some hard math but was open to mathematical problems in the sciences. Millett and Rawdon then team up with Andrzej Stasiak (biologist, University of Lausanne, Switzerland).

When it comes to identifying himself, Rawdon isn’t really sure what to call himself.  “I was trained as a mathematician, but I tend to publish in biology, chemistry, and physics journals.  So honestly, I’m not sure what to call myself.  But deep down inside, I think I am more mathematician than anything.”

Rawdon has continued to attend the interdisciplinary conferences he was introduced to as a graduate student.  He says the meetings he goes to typically have researchers from a wide-variety of fields, and the researchers tend to be open to interdisciplinary work. He met Joanna Sulkowska (physicist, University of Warsaw and one of the organizers of the BPS thematic meeting on Knotted Structures), at one such meeting, and she is the one who interested him in knotted proteins.

When working with scientists trained in other disciplines, Rawdon finds the biggest barrier to be language He offers the following example:  “My collaborator Andrzej Stasiak and I occasionally have disagreements over email, only to discover later that we were not in disagreement at all.  We simply both had interpreted the others’ words in terms of the language of our own fields.  If I say “protein topology” to a biologist and a mathematician, they are likely to interpret the phrase very differently.”

When asked if he has had any surprise research findings, Rawdon recounts the following collaboration from 2012:

“My collaborators and I were searching for knots in proteins. For each protein, we would generate a picture that encoded the knotting.  We created a web page of these pictures and I put them together in groups because there were many pictures that looked the same.  I sent the web page to Joanna who noticed that the similar pictures were coming from proteins that performed common functions in different organisms.  These families of proteins had diverged over hundreds of millions of years of evolution, yet the knotting patterns stayed the same.  That suggests that the knot is there for a reason. For a knot guy like me, that was pretty cool.  Our results are in a paper titled “Conservation of complex knotting and slipknotting patterns in proteins” published in the Proceedings of the National Academy of Sciences in 2012 (with Joanna Sulkowska, Ken Millett, Jose Onuchic, and Andrzej Stasiak).”

For those very interested in the topic, Rawdon directs readers to visit their website KnotProt  that has all the information you would ever want about knotted proteins.

For a general audience, Rawdon thinks his work is appealing because of all of the places where knotting appears in the sciences.  Here are just a few examples:

  • A large number of cancer drugs attack topoisomerases, enzymes that are necessary for DNA untangling during replication.
  • The antibiotic Ciprofloxacin Hydrochloride, which also targets topoisomerases, is used to treat anthrax exposure.
  • Recently, Chunfeng Zhao, M.D., of the Mayo Clinic proposed that surgeons use a new type of knot for certain types of surgeries.
  • It has been proposed that there are subatomic particles, called glueballs, which form tight knots.

As for Pi, it is not clear cut whether Rawdon uses it in his work.  He says, “Yes and no.  I think a lot about knots made out of tubes and any time you are you dealing with anything round, Pi is lurking in the shadows. Plus, I teach math, so I probably say Pi and mean the number, as opposed to the dessert, more than the average person.  But I do not think about Pi every day.  Still, each March 14, I take a moment to recognize Pi.

Tomorrow, to celebrate, the Math and Actuarial Science Club at the University of St. Thomas will buy some pies, as they do every year on Pi Day.  Since Pi Day is on the weekend this year, they are celebrating on Friday, March 13.  There are t-shirts and a pie-eating contest.  It promises to be a special event.

This image comes from a paper that was just published and is freely available for downloading: Eric Rawdon, Ken Millett, and Andrzej Stasiak, Subknots in ideal knots, random knots, and knotted proteins Scientific Reports 5:8928 (2015) In the paper, we are trying to understand what sort of simpler knots lie inside more complicated knots.  These disks are our way of encoding the information.  But in and of themselves, I find them very beautiful.

This image comes from a paper that was just published and is freely available for downloading:
Eric Rawdon, Ken Millett, and Andrzej Stasiak, Subknots in ideal knots, random knots, and knotted proteins Scientific Reports 5:8928 (2015)
In the paper, we are trying to understand what sort of simpler knots lie inside more complicated knots. These disks are our way of encoding the information. But in and of themselves, I find them very beautiful.

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Coarse-Grained Model of RNA Provides Insight into RNA Strand Displacement Reaction












The cover image of Biophysical Journal (March 10, 2015 [Volume 108, Issue 5]) shows an RNA toehold mediated strand displacement reaction, as represented by the coarse-grained oxRNA model. The invading strand (shown in blue) attaches to a single stranded overhang (the “toehold”) of the substrate strand (shown in red) and will eventually replace the incumbent strand (shown in green) because it forms the more stable complex. This process “catalyzes” the detachment of the incumbent strand, which is then available for other reactions.

RNA shows great promise as a material for nanotechnology. Like DNA, it has a four-letter alphabet that facilitates the design of stable, three-dimensional structures with near-atomic precision. Moreover, in vivo, it not only stores genetic material, as DNA does, but also acts as a structural element and can exhibit catalytic activity, much like proteins do. This versatility makes the prospect of using RNA nanotechnology for sophisticated biomedical applications, both in vitro and in vivo, particularly appealing.

Toehold-mediated strand displacement has long been an essential component for designing active DNA machines, because it allows kinetic control over the rates and ordering of key reactions. By combining multiple strand displacement reactions, complex logic operations and computation have been realized. Such success naturally raises the question of how this process could be used to create new applications in RNA nanotechnology. It also suggests that nature may exploit this relatively simple reaction inside the cell.

To unravel the underlying biophysics of strand displacement for RNA, we employed a recently derived nucleotide level coarse-grained model of RNA called oxRNA. Coarse-grained models are necessary to describe such processes that rely on rare events since the relevant time and length-scales are typically not accessible to more detailed atomistic models. OxRNA shares many features with the previously derived oxDNA model, which has successfully been used to describe many processes that are fundamental to DNA nanotechnology. In particular, these processes have reproduced experimentally measured relative rates for DNA displacement reactions with near quantitative accuracy.

We find that RNA displacement reaction rates are dominated by a complex interplay of enthalpic and entropic effects at the junction between the invading and incumbent strands. These processes cannot be captured by simple secondary structure models, and so a fully three-dimensional model such as oxRNA is necessary. We predict up to six orders of magnitude speedup between the rate for a toehold of length 1 and the saturated maximum speed for a toehold of length 5 and more. However, in contrast with DNA systems, we find that the displacement reaction is faster (by about a factor of two to nine) depending on which end of the substrate (3′ or 5′) the toehold is placed, with the 5′ toehold being faster. This difference arises from the asymmetry of the A-form helix adopted by RNA duplexes, which results in bigger stabilization of an invading strand at the 5′ end of the incumbent-substrate duplex. We also study the displacement rate at different temperatures, and find that for longer toeholds, the displacement slows down with increasing temperature.

Our results provide new insight into the fundamental biophysics of the RNA strand displacement reaction, which can be exploited to modulate reaction rates. Thus, our results improve the accuracy and flexibility of RNA nanotechnology design.

Further information about oxRNA, including a publicly accessible code and instructions for its use, can be found at

– Petr Sulc, Thomas Ouldridge, Flavio Romano, Jonathan Doye, and Ard Louis

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