Simple Growth Laws Research Articles

Computationally enhanced quantitative phase microscopy reveals autonomous oscillations in mammalian cell growth

The fine balance of growth and division is a fundamental property of the physiology of cells, and one of the least understood. Its study has been thwarted by difficulties in the accurate measurement of cell size and the even greater challenges of measuring growth of a single cell over time. We address these limitations by demonstrating a computationally enhanced methodology for quantitative phase microscopy for adherent cells, using improved image processing algorithms and automated cell-tracking software. Accuracy has been improved more than twofold and this improvement is sufficient to establish the dynamics of cell growth and adherence to simple growth laws. It is also sufficient to reveal unknown features of cell growth, previously unmeasurable. With these methodological and analytical improvements, in several cell lines we document a remarkable oscillation in growth rate, occurring throughout the cell cycle, coupled to cell division or birth yet independent of cell cycle progression. We expect that further exploration with this advanced tool will provide a better understanding of growth rate regulation in mammalian cells.

Unified description of thermal behaviors by macroscopic growth laws

Complex systems, in many different scientific sectors, show coarse-grain properties with simple growth laws with respect to fundamental microscopic algorithms. The known classification schemes of the growth laws refer to time evolution of biological and technical systems. We propose to apply the previous classifications to phenomenological analysis of thermal systems with a cross-fertilization among different sectors. As an example, the Fermi–Dirac distribution function and the electrical activation in implanted silicon carbide are discussed.

Modeling the Flat to Curved Transition during Clathrin Mediated Endocytosis

Clathrin-mediated endocytosis is essential for the cellular uptake of receptors and nutrients. Although under investigation since decades, the exact sequence of structural and molecular events remains elusive. There are two basic models that have been suggested for the way it proceeds. In the constant curvature model, it is assumed that clathrin-coated pits grow with constant curvature, determined by the geometry of clathrin triskelia. In the constant area model, it is assumed that clathrin triskelia first assemble into flat hexagonal arrays that later invaginate at constant surface area. This second model implicitly assumes that during bending, some hexagons are converted into pentagons. Here, we integrate data sets from correlative electron and light microscopy and quantify the sequence of ultrastructural rearrangements of the clathrin coat during endocytosis in mammalian cells with the help of some simple mathematical growth laws. Our main assumption is that the clathrin domain can grow only over the boundary. In the case of flat arrays, this requires some balancing process to prevent a run-away process, which we assume to grow in proportion to the domain area. In the case of curved arrays, pit closure is sufficient to limit growth and thus an additional process is not required. Our analysis shows that clathrin-coated structures initially grow flat but start to acquire curvature when 70% of the final clathrin content is reached. We find that this transition correlates with a change in the ratio of clathrin to adaptor protein AP2, and that membrane tension suppresses this transition. Hence, our analysis suggests that elements of both suggested models are present and that mechanical and cellular factors will decide about the relative weights of growth versus curvature formation.

Emergence of robust growth laws from optimal regulation of ribosome synthesis.

Bacteria must constantly adapt their growth to changes in nutrient availability; yet despite large-scale changes in protein expression associated with sensing, adaptation, and processing different environmental nutrients, simple growth laws connect the ribosome abundance and the growth rate. Here, we investigate the origin of these growth laws by analyzing the features of ribosomal regulation that coordinate proteome-wide expression changes with cell growth in a variety of nutrient conditions in the model organism Escherichia coli. We identify supply-driven feedforward activation of ribosomal protein synthesis as the key regulatory motif maximizing amino acid flux, and autonomously guiding a cell to achieve optimal growth in different environments. The growth laws emerge naturally from the robust regulatory strategy underlying growth rate control, irrespective of the details of the molecular implementation. The study highlights the interplay between phenomenological modeling and molecular mechanisms in uncovering fundamental operating constraints, with implications for endogenous and synthetic design of microorganisms.

Critical Point in Space: A Quest for Universality

The behavior of matter near a 2nd order phase transition is expected to obey universal features. In particular, fluids, liquid mixtures, polymers, which belong to the same class of universality (the class of fluids) should exhibit the same universal scaling laws for many thermodynamics and kinetic parameters. Critical point slowing down is the most notorious. Such divergence or convergence makes the class of fluids extremely sensitive to even minute external disturbances and especially gravity: on earth the fluid becomes compressed under its own weight. Compensating for these effects by space experiments and/or magnetic forces or isotopic density matching has led to enlarge our vision of universality for phase transition. New phenomena have been discovered by suppressing gravity effects, as the thermal “Piston Effect”, which leads to a paradoxical critical point speeding up and the apparent violation of the 2nd thermodynamic law. Another finding is concerned with the use of critical slowing down and weightlessness to investigate the dynamics of phase separation with no gravity-induced sedimentation. The key role of the coalescence of domains makes valid only two simple growth laws. The latter can be successfully applied to a quite different situation, the evolution laws in the well-known biological problem of sorting of embryonic cells. Due to the extreme sensitivity of fluids near their critical point, the effect of vibration can be investigated in much detail, using only one fluid, which represents the whole class of fluids. The investigation of the above thermal and phase transition problems under vibrations indeed suggests that a periodic excitation can act as a kind of artificial gravity, which induces thermal convection, speeds up phase transition and localizes the liquid and vapor phases perpendicular to it.

Unified approach to growth and aging in biological, technical and biotechnical systems

Complex systems, in many different scientific sectors, show coarse-grain properties with simple growth laws with respect to fundamental microscopic algorithms. We propose a classification scheme of growth laws which includes human aging, tumor (and/or tissue) growth, logistic and generalized logistic growth and the aging of technical devices. The proposed classification permits to evaluate the aging/failure of combined new bio-technical “manufactured products”, where part of the system evolves in time according to biological-mortality laws and part according to technical device behaviors. Moreover it suggests a direct relation between the mortality leveling-off for humans and technical devices and the observed small cure probability for large tumors.

MOPOD: a generic model of porosity development

Abstract A code, MOPOD, has been developed to investigate general relationships between simple porosity growth laws and pore growth phenomena. MOPOD has been formulated as an ‘initial value problem’ and to date, investigations have focused on a very simple porosity growth law of the form da i (t)/dt = v e i , where e is the aperture growth rate exponent. A range of qualitatively distinct evolved geometries have been described for porosity growth on 2D and 3D arrays of varying geometries and connectivities as a function of the exponent, e , of the aperture growth-rate law, and the width of the initial aperture distribution, σ z . At low growth-rate exponents and moderate values of σ z over time there is a homogenization of apertures oriented sub-parallel to the head gradient. At moderate growth-rate exponents these apertures become increasingly heterogeneous in evolved arrays, with planar heterogeneities developing sub-parallel to the head gradient for low values of σ z while anastomosing structures develop at higher values of σ z . For larger growth-rate exponents preferentially enlarged array-spanning paths develop. No self-organization phenomena have been observed because periodic or cyclic behaviour is not inherent in the simple growth laws investigated to date.

A combined model for the description of austenitization, homogenization and grain growth in hypoeutectoid Fe–C steels during heating

A combined model which allows one to simulate all the steps of the reaustenitization process of ferrito-pearlitic plain carbon steel has been developed. The dissolution of pearlite, the transformation of ferrite into austenite and the homogenization of the carbon distribution is described with a finite volume method. The simulation is performed on a bidimensional domain where ferrite ( α), pearlite (P) and austenite ( γ) grains are represented. The dissolution of pearlite is described by the growth of spherical grains and simple nucleation and growth laws. The movement of α/ γ interfaces is calculated by solving the diffusion equation for carbon in the α and γ phases and accounting for the solute flux balance at the interface using a pseudo-front tracking method. The diffusion model is coupled with a Monte Carlo simulation which describes the grain growth occurring in austenite at a later stage of austenitization. The evolution of the volume fractions of pearlite and ferrite, the maximum and minimum carbon concentrations in the domain and the mean austenite grain size are represented as a function of the temperature for a typical case of constant heating rate. The influence of the different steps of the austenitization process on the global kinetics is discussed.

Simple growth laws and selection consequences

It is commonly thought that various types of population growth can be satisfactorily modelled as deviations from an inherently exponential (malthusian) growth law. Consideration of kinetic results from research on the origin of life, laser physics and more-conventional population dynamics makes it clear, however, that in certain cases the simplest and mechanistically most satisfactory assumption is either a basic subexponential or a hyperbolic growth law. Although these simple growth laws cannot be used instead of more-complicated models of density-dependent population growth when exact quantities are important, the insight gained by thinking them over can be substantial. Ideas about species packing, for example, await reconsideration.

Germanium Oxidation in Nitric Acid

The oxidation in nitric acid of single crystal surfaces and of polycrystalline Ge (111) surfaces has been studied at 27.5°C over the concentration range . The surface oxide growth rate decreases smoothly with time and is not described by simple film growth laws. The average oxide nuclei size at saturation thickness decreases with increasing acid concentration, and more rapid surface saturation occurs with increasing acid concentration. No induction period for surface oxide growth was observed over the range of concentrations studied. The oxide films which grew on the Ge surfaces had saturation thicknesses inversely dependent on acid concentration, and the saturation thickness was also observed to be dependent on the crystallographic orientation of the Ge surface. Structural studies of the oxide layers by infrared, x‐ray, and electron diffraction techniques indicate that the surface oxide grown under these conditions is crystalline hexagonal germanium dioxide.