A growth-controlled model of the shape of a sunflower head

A mathematical model is presented which predicts the shape of a sunflower receptacle (or the compact receptacle of various other taxa) and the pattern of its floral parts (florets) from the time of their initiation to maturity. The model assumes that the expansion and curving of the receptacle surface is just sufficient to accommodate the development of the florets, thus minimizing the quantity of plant tissue involved. The model assumes a fixed angular separation (divergence) between successive florets, an S-shaped (sigmoidal) growth function followed by each florets, and a fixed time delay (period) between the initiation of successive florets. It is further assumes that the shape and relative position occupied by the florets on the receptacle surface are invariant in time. By this theory, the shape of the receptacle surface is fully determined once the mathematical form of the growth function is specified. Using the logistic growth function, the theory is tested against the measured shapes of plant receptacles from different taxa at various points in their development. The least-squares adjusted fits to the theory are, in most cases, very good indeed.     

A minimal mechanism for bacterial pattern formation

Colonies of Escherichia coli or Salmonella typhimurium form geometrically complex patterns when exposed to, or feeding on, intermediates of the tricarboxylic acid (TCA) cycle. In response to the TCA cycle intermediate, the bacteria secrete aspartate, a potent chemo-attractant. As a result, the cells form high-density aggregates arranged in striking regular patterns. The simplest are temporary spots formed in a liquid medium by both E. coli and S. typhimurium. In semi-solid medium S. typhimurium forms concentric rings arising from a low-density bacterial lawn, which are either continuous or spotted, whereas E. coli forms complex patterns arising from a dense swarm ring, including interdigitated spots (also called sunflower spirals), radial spots, radial stripes and chevrons. We present a mathematical model that captures all three of the pattern-forming processes experimentally observed in both E. coli and S. typhimurium, using a minimum of assumptions.     

A two-step mechanism for myotome formation in chick

The study of the morphogenetic cell movements underlying myotome formation in the chick embryo has led to the emergence of highly controversial models. Here we report a real-time cell lineage analysis of myotome development using electroporation of a GFP reporter in newly formed chick somites. Confocal analysis of cell movements demonstrates that myotome formation involves two sequential steps. In a first phase, incremental myotome growth results from a contribution of myocytes derived solely from the medial border of the dermomyotome. In a second phase, myocytes are produced from all four borders of the dermomyotome. The relative distribution of myocytes demonstrates that the medial and the lateral borders of the somite generate exclusively epaxial and hypaxial muscles. This analysis also identified five myotomal regions, characterized by the origin of the myocytes that constitute them. Together, our results provide a comprehensive model describing the morphogenesis of the early myotome in higher vertebrates.     

A Pre-pattern formation mechanism for animal coat markings

It is generally accepted that colour patterns in animals are genetically determined but the mechanism is not known. We suggest that a single mechanism which can exhibit an infinite variety of patterns is a candidate for it. We thus propose that a reaction-diffusion system which can be diffusively driven unstable could be responsible for the laying down of the pre-pattern for animal coat markings.For illustrative purposes only we consider a specific practical substrate inhibition reaction mechanism in detail and show that the geometry and scale of the domain, the relevant part of the integument, during the time of laying down plays a crucial role in the structural patterns which result. Patterns which exhibit a limited randomness are obtained for a selection of geometries and are specifically related to the coat colour distribution in the spotted felidae, zebra and other animals.     

A clock and wavefront mechanism for somite formation

Somitogenesis, the sequential formation of a periodic pattern along the antero-posterior axis of vertebrate embryos, is one of the most obvious examples of the segmental patterning processes that take place during embryogenesis and also one of the major unresolved events in developmental biology. In this article, we develop a mathematical formulation of a new version of the Clock and Wavefront model proposed by Pourquié and co-workers (Dubrulle, J., McGrew, M.J., Pourquié, O., 2001. FGF signalling controls somite boundary position and regulates segmentation clock control of spatiotemporal Hox gene activation. Cell 106, 219-232). Dynamic expression of FGF8 in the presomitic mesoderm constitutes the wavefront of determination which sweeps along the body axis interacting as it moves with the segmentation clock to gate cells into somites. We also show that the model can mimic the anomalies formed when progression of the wavefront is disturbed and make some experimental predictions that can be used to test the hypotheses underlying the model.     

A directional nucleation-zipping mechanism for triple helix formation

A detailed kinetic study of triple helix formation was performed by surface plasmon resonance. Three systems were investigated involving 15mer pyrimidine oligonucleotides as third strands. Rate constants and activation energies were validated by comparison with thermodynamic values calculated from UV-melting analysis. Replacement of a T·A base pair by a C·G pair at either the 5′ or the 3′ end of the target sequence allowed us to assess mismatch effects and to delineate the mechanism of triple helix formation. Our data show that the association rate constant is governed by the sequence of base triplets on the 5′ side of the triplex (referred to as the 5′ side of the target oligopurine strand) and provides evidence that the reaction pathway for triple helix formation in the pyrimidine motif proceeds from the 5′ end to the 3′ end of the triplex according to the nucleation-zipping model. It seems that this is a general feature for all triple helices formation, probably due to the right-handedness of the DNA double helix that provides a stronger base stacking at the 5′ than at the 3′ duplex–triplex junction. Understanding the mechanism of triple helix formation is not only of fundamental interest, but may also help in designing better triple helix-forming oligonucleotides for gene targeting and control of gene expression.     

A possible mechanism for cholesteryl ester formation during demyelination

Lecithin: cholesterol acyltransferase (LCAT) activity has been examined in the rat by using a brain homogenate preparation as the phospholipid substrate and blood plasma as the enzyme source. LCAT activity was detected on using 60 l of serum onwards. Successive experiments have also shown that LCAT activity is present in the edematous rat brain tissue homogenate when incubated with inactivated rat plasma as substrate. The results are discussed in relation to cholesteryl ester accumulation in brain during demyelinating diseases.     

A stochastic mechanism for biofilm formation by Mycoplasma pulmonis

Bacterial biofilms are communities of bacteria that are enclosed in an extracellular matrix. Within a biofilm the bacteria are protected from antimicrobials, environmental stresses, and immune responses from the host. Biofilms are often believed to have a highly developed organization that is derived from differential regulation of the genes that direct the synthesis of the extracellular matrix and the attachment to surfaces. The mycoplasmas have the smallest of the prokaryotic genomes and apparently lack complex gene-regulatory systems. We examined biofilm formation by Mycoplasma pulmonis and found it to be dependent on the length of the tandem repeat region of the variable surface antigen (Vsa) protein. Mycoplasmas that produced a short Vsa protein with few tandem repeats formed biofilms that attached to polystyrene and glass. Mycoplasmas that produced a long Vsa protein with many tandem repeats formed microcolonies that floated freely in the medium. The biofilms and the microcolonies contained an extracellular matrix which contained Vsa protein, lipid, DNA, and saccharide. As variation in the number of Vsa tandem repeats occurs by slipped-strand mispairing, the ability of the mycoplasmas to form a biofilm switches stochastically.     

A proteolytic mechanism for the action of insulin via oligopeptide mediator formation

Evidence is presented that the chemical mediator of insulin action is a peptide(s) and most likely glycopeptide(s). The mediator is formed proteolytically because 1) protease inhibitors inhibit insulin action and 2) trypsin mimicks insulin action via mediator formation. Trypsin mediator does not faithfully reproduce the action of insulin mediator, which indicates that the sites of proteolytic cleavage by insulin and trypsin differ. A coordinated multivalent proteolytic mechanism by which insulin acts to trigger an external membrane-bound protease to cleave mediator from a membrane glycoprotein precursor is presented.     

A neural mechanism of synergy formation for whole body reaching

The present study proposes a computational model for the formation of whole body reaching synergy, i.e., coordinated movements of lower and upper limbs, characterized by a focal component (the hand must reach a target) and a postural component (the center of mass must remain inside the support base). The model is based on an extension of the equilibrium point hypothesis that has been called Passive Motion Paradigm (PMP), modified in order to achieve terminal attractor features and allow the integration of multiple constraints. The model is a network with terminal attractor dynamics. By simulating it in various conditions it was possible to show that it exhibits many of the spatio-temporal features found in experimental data. In particular, the motion of the center of mass appears to be synchronized with the motion of the hand and with proportional amplitude. Moreover, the joint rotation patterns can be accounted for by a single functional degree of freedom, as shown by principal component analysis. It is also suggested that recent findings in motor imagery support the idea that the PMP network may represent the motor cognitive part of synergy formation, uncontaminated by the effect of execution.     

A novel mechanism for the formation of actin-filament bundles by a nonprocessive formin

Actin-filament bundles (or cables) have a structural role during cell division and morphogenesis, but also serve as important "tracks" for the transport of materials during cytokinesis and polarized cell growth. However, the dynamic formation of these longitudinal actin-filament higher-order structures is not understood. Recently, several lines of evidence suggest that formins provide one avenue for the initiation of actin cables in vivo. A popular model for the mechanism of polymerization of actin filaments by formin involves the processive movement of formin attached at the barbed end of an elongating filament. In the present study, we use an in vitro system to reconstitute the dynamic formation of actin-filament bundles generated by Arabidopsis FORMIN1 (AFH1). To be able to visualize individual events in such a complex system, we used real-time evanescent-wave microscopy. Surprisingly, we find that AFH1 is a nonprocessive formin that moves from the barbed end to the side of an actin filament after the nucleation event. We show why this new mechanism of nucleation by a member of the formin family is important for bundle formation. Finally, we analyze the different parameters controlling the dynamic formation of such longitudinal actin-filament bundles.     

A possible mechanism for the formation of annual growth lines in bivalve shells

We report a unique shell margin that differed from the usual shell structure of Pinctada fucata. We observed empty organic envelopes in the prismatic layer and the formation of the nacreous layer in the shell margin. All the characteristics of the growing margin indicated that the shell was growing rapidly. To explain this anomaly, we propose the concept of “jumping development”. During jumping development, the center of growth in the bivalve shell jumps forward over a short time interval when the position of the mantle changes. Jumping development explains the unusual structure of the anomalous shell and the development of annual growth lines in typical shells. Annual growth lines are the result of a discontinuity in the shell microstructure induced by jumping development.     

A common mechanism for the ATP-DnaA-dependent formation of open complexes at the replication origin

Initiation of chromosomal replication and its cell cycle-coordinated regulation bear crucial and fundamental mechanisms in most cellular organisms. Escherichia coli DnaA protein forms a homomultimeric complex with the replication origin (oriC). ATP-DnaA multimers unwind the duplex within the oriC unwinding element (DUE). In this study, structural analyses suggested that several residues exposed in the central pore of the putative structure of DnaA multimers could be important for unwinding. Using mutation analyses, we found that, of these candidate residues, DnaA Val-211 and Arg-245 are prerequisites for initiation in vivo and in vitro. Whereas DnaA V211A and R245A proteins retained normal affinities for ATP/ADP and DNA and activity for the ATP-specific conformational change of the initiation complex in vitro, oriC complexes of these mutant proteins were inactive in DUE unwinding and in binding to the single-stranded DUE. Unlike oriC complexes including ADP-DnaA or the mutant DnaA, ATP-DnaA-oriC complexes specifically bound the upper strand of single-stranded DUE. Specific T-rich sequences within the strand were required for binding. The corresponding conserved residues of the DnaA ortholog in Thermotoga maritima, an ancient eubacterium, were also required for DUE unwinding, consistent with the idea that the mechanism and regulation for DUE unwinding can be evolutionarily conserved. These findings provide novel insights into mechanisms for pore-mediated origin unwinding, ATP/ADP-dependent regulation, and helicase loading of the initiation complex.     

A mechanism for NADPH inhibition of catalase compound II formation.

Catalase-bound NADPH both prevents and reverses the accumulation of inactive bovine liver catalase peroxide compound II generated by 'endogenous' donors under conditions of steady H2O2 formation without reacting rapidly with either compound I or compound II. It thus differs both from classical 2-electron donors of the ethanol type, and from 1-electron donors of the ferrocyanide/phenol type. NADPH also inhibits compound II formation induced by the exogenous one-electron donor ferrocyanide. A catalase reaction scheme is proposed in which the initial formation of compound II from compound I involves production of a neighbouring radical species. NADPH blocks the final formation of stable compound II by reacting as a 2-electron donor to compound II and to this free radical. The proposed behaviour resembles that of labile free radicals formed in cytochrome c peroxidase and myoglobin. Such radical migration patterns within haem enzymes are increasingly common motifs.     

Branching-diffusion model for the formation of distributional patterns in populations

A continuous time branching-diffusion process model is presented to describe the development of spatial distributional patterns of a biological population. In the model each unit moves independently following diffusion processes on a plane, and multiplies or goes extinct at random times. Standard methods for measuring the degree of aggregation used in field ecology are applied to this model population. Kuno's C _Aindex using quadrat sampling is calculated, and the dependence of the index on time, quadrat size, initial density, and diffusion and branching rules, is discussed. Pielou's index based on distance measurement is evaluated by the solution of a nonlinear partial differential equation. Both methods show that continuous-time branching-diffusion processes produce a contagious spatial pattern; as in a discrete-time model studied by Iwasa and Teramoto (1977).     

A mechanism for the RNA-catalyzed formation of 5'-phosphates. The origin of nucleases

Processes involved in RNA metabolism can be distinguished by the nature of the sugar phosphate substitution (5' or 3') in intermediates or products. Although it is known that 3'-phosphates are produced via a 2',3'-cyclic phosphate intermediate, formed by nucleophilic attack on the phosphodiester bond by the adjacent 2'-OH, little is known about the production of 5'-phosphate products. We attribute 5'-phosphate intermediates and products to a preferred configuration of the pentavalent phosphorus intermediate resulting from the attack of a distant nucleophile. This intermediate is favored, since its formation is possible without major conformational changes in the molecule. Based on the two products of nucleic acid hydrolysis we define: the conjunct and disjunct nucleophile mechanisms, each of which would have independent origins. Indeed, the products of an overwhelming number of nucleases and RNases are consistent with one of these mechanistic models demonstrating that the origin of these enzymes are deeply rooted in the intrinsic chemistry of phosphate esters.     

Self-organizing mechanism for the formation of ordered neural mappings

A model for the formation of ordered neural mappings in general, and of retinotectal connections, in particular is given. The main point came from the theory of noise induced transitions, i.e. order may be the result of the interplay between deterministic and random interactions. An activity-dependent self-organizing mechanism is presented in terms of modifiable synapses. Simulation experiments were done not only for the normal ontogenetic development but also for the plastic behaviour of the retinotopic connections.