The mechanisms responsible for 2-dimensional pattern formation in bacterial macrofiber populations grown on solid surfaces: fiber joining and the creation of exclusion zones

BACKGROUND: When Bacillus subtilis is cultured in a complex fluid medium under conditions where cell separation is suppressed, populations of multicellular macrofibers arise that mature into ball-like structures. The final sedentary forms are found distributed in patterns on the floor of the growth chamber although individual cells have no flagellar-driven motility. The nature of the patterns and their mode of formation are described in this communication. RESULTS: Time-lapse video films reveal that fiber-fiber contact in high density populations of macrofibers resulted in their joining either by entwining or supercoiling. Joining led to the production of aggregate structures that eventually contained all of the fibers located in an initial area. Fibers were brought into contact by convection currents and motions associated with macrofiber self-assembly such as walking, pivoting and supercoiling. Large sedentary aggregate structures cleared surrounding areas of other structures by dragging them into the aggregate using supercoiling of extended fibers to power dragging. The spatial distribution of aggregate structures in 6 mature patterns containing a total of 637 structures was compared to that expected in random theoretical populations of the same size distributed in the same surface area. Observed and expected patterns differ significantly. The distances separating all nearest neighbors from one another in observed populations were also measured. The average distance obtained from 1451 measurements involving 519 structures was 0.73 cm. These spacings were achieved without the use of flagella or other conventional bacterial motility mechanisms. A simple mathematical model based upon joining of all structures within an area defined by the minimum observed distance between structures in populations explains the observed distributions very well. CONCLUSIONS: Bacterial macrofibers are capable of colonizing a solid surface by forming large multicellular aggregate structures that are distributed in unique two-dimensional patterns. Cell growth geometry governs in an hierarchical way the formation of these patterns using forces associated with twisting and supercoiling to drive motions and the joining of structures together. Joining by entwining, supercoiling or dragging all require cell growth in a multicellular form, and all result in tightly fused aggregate structures

Twirling Elastica: Kinks, Viscous Drag, and Torsional Stress

Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state torsional stress and shape of a rotating rod with a kink. Drag deforms the rod, ultimately extending or folding it depending on the kink angle. For certain kink angles and kink locations, both states are possible at high rotation rates. The agreement between our macroscopic experiments and the theory is good, with no adjustable parameters.Comment: 4 pages, 4 figure

The Viscous Nonlinear Dynamics of Twist and Writhe

Exploiting the "natural" frame of space curves, we formulate an intrinsic dynamics of twisted elastic filaments in viscous fluids. A pair of coupled nonlinear equations describing the temporal evolution of the filament's complex curvature and twist density embodies the dynamic interplay of twist and writhe. These are used to illustrate a novel nonlinear phenomenon: ``geometric untwisting" of open filaments, whereby twisting strains relax through a transient writhing instability without performing axial rotation. This may explain certain experimentally observed motions of fibers of the bacterium B. subtilis [N.H. Mendelson, et al., J. Bacteriol. 177, 7060 (1995)].Comment: 9 pages, 4 figure

Application of Design of Experiments (DOE) on the Processing of Rapid Prototyped Samples

The purpose of this experiment was to improve the Fused Deposition Modeling Process by examining the tensile strength of samples fabricated in a Stratasys FDM 1650 Machine utilizing the methods of Design of Experiments. A two-level, four-factor, full factorial experiment was conducted. The selected factors were temperature, air gap, slice thickness, and raster orientation. A regression equation determined the level each factor should be set in order to optimize the FDM machine settings. It was found that single factors - small air gap, small layer thickness and low raster orientation, as well as the interaction between high temperature and small layer thickness yielded the greatest effect the response.Mechanical Engineerin

The dynamic behavior of bacterial macrofibers growing with one end prevented from rotating: variation in shaft rotation along the fiber's length, and supercoil movement on a solid surface toward the constrained end

BACKGROUND: Bacterial macrofibers twist as they grow, writhe, supercoil and wind up into plectonemic structures (helical forms the individual filaments of which cannot be taken apart without unwinding) that eventually carry loops at both of their ends. Terminal loops rotate about the axis of a fiber's shaft in contrary directions at increasing rate as the shaft elongates. Theory suggests that rotation rates should vary linearly along the length of a fiber ranging from maxima at the loop ends to zero at an intermediate point. Blocking rotation at one end of a fiber should lead to a single gradient: zero at the blocked end to maximum at the free end. We tested this conclusion by measuring directly the rotation at various distances along fiber length from the blocked end. The movement of supercoils over a solid surface was also measured in tethered macrofibers. RESULTS: Macrofibers that hung down from a floating wire inserted through a terminal loop grew vertically and produced small plectonemic structures by supercoiling along their length. Using these as markers for shaft rotation we observed a uniform gradient of initial rotation rates with slopes of 25.6°/min. mm. and 36.2°/min. mm. in two different fibers. Measurements of the distal tip rotation in a third fiber as a function of length showed increases proportional to increases in length with constant of proportionality 79.2 rad/mm. Another fiber tethered to the floor grew horizontally with a length-doubling time of 74 min, made contact periodically with the floor and supercoiled repeatedly. The supercoils moved over the floor toward the tether at approximately 0.06 mm/min, 4 times faster than the fiber growth rate. Over a period of 800 minutes the fiber grew to 23 mm in length and was entirely retracted back to the tether by a process involving 29 supercoils. CONCLUSIONS: The rate at which growing bacterial macrofibers rotated about the axis of the fiber shaft measured at various locations along fibers in structures prevented from rotating at one end reveal that the rate varied linearly from zero at the blocked end to maximum at the distal end. The increasing number of twisting cells in growing fibers caused the distal end to continuously rotate faster. When the free end was intermittently prevented from rotating a torque developed which was relieved by supercoiling. On a solid surface the supercoils moved toward the end permanently blocked from rotating as a result of supercoil rolling over the surface and the formation of new supercoils that reduced fiber length between the initial supercoil and the wire tether. All of the motions are ramifications of cell growth with twist and the highly ordered multicellular state of macrofibers

Molecular elasticity and the geometric phase

We present a method for solving the Worm Like Chain (WLC) model for twisting semiflexible polymers to any desired accuracy. We show that the WLC free energy is a periodic function of the applied twist with period 4 pi. We develop an analogy between WLC elasticity and the geometric phase of a spin half system. These analogies are used to predict elastic properties of twist-storing polymers. We graphically display the elastic response of a single molecule to an applied torque. This study is relevant to mechanical properties of biopolymers like DNA.Comment: five pages, one figure, revtex, revised in the light of referee's comments, to appear in PR

Spontaneous periodic travelling waves in oscillatory systems with cross-diffusion

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently large domain, spatially uniform oscillations in such systems are unstable with respect to small perturbations. This instability, through a transient regime appearing as spontanous focal sources, leads to establishment of periodic traveling waves. The traveling waves regime is established even if boundary conditions do not favor such solutions. The stable wavelength are within a range bounded both from above and from below, and this range does not coincide with instability bands of the spatially uniform oscillations.Comment: 7 pages, 4 figures, as accepted to Phys Rev E 2009/10/2

Using support vector machines on photoplethysmographic signals to discriminate between hypovolemia and euvolemia

Identifying trauma patients at risk of imminent hemorrhagic shock is a challenging task in intraoperative and battlefield settings given the variability of traditional vital signs, such as heart rate and blood pressure, and their inability to detect blood loss at an early stage. To this end, we acquired N = 58 photoplethysmographic (PPG) recordings from both trauma patients with suspected hemorrhage admitted to the hospital, and healthy volunteers subjected to blood withdrawal of 0.9 L. We propose four features to characterize each recording: goodness of fit (r2), the slope of the trend line, percentage change, and the absolute change between amplitude estimates in the heart rate frequency range at the first and last time points. Also, we propose a machine learning algorithm to distinguish between blood loss and no blood loss. The optimal overall accuracy of discriminating between hypovolemia and euvolemia was 88.38%, while sensitivity and specificity were 88.86% and 87.90%, respectively. In addition, the proposed features and algorithm performed well even when moderate blood volume was withdrawn. The results suggest that the proposed features and algorithm are suitable for the automatic discrimination between hypovolemia and euvolemia, and can be beneficial and applicable in both intraoperative/emergency and combat casualty care

Twirling and Whirling: Viscous Dynamics of Rotating Elastica

Motivated by diverse phenomena in cellular biophysics, including bacterial flagellar motion and DNA transcription and replication, we study the overdamped nonlinear dynamics of a rotationally forced filament with twist and bend elasticity. Competition between twist injection, twist diffusion, and writhing instabilities is described by a novel pair of coupled PDEs for twist and bend evolution. Analytical and numerical methods elucidate the twist/bend coupling and reveal two dynamical regimes separated by a Hopf bifurcation: (i) diffusion-dominated axial rotation, or twirling, and (ii) steady-state crankshafting motion, or whirling. The consequences of these phenomena for self-propulsion are investigated, and experimental tests proposed.Comment: To be published in Physical Review Letter

Labels for non-individuals

Quasi-set theory is a first order theory without identity, which allows us to cope with non-individuals in a sense. A weaker equivalence relation called ``indistinguishability'' is an extension of identity in the sense that if $x$ is identical to $y$ then $x$ and $y$ are indistinguishable, although the reciprocal is not always valid. The interesting point is that quasi-set theory provides us a useful mathematical background for dealing with collections of indistinguishable elementary quantum particles. In the present paper, however, we show that even in quasi-set theory it is possible to label objects that are considered as non-individuals. We intend to prove that individuality has nothing to do with any labelling process at all, as suggested by some authors. We discuss the physical interpretation of our results.Comment: 11 pages, no figure