Numerical studies of unreactive contractile networks.

We present a finite difference algorithm for integrating the reactive flow model of contractile biological polymer networks on a fixed Eulerian mesh. We discuss the accuracy and limits of the algorithm. To illustrate the application of the algorithm, we carry out a family of computations involving an unreactive contractile network contained in a two-dimensional square reaction vessel. By numerical experiments using different values of the physical parameters of the model, we find that for this simple sort of system two major dynamical modes of contraction are predicted to occur. There is the squeezing type contraction in which the network contracts to a single small clump with gradual expulsion of solution material, and the rending type contraction in which the network tears itself into a number of separate pieces. We find that to a good approximation the transition between the squeezing mode and the rending mode is controlled by a single nondimensional number (the rending number). We discuss the relevance of these results for the analysis of various experimental observations.     

The physics of flagellar motion of E. coli during chemotaxis

Flagellar motion has been an active area of study right from the discovery of bacterial chemotaxis in 1882. During chemotaxis, E. coli moves with the help of helical flagella in an aquatic environment. Helical flagella are rotated in clockwise or counterclockwise direction using reversible flagellar motors situated at the base of each flagellum. The swimming of E. coli is characterized by a low Reynolds number that is unique and time reversible. The random motion of E. coli is influenced by the viscosity of the fluid and the Brownian motion of molecules of fluid, chemoattractants, and chemorepellants. This paper reviews the literature about the physics involved in the propulsion mechanism of E. coli. Starting from the resistive-force theory, various theories on flagellar hydrodynamics are critically reviewed. Expressions for drag force, elastic force and velocity of flagellar elements are derived. By taking the elastic nature of flagella into account, linear and nonlinear equations of motions are derived and their solutions are presented.     

Cell molecular computer. VII. Cell biophysics and realistic or information physics (1)]

Living organisms measure many parameters in order to have orientation in the outer medium. That is why biophysics cannot use the ordinary laws of physics and must take into account the influence on the phenomena to be studied not only of a measurement but also of a calculation process in the real physical and biophysical device predicting the future. Science taking into account the effects of the calculating process-realistical or informative (RI) physics-has different (laws) for different times, distances and numbers of measuring and predicting parameters. RI-physics deals with unreproducible events and considers only such time intervals and distances for which the prediction can be made on the basis of earlier measurements and calculations according to the laws with optimal difficulty. It is suggested that the living cell uses the laws which are close to these optimal (limiting) laws of RI-physics. Physics and quantum mechanics can be considered as a limiting case of RI-physics. In this case values of distances and times are large enough and the number of simultaneously measured independent parameters is such that the heat effect of the calculating device would become negligible. Molecular cell computer (MCC) [I] cannot calculate the interaction of a great quantity of different molecules, using the equations of quantum mechanics because the expense of the (price of action) would be very large and both MCC and the surrounding world could change.     

Scale-free flow of life: on the biology, economics, and physics of the cell

The present work is intended to demonstrate that most of the paradoxes, controversies, and contradictions accumulated in molecular and cell biology over many years of research can be readily resolved if the cell and living systems in general are re-interpreted within an alternative paradigm of biological organization that is based on the concepts and empirical laws of nonequilibrium thermodynamics. In addition to resolving paradoxes and controversies, the proposed re-conceptualization of the cell and biological organization reveals hitherto unappreciated connections among many seemingly disparate phenomena and observations, and provides new and powerful insights into the universal principles governing the emergence and organizational dynamics of living systems on each and every scale of biological organizational hierarchy, from proteins and cells to economies and ecologies.     

Dynamics and regulation of contractile actin-myosin networks in morphogenesis

Contractile actin-myosin networks generate forces that drive cell shape changes and tissue remodeling during development. These forces can also actively regulate cell signaling and behavior. Novel features of actin-myosin network dynamics, such as pulsed contractile behaviors and the regulation of myosin localization by tension, have been uncovered in recent studies of Drosophila. In vitro studies of single molecules and reconstituted protein networks reveal intrinsic properties of motor proteins and actin-myosin networks, while in vivo studies have provided insight into the regulation of their dynamics and organization. Analysis of the complex behaviors of actin-myosin networks will be crucial for understanding force generation in actively remodeling cells and the coordination of cell shape and movement at the tissue level.     

Effect of contraction frequency on the contractile and noncontractile phases of muscle venous blood flow.

The purpose of this study was to test the hypothesis that increasing muscle contraction frequency, which alters the duty cycle and metabolic rate, would increase the contribution of the contractile phase to mean venous blood flow in isolated skeletal muscle during rhythmic contractions. Canine gastrocnemius muscle (n = 5) was isolated, and 3-min stimulation periods of isometric, tetanic contractions were elicited sequentially at rates of 0.25, 0.33, and 0.5 contractions/s. The O2 uptake, tension-time integral, and mean venous blood flow increased significantly (P < 0.05) with each contraction frequency. Venous blood flow during both the contractile (106 +/- 6, 139 +/- 8, and 145 +/- 8 ml x 100 g-1 x min-1) and noncontractile phases (64 +/- 3, 78 +/- 4, and 91 +/- 5 ml x 100 g-1 x min-1) increased with contraction frequency. Although developed force and duration of the contractile phase were never significantly different for a single contraction during the three contraction frequencies, the amount of blood expelled from the muscle during an individual contraction increased significantly with contraction frequency (0.24 +/- 0.03, 0.32 +/- 0.02, and 0.36 +/- 0.03 ml x N-1 x min-1, respectively). This increased blood expulsion per contraction, coupled with the decreased time in the noncontractile phase as contraction frequency increased, resulted in the contractile phase contribution to mean venous blood flow becoming significantly greater (21 +/- 4, 30 +/- 4, and 38 +/- 6%) as contraction frequency increased. These results demonstrate that the percent contribution of the muscle contractile phase to mean venous blood flow becomes significantly greater as contraction frequency (and thereby duty cycle and metabolic rate) increases and that this is in part due to increased blood expulsion per contraction.     

Cell prestress. I. Stiffness and prestress are closely associated in adherent contractile cells

The tensegrity hypothesis holds that the cytoskeleton is a structure whose shape is stabilized predominantly by the tensile stresses borne by filamentous structures. Accordingly, cell stiffness must increase in proportion with the level of the tensile stress, which is called the prestress. Here we have tested that prediction in adherent human airway smooth muscle (HASM) cells. Traction microscopy was used to measure the distribution of contractile stresses arising at the interface between each cell and its substrate; this distribution is called the traction field. Because the traction field must be balanced by tensile stresses within the cell body, the prestress could be computed. Cell stiffness (G) was measured by oscillatory magnetic twisting cytometry. As the contractile state of the cell was modulated with graded concentrations of relaxing or contracting agonists (isoproterenol or histamine, respectively), the mean prestress ((t)) ranged from 350 to 1,900 Pa. Over that range, cell stiffness increased linearly with the prestress: G (Pa) = 0.18(t) + 92. While this association does not necessarily preclude other interpretations, it is the hallmark of systems that secure shape stability mainly through the prestress. Regardless of mechanism, these data establish a strong association between stiffness of HASM cells and the level of tensile stress within the cytoskeleton.     

Myosin II dynamics and cortical flow during contractile ring formation in Dictyostelium cells.

Myosin II is a major component of a contractile ring. To examine if myosin II turns over in contractile rings, fluorescence of GFP-myosin II expressed in Dictyostelium cells was bleached locally by laser illumination, and the recovery was monitored. The fluorescence recovered with a half time of 7.01 +/- 2.62 s. This recovery was not caused by lateral movement of myosin II from the nonbleached area, but by an exchange with endoplasmic myosin II. Similar experiments were performed in cells expressing GFP-3ALA myosin II, of which three phosphorylatable threonine residues were replaced with alanine residues. In this case, recovery was not detected within a comparable time range. These results indicate that myosin II in the contractile ring performs dynamic turnover via its heavy chain phosphorylation. Because GFP-3ALA myosin II did not show the recovery, it served as a useful marker of myosin II movement, which enabled us to demonstrate cortical flow of myosin II toward the equator for the first time. Thus, cortical flow accompanies the dynamic exchange of myosin II during the formation of contractile rings.     

Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks

The role of cell size and shape in controlling local intracellular signaling reactions, and how this spatial information originates and is propagated, is not well understood. We have used partial differential equations to model the flow of spatial information from the beta-adrenergic receptor to MAPK1,2 through the cAMP/PKA/B-Raf/MAPK1,2 network in neurons using real geometries. The numerical simulations indicated that cell shape controls the dynamics of local biochemical activity of signal-modulated negative regulators, such as phosphodiesterases and protein phosphatases within regulatory loops to determine the size of microdomains of activated signaling components. The model prediction that negative regulators control the flow of spatial information to downstream components was verified experimentally in rat hippocampal slices. These results suggest a mechanism by which cellular geometry, the presence of regulatory loops with negative regulators, and key reaction rates all together control spatial information transfer and microdomain characteristics within cells.     

Cell signalling following plant/pathogen interactions involves the generation of reactive oxygen and reactive nitrogen species

It is now clear that reactive oxygen species (ROS), such as hydrogen peroxide (H₂O₂), and reactive nitrogen species, such as nitric oxide (NO), are produced by plant cells in response to a variety of stresses, including pathogen challenge. Such molecules may be involved in direct defence mechanisms, such as cross-linking of plant cell walls, or as antimicrobial agents. However, it is also apparent that cells generate such reactive species as signalling molecules, produced at controlled levels, and leading to defined responses. Signalling responses to ROS and NO include the activation of mitogen-activated protein kinases, and the up- and down-regulation of gene expression, often leading to localised programmed cell death, characteristic of the hypersensitive response. Therefore, ROS and NO are key molecules which may help to orchestrate events following pathogen challenge. Here we review the generation and role of both reactive oxygen and reactive nitrogen species in plant cells.     

Mechanisms initiating integrin-stimulated flow recruitment in arteriolar networks.

Our purpose was to investigate the local mechanisms involved in network-wide flow and diameter changes observed with localized downstream vitronectin receptor ligation; we tested specific K or Cl channels known to be involved in either dilation or elevated permeability following vitronectin receptor activation and tested integrin-linked pathway elements of tyrosine phosphorylation and protein kinase C (PKC). Arteriolar networks were observed in the cheek pouch tissue of anesthetized (pentobarbital sodium, 70 mg/kg) hamsters (n=86) using intravital microscopy. Terminal arteriolar branches of the networks were stimulated with micropipette LM609 (0.5-10 microg/ml, 60 s) alone or with inhibitors (separate micropipette). Hemodynamic changes (diameter, red blood cell flux, velocity) were observed at the upstream entrance to the network. LM609 alone stimulated first an increase in wall shear stress (WSS), followed by a dilation that recovered WSS to baseline or below. K channel inhibition (glybenclamide, 4-AP) had no effect on the initial peak in WSS, but decreased remote vasodilation. Cl channel inhibition (DIDS, IAA-94, niflumic acid) or inhibition of PKC (chelerythrine) prevented the initial peak in WSS and decreased remote vasodilation. Inhibition of tyrosine phosphorylation (genistein) prevented both. With the use of nitro-arginine at the observation site, the initial peak in WSS was not affected, but remote vasodilation was decreased. We conclude the remote response consists of an initial peak in WSS that relies on both PKC activity and depolarization downstream, leading to an upstream flow mediated dilation and a secondary remote dilation that relies on hyperpolarization downstream at the stimulus site; both components require tyrosine phosphorylation downstream.     

Signal flow graphs and neural networks

The application of signal flow graphs to the learning process of neural networks is presented. By introducing the so-called adjoint graph, new insight into the mechanism of learning phenomena of the weights in neural networks has been obtained. The derived updating formulas are valid for both feedforward and recurrent neural networks and are especially useful from the hardware implementation point of view of the self-learning networks. The presented numerical experiments confirmed the usefulness of the presented approach. Received: 24 February 1993/Accepted in revised form: 28 July 1993     

Cell influx and contractile actomyosin force drive mammary bud growth and invagination

The mammary gland develops from the surface ectoderm during embryogenesis and proceeds through morphological phases defined as placode, hillock, bud, and bulb stages followed by branching morphogenesis. During this early morphogenesis, the mammary bud undergoes an invagination process where the thickened bud initially protrudes above the surface epithelium and then transforms to a bulb and sinks into the underlying mesenchyme. The signaling pathways regulating the early morphogenetic steps have been identified to some extent, but the underlying cellular mechanisms remain ill defined. Here, we use 3D and 4D confocal microscopy to show that the early growth of the mammary rudiment is accomplished by migration-driven cell influx, with minor contributions of cell hypertrophy and proliferation. We delineate a hitherto undescribed invagination mechanism driven by thin, elongated keratinocytes—ring cells—that form a contractile rim around the mammary bud and likely exert force via the actomyosin network. Furthermore, we show that conditional deletion of nonmuscle myosin IIA (NMIIA) impairs invagination, resulting in abnormal mammary bud shape.