Analysis of a model of a virus that replicates selectively in tumor cells

We consider a procedure for cancer therapy which consists of injecting replication-competent viruses into the tumor. The viruses infect tumor cells, replicate inside them, and eventually cause their death. As infected cells die, the viruses inside them are released and then proceed to infect adjacent tumor cells. This process is modelled as a free boundary problem for a nonlinear system of hyperbolic-parabolic differential equations, where the free boundary is the surface of the tumor. The unknowns are the densities of uninfected cells, infected cells, necrotic cells and free virus particles, and the velocity of cells within the tumor as well as the free boundary r=R(t). The purpose of this paper is to establish a rigorous mathematical analysis of the model, and to explore the reduction of the tumor size that can be achieved by this therapy. Mathematics Subject Classification (2000):35R35; 92A15     

External and internal glucose mass transfers in succinic acid fermentation with stirred bed of immobilized Actinobacillus succinogenes under substrate and product inhibitions

This paper is dedicated to the study on the external and internal mass transfers of glucose for succinic acid fermentation under substrate and product inhibitions using a bioreactor with stirred bed of immobilized Actinobacillus succinogenes cells. By means of the substrate mass balance for a single particle of biocatalysts, considering the kinetic model adapted for both inhibitory effects, specific mathematical models were developed for describing the profiles of the substrate concentration in the outer and inner regions of biocatalysts and for estimating the substrate mass flows in the liquid boundary layer surrounding the particle and inside the particle. The values of the mass flows were significantly influenced by the internal diffusion velocity and rate of the biochemical reaction of substrate consumption. These cumulated influences led to the appearance of a biological inactive region near the particle center, its magnitude varying from 0 to 5.3% of the overall volume of particles.     

Morphological boundary forms by a novel inductive event mediated by Lunatic fringe and Notch during somitic segmentation

Boundary formation plays a central role in differentiating the flanking regions that give rise to discrete tissues and organs during early development. We have studied mechanisms by which a morphological boundary and tissue separation are regulated by examining chicken somite segmentation as a model system. By transplanting a small group of cells taken from a presumptive border into a non-segmentation site, we have found a novel inductive event where posteriorly juxtaposed cells to the next-forming border instruct the anterior cells to become separated and epithelialized. We have further studied the molecular mechanisms underlying these interactions by focusing on Lunatic fringe, a modulator of Notch signaling, which is expressed in the region of the presumptive boundary. By combining DNA in ovo electroporation and embryonic transplantation techniques we have ectopically made a sharp boundary of Lunatic fringe activity in the unsegmented paraxial mesoderm and observed a fissure formed at the interface. In addition, a constitutive active form of Notch mimics this instructive phenomenon. These suggest that the boundary-forming signals emanating from the posterior border cells are mediated by Notch, the action of which is confined to the border region by Lunatic fringe within the area where mRNAs of Notch and its ligand are broadly expressed in the presomitic mesoderm.     

Dynamics of intramural scroll waves in three-dimensional continuous myocardium with rotational anisotropy.

It has been suggested that reentrant activity in three-dimensional cardiac muscle may be organized as a scroll wave rotating around a singularity line called the filament. Experimental studies indicate that filaments are often concealed inside the ventricular wall and consequently, scroll waves do not manifest reentrant activity on the surface. Here we analyse how such concealed scroll waves are affected by a twisted anisotropy resulting from rotation of layers of muscle fibers inside the ventricular wall. We used a computer model of a ventricular slab (15x15x15 mm(3)) with a fiber twist of 120 degrees from endocardium to epicardium. The action potential was simulated using FitzHugh-Nagumo equations. Scroll waves with rectilinear filaments were initiated at various depths of the slab and at different angles with respect to fiber orientation. The analysis shows that independent of initial conditions, after a certain transitional period, the filament aligns with the local fiber orientation. The alignment of the filament is determined by the directional variations in cell coupling due to fiber rotation and by boundary conditions. Our findings provide a mechanistic explanation for the prevalence of intramural reentry over transmural reentry during polymorphic ventricular tachycardia and fibrillation.     

The Biophysical Origin of Traveling-Wave Dispersion in the Cochlea

Sound processing begins at the peripheral auditory system, where it undergoes a highly complex transformation and spatial separation of the frequency components inside the cochlea. This sensory signal processing constitutes a neurophysiological basis for psychoacoustics. Wave propagation in the cochlea, as shown by measurements of basilar membrane velocity and auditory nerve responses to sound, has demonstrated significant frequency modulation (dispersion), in addition to tonotopic gain and active amplification. The physiological and physical basis for this dispersion remains elusive. In this article, a simple analytical model is presented, along with experimental validation using physiological measurements from guinea pigs, to identify the origin of traveling-wave dispersion in the cochlea. We show that dispersion throughout the cochlea is fundamentally due to the coupled fluid-structure interaction between the basilar membrane and the scala fluids. It is further influenced by the variation in physical and geometrical properties of the basilar membrane, the sensitivity or gain of the hearing organ, and the relative dominance of the compression mode at about one-third octave beyond the best frequency.     

Evolution of developmental cyclic adenosine monophosphate signaling in the Dictyostelia from an amoebozoan stress response

The Dictyostelid social amoebas represent one of nature's several inventions of multicellularity. Though normally feeding as single cells, nutrient stress triggers the collection of amoebas into colonies that form delicately shaped fruiting structures in which the cells differentiate into spores and up to three cell types to support the spore mass. Cyclic adenosine monophosphate (cAMP) plays a very dominant role in controlling morphogenesis and cell differentiation in the model species Dictyostelium discoideum. As a secreted chemoattractant cAMP coordinates cell movement during aggregation and fruiting body morphogenesis. Secreted cAMP also controls gene expression at different developmental stages, while intracellular cAMP is extensively used to transduce the effect of other stimuli that control the developmental program. In this review, I present an overview of the different roles of cAMP in the model D. discoideum and I summarize studies aimed to resolve how these roles emerged during Dictyostelid evolution.     

Foundations of modeling in cryobiology—II: Heat and mass transport in bulk and at cell membrane and ice-liquid interfaces

Modeling coupled heat and mass transport in biological systems is critical to the understanding of cryobiology. In Part I of this series we derived the transport equation and presented a general thermodynamic derivation of the critical components needed to use the transport equation in cryobiology. Here we refine to more cryobiologically relevant instances of a double free-boundary problem with multiple species. In particular, we present the derivation of appropriate mass and heat transport constitutive equations for a system consisting of a cell or tissue with a free external boundary, surrounded by liquid media with an encroaching free solidification front. This model consists of two parts–namely, transport in the “bulk phases” away from boundaries, and interfacial transport. Here we derive the bulk and interfacial mass, energy, and momentum balance equations and present a simplification of transport within membranes to jump conditions across them. We establish the governing equations for this cell/liquid/solid system whose solution in the case of a ternary mixture is explored in Part III of this series.     

Determination of the asymptotic shapes of sedimentation velocity patterns for reversibly polymerizing solutes

A simple method is described for the determination of the asymptotic boundary shape from a series of schlieren patterns taken during a sedimentation velocity experiment on a rapidly and reversibly associating solute. The form of the boundary so obtained reflects effects of sedimentation and chemical reaction but is free from effects of diffusion. The procedure is illustrated with analyses of experiments on diisopropyl fluorophosphate-inhibited α-chymotrypsin in 0.29 I phosphate, pH 7.9 (a monomer-dimer system), and on β-lactoglobulin A in 0.1 I acetate, pH 4.65 (a monomer-dimer-trimer-tetramer system). Asymptotic patterns so determined exhibit close agreement with those predicted by Gilbert theory.     

Multiple roles of the Dcdc42 GTPase during wing development in Drosophila melanogaster

The Rho sub-family of GTPases, comprising Rho, Rac and Cdc42. regulates many biological processes, including morphogenesis, cell polarity, migration, the cell cycle and gene expression. It is important to develop genetic approaches to allow the dissection, in vivo, of the mechanisms of GTPase regulation and signal transmission, and their biological consequences. In this regard, wing development in Drosophila melanogaster is an excellent model system. To investigate the functions of the Drosophila Cdc42 GTPase (Dcdc42), we generated phenotypes during wing development, by expression of the dominant-negative N17 and L89 mutants of Dcdc42. We have identified roles for Dcdc42 in wing growth, and in cell fate choice during the development of the wing veins and the peripheral nervous system. Reduction of Dcdc42 signalling following over-expression of Dcdc42N17 resulted in a broader but more diffuse domain characterised by wing-margin sensory bristles. This was correlated with a broadened stripe of wingless expression along the dorsal-ventral boundary of third-instar wing imaginal discs. Together with genetic interactions with loss- and gain-of-function Notch alleles, these data support a role for wild-type Dcdc42 as a negative regulator of Notch signalling.     

粘细菌的多细胞形态发生及其分子调控

粘细菌的多细胞形态发生是粘细菌细胞社会性行为的主要表现.包括细胞有序聚集、细胞自溶、子实体发育和粘孢子的分化形成等.粘细菌的形态发生过程涉及复杂的信号系统和调控,与真核生物具有较大的相似性.是研究原核生物细胞分化发育以及生物进化的重要模式材料.     

Kelvin-Helmholtz instability in a bounded plasma flow

Kelvin-Helmholtz instability in a three-layer plane geometry is investigated theoretically. It is shown that, in a three-layer system (in contrast to the traditionally considered case in which instability develops at the boundary between two plasma flows), instability can develop at an arbitrary ratio of the plasma flow velocity to the ion-acoustic velocity. Perturbations with wavelengths on the order of the flow thickness or longer can increase even at a zero temperature. The system can also be unstable against long-wavelength perturbations if the flow velocity at one of the boundaries is lower than the sum of the Alfvén velocities in the flow and the ambient plasma. The possibility of applying the results obtained to interpret the experimental data acquired in the framework of the CLUSTER multisatellite project is discussed. It follows from these data that, in many cases, the propagation of an accelerated particle flow in the plasma-sheet boundary layer of the Earth’s magnetotail is accompanied by the generation of magnetic field oscillations propagating with a velocity on the order of the local Alfvén velocity.     

Modeling cell apoptosis for simulating three-dimensional multicellular morphogenesis based on a reversible network reconnection framework

Morphogenesis in multicellular organisms is accompanied by apoptotic cell behaviors: cell shrinkage and cell disappearance. The mechanical effects of these behaviors are spatiotemporally regulated within multicellular dynamics to achieve proper tissue sizes and shapes in three-dimensional (3D) space. To analyze 3D multicellular dynamics, 3D vertex models have been suggested, in which a reversible network reconnection (RNR) model has successfully expressed 3D cell rearrangements during large deformations. To analyze the effects of apoptotic cell behaviors on 3D multicellular morphogenesis, we modeled cell apoptosis based on the RNR model framework. Cell shrinkage was modeled by the potential energy as a function of individual cell times during the apoptotic phase. Cell disappearance was modeled by merging neighboring polyhedrons at their boundary surface according to the topological rules of the RNR model. To establish that the apoptotic cell behaviors could be expressed as modeled, we simulated morphogenesis driven by cell apoptosis in two types of tissue topology: 3D monolayer cell sheet and 3D compacted cell aggregate. In both types of tissue topology, the numerical simulations successfully illustrated that cell aggregates gradually shrank because of successive cell apoptosis. During tissue shrinkage, the number of cells in aggregates decreased while maintaining individual cell size and shape. Moreover, in case of localizing apoptotic cells within a part of the 3D monolayer cell aggregate, the cell apoptosis caused the global tissue bending by pulling on surrounding cells. In case of localizing apoptotic cells on the surface of the 3D compacted cell aggregate, the cell apoptosis caused successive, directional cell rearrangements from the inside to the surface. Thus, the proposed model successfully provided a basis for expressing apoptotic cell behaviors during 3D multicellular morphogenesis based on an RNR model framework.     

The Fog signaling pathway: Insights into signaling in morphogenesis

Epithelia form the building blocks of many tissue and organ types. Epithelial cells often form a contiguous 2-dimensional sheet that is held together by strong adhesions. The mechanical properties conferred by these adhesions allow the cells to undergo dramatic three-dimensional morphogenetic movements while maintaining cell–cell contacts during embryogenesis and post-embryonic development. The Drosophila Folded gastrulation pathway triggers epithelial cell shape changes that drive gastrulation and tissue folding and is one of the most extensively studied examples of epithelial morphogenesis. This pathway has yielded key insights into the signaling mechanisms and cellular machinery involved in epithelial remodeling. In this review, we discuss principles of morphogenesis and signaling that have been discovered through genetic and cell biological examination of this pathway. We also consider various regulatory mechanisms and the system?s relevance to mammalian development. We propose future directions that will continue to broaden our knowledge of morphogenesis across taxa.     

ATP hydrolysis stimulates large length fluctuations in single actin filaments

Polymerization dynamics of single actin filaments is investigated theoretically using a stochastic model that takes into account the hydrolysis of ATP-actin subunits, the geometry of actin filament tips, and the lateral interactions between the monomers as well as the processes at both ends of the polymer. Exact analytical expressions are obtained for the mean growth velocity, for the dispersion in the length fluctuations, and the nucleotide composition of the actin filaments. It is found that the ATP hydrolysis has a strong effect on dynamic properties of single actin filaments. At high concentrations of free actin monomers, the mean size of the unhydrolyzed ATP-cap is very large, and the dynamics is governed by association/dissociation of ATP-actin subunits. However, at low concentrations the size of the cap becomes finite, and the dissociation of ADP-actin subunits makes a significant contribution to overall dynamics. Actin filament length fluctuations reach a sharp maximum at the boundary between two dynamic regimes, and this boundary is always larger than the critical concentration for the actin filament's growth at the barbed end, assuming the sequential release of phosphate. Random and sequential mechanisms of hydrolysis are compared, and it is found that they predict qualitatively similar dynamic properties at low and high concentrations of free actin monomers with some deviations near the critical concentration. The possibility of attachment and detachment of oligomers in actin filament's growth is also discussed. Our theoretical approach is successfully applied to analyze the latest experiments on the growth and length fluctuations of individual actin filaments.     

Cell cycle progression is required for zebrafish somite morphogenesis but not segmentation clock function

Cell division, differentiation and morphogenesis are coordinated during embryonic development, and frequently are in disarray in pathologies such as cancer. Here, we present a zebrafish mutant that ceases mitosis at the beginning of gastrulation, but that undergoes axis elongation and develops blood, muscle and a beating heart. We identify the mutation as being in early mitotic inhibitor 1 (emi1), a negative regulator of the Anaphase Promoting Complex, and use the mutant to examine the role of the cell cycle in somitogenesis. The mutant phenotype indicates that axis elongation during the segmentation period is driven substantially by cell migration. We find that the segmentation clock, which regulates somitogenesis, functions normally in the absence of cell cycle progression, and observe that mitosis is a modest source of noise for the clock. Somite morphogenesis involves the epithelialization of the somite border cells around a core of mesenchyme. As in wild-type embryos, somite boundary cells are polarized along a Fibronectin matrix in emi1(-/-). The mutants also display evidence of segment polarity. However, in the absence of a normal cell cycle, somites appear to hyper-epithelialize, as the internal mesenchymal cells exit the core of the somite after initial boundary formation. Thus, cell cycle progression is not required during the segmentation period for segmentation clock function but is necessary for the normal segmental arrangement of epithelial borders and internal mesenchymal cells.     

Modeling of immobilized cell columns for bioconversion and wastewater treatment

Immobilized cells are widely used in bioconversions to produce biological products as well as in wastewater treatment such as solvent removal from wastewater streams. In this work, a rate model is proposed to simulate this kind of process in an axial-flow fixed-bed column packed with porous particles containing immobilized cells. The transient model considered various mass transfer mechanisms including axial dispersion, interfacial film mass transfer, and intraparticle diffusion. Cell death in the immobilized cell system was also considered. Effects of various parameters such as kinetic constants and mass transfer parameters were studied. Operational situations such as feed fluctuation flow rate increase and two columns in series were also investigated. The model can be used to study the behavior and characteristics of immobilized cell columns in order to perform scale-up predictions of effluent profiles and for the purpose of process optimization.     

On polar auxin transport in plant cells

We present here explicit mathematical formulas for calculating the concentration, mass, and velocity of movement of the center of mass of the plant growth regulator auxin during its polar movement through a linear file of cells. The results of numerical computations for two cases, (a) the conservative, in which the mass in the system remains constant and (b) the non-conservative, in which the system acquires mass at one end and loses it at the other, are graphically presented. Our approach differs from that of Mitchison's (Mitchison 1980) in considering both initial effects of loading and end effects of substance leaving the file of cells. We find the velocity varies greatly as mass is entering or leaving the file of cells but remains constant as long as most of the mass is within the cells. This is also the time for which Mitchison's formula for the velocity, which neglects end effects, reflects the true velocity of auxin movement. Finally, the predictions of the model are compared with two sets of experimental data. Movement of a pulse of auxin through corn coleoptiles is well described by the theory. Movement of auxin through zucchini shoots, however, shows the need to take into account immobilization of auxin by this tissue during the course of transport.     

Plasmonic Slot Waveguides with Core Nonlinearity

We analytically study the interplay between group velocity dispersion and material dispersion due to femtosecond ultrafast pulse inside plasmonic slot waveguides with nonlinear dielectric core. The analytic investigation of the role of the core nonlinearity on pulse propagation has been investigated. Interestingly, our model shows that the focusing and defocusing effects of the material can be revered if the material is confined inside the core of a plasmonic slot. We confirm our analytical results with nonlinear finite difference time domain (FDTD) simulations.     

The spring-mass model for running and hopping

A simple spring-mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed. The bouncing mechanism itself results in a confinement of the free parameter space where solutions can be found. In particular, bouncing frequency and vertical displacement are closely related. Only a few parameters, such as the vector of the specific landing velocity and the specific leg length, are sufficient to determine the point of operation of the system. There are more physiological constraints than independent parameters. As constraints limit the parameter space where hopping is possible, they must be tuned to each other in order to allow for hopping at all. Within the range of physiologically possible hopping frequencies, a human hopper selects a frequency where the largest amount of energy can be delivered and still be stored elastically. During running and hopping animals use flat angles of the landing velocity resulting in maximum contact length. In this situation ground reaction force is proportional to specific contact time and total displacement is proportional to the square of the step duration. Contact time and hopping frequency are not simply determined by the natural frequency of the spring-mass system, but are influenced largely by the vector of the landing velocity. Differences in the aerial phase or in the angle of the landing velocity result in the different kinematic and dynamic patterns observed during running and hopping. Despite these differences, the model predicts the mass specific energy fluctuations of the center of mass per distance to be similar for runners and hoppers and similar to empirical data obtained for animals of various size.