Session W17: General Biological Physics

Actin-mediated bacterial propagation as dissipative dynamics of F-actin concentration: onset of motion, comet profile, velocity fluctuations

Bacterial motion under the action of an actin gel network is described in terms of the F-actin concentration dynamics driven by polymerization, elasticity, and coupling with the bacterium. An explicit formula for the velocity clarifies the role of the different factors contributing to propagation. As regards the onset of motion, we find that smaller ratios of the branching/nucleation rates give rise to an increasingly long buildup time before startup. In the cruise regime the linear growth of the comet length versus velocity is analytically shown and numerically verified; as the length increases the concentration maximum decreases. Both features have been observed in kinematics experiments [1]. By expanding our previous work [2], we show that a larger elasticity modulus makes a larger velocity but with a smaller contribution from the interface polymerization. At steady state we find two regimes: constant velocity when the branching rate dominates over the nucleation rate, intermittent velocity when the two rates are comparable. In this case the concentration profile does not display macroscopic fluctuations, but the distance of its maximum from the bacterium surface oscillates: this behavior has its counterpart in the intermittency of the cruise velocity. [1] F.S.Soo, J.A.Theriot, Biophysical Journal 89 :703-723 (2005). [2] V.G.Benza, arXiv:q-bio/0702061 (February 2007)   

The contraction of Vorticella in different Ca concentration solutions

The contraction of the stalk of \textit{Vorticella Convallaria} was studied in media with different concentrations of calcium ion solution. Seven solutions were prepared by adding different amounts of CaCl$_{2}$ in the range of 0.001M to 0.004M in 0.005M EGTA, 0.1M KCl and 0.02M MOPS. The pH values of the solutions were maintained between 6.7 and 6.9. The contractions were recorded as cines (image sequences) by a Phantom V5 camera (Vision Research) on a bright field microscope with 20X objective, with the image resolution of 256 $\times $ 128 pixels at 7000 pictures per second. The change in length of stalk as a function of time was analyzed to compute velocity, acceleration, force and force coefficient. The apparent force coefficient increases linearly with time until the whole stalk is contracting. Considering time dependence of force coefficient, the contracting length is modeled as: \[ L(t)=\frac{L_0 }{2}\left[ {\left( {1+\frac{C}{A}} \right)\exp \left( {\frac{-C+A}{2m}t} \right)+\left( {1-\frac{C}{A}} \right)\exp \left( {\frac{-C-A}{2m}t} \right)} \right] \] Where $L_0 $ is initial contractile length, $C=6\pi \eta r$, $A=\sqrt {C^2-4mK(t)} $, $\eta $ is coefficient of viscosity, $m$ is mass and$ r$ is radius of zooid.   

Kinetics of Multidentate Ligand Binding

The binding of multivalent ligands to cell surface receptors is an inherent feature of many biological processes and is technologically important in designing drug delivery systems. We analyze the binding and unbinding kinetics of a multi-armed ligand to normal and cancerous cells in terms of the residence time. By mapping the problem to a first passage time solution of the dynamics described by a multi-dimensional Fokker-Plank equation we are able to derive the residence times of the ligands on the cell surface as a function of the number of arms, binding affinity, polymer statistics of the linker arms as well as density, distribution and types of receptor binding sites. Our results point towards ways of optimizing these parameters so as to selectively target diseased cells with specially designed ligands that are capable of drug delivery. Our results also shed light on the recognition and response kinetics of a variety of cell types with specific functions that are triggered by the binding of surface receptors to exogenous ligands.   

Single cell visualization of DNA repair \textit{in vivo}.

The creation of a DNA double-strand-break constitutes the most dangerous type of DNA damage. Inefficient response to DNA damage may lead to hypersensitivity to cellular stressors, susceptibility to genomic defects and resistance to apoptosis, which can lead to cancer. Current research on DNA repair has enabled numerous breakthroughs in our understanding of the DNA repair mechanisms at the population level. However, similar understanding at the level of single cells has been lacking mainly because of two reasons: 1) population level measurements do not visualize the repair process and therefore the exact mechanism by which the donor and recipient sequences are brought together is not well understood. 2) they are only sensitive to the mean of a distribution and usually hide the cell-to-cell variability of the repair processes. In my lab we utilize a multidisciplinary approach to address specific aspects of the DNA repair at the single cell level. By tagging several locations on DNA, its dynamic is visualized. furthermore the exact timing of the repair process is measured. In our experiments, individual cells are followed over long periods of time and many cellular generations in a microfluidic device, in which a precise control of the microenvironment of the cells is possible   

Current reversal in collective rocking ratchets induces by ground state instability

A collective mechanism for current reversal in rocking ratchets is proposed. The mechanism is based on a two-dimensional instability of the ground state of the system. We illustrate our results with numerical simulations and experiments using the dynamics properties of superconducting vortex lattice in Nb superconducting films fabricated on top of Si substrates with array of asymmetric nanodefects.   

A Mathematical Exploration of MAP Kinase Behavior

Mitogen-Activated Protein (MAP) kinase pathways are highly conserved from yeast to humans and are implicated in cell survival and cell death. Signaling through these pathways starts with the phosphorylation of the most upstream component (MAP kinase kinase kinase, MAPKKK), continues with phosphorylation of a MAP kinase kinase (MAPKK), and ends with phosphorylation of the target MAP kinase (MAPK). Theoretical studies over the past few decades have generated important insights into the dynamical behavior and signal processing capability of these pathways, including bistability, oscillations, signal amplification, etc. Prompted by the possibility of complex behavior in simpler signaling units than a full MAP kinase pathway, we investigate the possibility of In-Band Detection (IBD) within a single step of the cascade. We show that a basal rate of target phosphorylation can lead to IBD in a simpler system than the one described before, and define a precise relationship between the various reaction rates that is necessary to obtain IBD.   

Electric field control of the cell orientation

Many physiological processes depend on the response of biological cells to external forces. The natural electric field at a wound controls the orientation of the cell and its division.[1] We model the cell as an elongated elliptical particle with given Young's modulus with surface charge distribution in the external electric field. Using this simple theoretical model that includes the forces due to electrostatics and the elasticity of cells, we calculated analytically the response of the cell orientation and its dynamics in the presence of time varying electric field. The calculations reflect many experimentally observed features. Our model predicts the response of the cellular orientation to a sinusoidally varying applied electric field as a function of frequency similar to recent stress-induced effects.[2] \begin{enumerate} \item Bing Song, Min Zhao, John V. Forrester, and Colin D. McCaig, ``Electrical cues regulate the orientation and frequency of cell division and the rate of wound healing \textit{in} \textit{vivo}'', PNAS 2002, vol. 99 , 13577-13582. \item R. De, A. Zemel, and S.A. Safran, ``Dynamics of cell orientation'', Nature Physics 2007, vol.3, 655. \end{enumerate}   

X-ray studies of crystal transformation in dehydrating trehalose

The disaccharide trehalose is known to assist in stabilizing dehydrated biological cellular structure. It is present in relatively large quantities in certain organisms whose bodies remain viable for significant periods of time under conditions of extreme drought. Whilst trehalose may not be unique among the sugars in this function, there have been several studies investigating the influence of water on trehalose structure in the hope of determining the mechanism responsible for the properties noted above. We report real-time wide angle X-ray diffraction studies as the commonly occurring crystalline dihydrate form of trehalose is dehydrated at a range of temperatures (in the range 40-70 C) and forms the `alpha' crystalline form of anhydrous trehalose. We find that there is evidence of a two-step process: the dehydration, followed by a crystalline-crystalline transition. The speed of the latter transition is surprising because the dehydrated amorphous form of trehalose has a glass transition temperature of roughly 120 C.   

Understanding a Period-Doubling Bifurcation in Cardiac Cells

Bifurcations in the electrical response of cardiac tissue can destabilize spatio-temporal waves of electrochemical activity in the heart, leading to tachycardia or even fibrillation. Therefore, it is important to classify these bifurcations so that we can understand the mechanisms that cause instabilities in cardiac tissue. We have determined that the period-doubling bifurcation in paced myocardium is of the unfolded border-collision type. To understand how this new type of bifurcation manifest itself in cardiac tissue, we have also studied the role of calcium in inducing the bifurcation. We will discuss the nature of the unfolded border-collision bifurcation and present our results of dual voltage and calcium measurements in a frog ventricle preparation.   

Line-defect spiral pattern formation during unstable spiral wave propagation in cardiac tissue

Spiral waves of voltage signaling in cardiac tissue are widely recognized to play an important role in the genesis of lethal heart rhythm disorders. Previous modeling studies have shown that the breakup of such waves, which has been proposed as a mechanism for heart fibrillation, can be mediated by a generic period doubling bifurcation. This bifurcation leads to beat-to-beat changes of action potential duration, and hence cellular refractoriness, known as alternans. Here we study the spatial pattern of the period two dynamics before spiral breakup. We find numerically that the line defects, the locus of all points where the dynamics has period one, can form either as a one- or a three-arm spiral pattern where each arm corresponds to a line defect emanating from the spiral core. Three-arm spirals form even when the spiral tip is meandering and lead to a greater dispersion of cellular refractoriness that is proarrhythmic. Analytical results are presented that shed light on the conditions for the formation of one- and three-arm line-defect spirals in the absence of meander.   

Multifrequency EPR study of Vanadyl and Copper complexes in the characterization of electron paramagnetic tensor parameters and dynamic parameters

Vanadyl acetylacetonate, Vanadyl meso-tetraphenylporphine, Cupric acetylacetonate, and Cupric meso-tetraphenylporphine have been studied at S-, X-, K- and Q-band in the rigid limit and in the motional narrowing regime. Data have been analyzed using the Nested Sampling Algorithm developed by J. Skilling based on methods of Bayesian inference. The EasySpin software package is used to simulate the spectral fitting function used in the parameter estimation process. Two different sets of model parameters(A$_{\vert }$, A$_{-}$ , g$_{\vert }$, g$_{-}$, D$_{xy}$ , lw and A$_{iso}$, $\Delta $A, g$_{iso}$, $\Delta $g, D$_{xy}$, lw) have been used for the data analysis at the various frequencies, both independently and in a simultaneous multifrequency fit. After comparing the results at all the frequencies, it is seen that the magnetic tensor parameters defined from the individual frequency fits fluctuate more among each other in the motional narrowing regime but dynamic parameters do not. The model parameters are better fitted in the case of porphin complexes than that in acac complexes.   

AC electrokinetics of dense inhomogeneous biological cells suspensions under nonuniform applied fields

When a biological cell is placed in a nonuniform AC (or DC) electric field, force would be induced because of the interaction between the induced electric dipole moment of the particle and the external electric field. This phenomenon is called dielectrophoresis (DEP). [1] In this study a new method is proposed to handle biological cells with arbitrary permittivity and conductivity profiles, and determine the importance of multipole effect as compared with the approximate point dipole calculation [2], which is valid if the external field is homogeneous. In real situations, cells often possess arbitrary graded profiles and the study of higher multipole effects can lead to a better understanding. We also extend the calculation to dense cells suspensions by the effective medium theories [3]. The study reveals significant effects on the DEP due to higher concentration. \newline \newline [1] \textbf{T. B. Jones,} \textit{Electromechanics of particles, Cambridge University Press, 1995} \newline [2] \textbf{C. Z. Fan, J. P. Huang, K. W. Yu,} \textit{J. Phys. Chem. B, 110, 25665 (2006).} \newline [3] \textbf{J. P}\textbf{. Huang}\textbf{, K. W. Yu}, \textit{Physics Reports 431, 87 (2006).}   

Folding of Pollen Grains

At dehiscence, which occurs when the anther reaches maturity and opens, pollen grains dehydrate and their volume is reduced. The pollen wall deforms to accommodate the volume loss, and the deformation pathway depends on the initial turgid pollen grain geometry and the mechanical properties of the pollen wall. We demonstrate, using both experimental and theoretical approaches, that the design of the apertures (areas on the pollen wall where the stretching and the bending modulus are reduced) is critical for controlling the folding pattern, and ensures the pollen grain viability. An excellent fit to the experiments is obtained using a discretized version of the theory of thin elastic shells.