A Geometro-mechanical model for pulsatile morphogenesis

A model is proposed which imitates the morphogenesis of several species of the lower invertebrate animals, the hydroid polyps and permits the derivation of the geometry (surface curvature) of each developmental stage from that of the preceding stage. The model is based upon two experimentally verified assumptions. First, neighbouring cells are assumed to compress each other laterally in a regular and species-specific pulsatile manner. It is this pressure, and/or an active cell reaction to it, which changes the curvature of a cell layer. Secondly, cell layers are assumed to have quasi-elastic properties tending to smooth out their curvature. With our model, the different pulsatile patterns of cell-cell pressure are reproduced and the elasticity parameters are modulated. As a result, within a large zone of parameter values (a so-called "morphogenetic zone", MZ) realistic shapes of the rudiments are reproduced. The main principles of the model can also be used for interpreting the morphogenesis of other groups of animals. A suggested model emphasizes the self-organizing properties of a "stressed geometry" of embryonic rudiments.     

A mechanism for early branching in lung morphogenesis

The lung is a highly branched fluid-filled structure, that develops by repeated dichotomous branching of a single bud off the foregut, of epithelium invaginating into mesenchyme. Incorporating the known stress response of developing lung tissues, we model the developing embryonic lung in fluid mechanical terms. We suggest that the repeated branching of the early embryonic lung can be understood as the natural physical consequence of the interactions of two or more plastic substances with surface tension between them. The model makes qualitative and quantitative predictions, as well as suggesting an explanation for such observed phenomena as the asymmetric second branching of the embryonic bronchi.     

A simple model for plankton patchiness

Recent work on zooplankton spatial variability shows that thepower spectrum of the wave-number variance is flatter than thatfor chlorophyll, as a consequence of greater fine structurein the herbivores. The relative slopes of the power spectracan result from white noise forcing of simple coupled phytoplankton-herbivoremodels with diffusion.     

A simple model for gene targeting

Sequence-specific binding to genomic-size DNA sequences by artificial agents is of major interest for the development of gene-targeting strategies, gene-diagnostic applications, and biotechnical tools. The binding of one such agent, peptide nucleic acid (PNA), to a randomized human genome has been modeled with statistical mass action calculations. With the length of the PNA probe, the average per-base binding constant k(0), and the binding affinity loss of a mismatched base pair as main parameters, the specificity was gauged as a "therapeutic ratio" G = maximum safe [PNA](tot)/minimal efficient [PNA](tot). This general, though simple, model suggests that, above a certain threshold length of the PNA, the microscopic binding constant k(0) is the primary determinant for optimal discrimination, and that only a narrow range of rather low k(0) values gives a high therapeutic ratio G. For diagnostic purposes, the value of k(0) could readily be modulated by changing the temperature, due to the substantial Delta H degrees associated with the binding equilibrium. Applied to gene therapy, our results stress the need for appropriate control of the binding constant and added amount of the gene-targeting agent, to meet the varying conditions (ionic strength, presence of competing DNA-binding molecules) found in the cell.     

A model of morphogenesis for protein secondary structures.

This paper proposes a model for the expected probability distribution for a certain class of biological structures. In particular, a model is derived for the distribution of lengths of helices, sheets, turns, and coils as a function of the length of the structure divided by the length of the protein it is contained in. A fit between the derived lognormal function and the structures for some proteins whose three-dimensional structure is known was significant. The fit produces fundamental parameters particular to each structure type that are related to the underlying structure and its morphogenesis. The importance of the result is that a universal mathematical distribution can be used to explain certain protein morphogeneses. Also, these fundamental parameters can be used as an aid in predicting whether a given sequence is a particular secondary structure or not, without a knowledge of its three-dimensional structure.     

A simple work flow for biologically inspired model reduction - application to early JAK-STAT signaling

Background  

Modeling of biological pathways is a key issue in systems biology. When constructing a model, it is tempting to incorporate all known interactions of pathway species, which results in models with a large number of unknown parameters. Fortunately, unknown parameters need not necessarily be measured directly, but some parameter values can be estimated indirectly by fitting the model to experimental data. However, parameter fitting, or, more precisely, maximum likelihood parameter estimation, only provides valid results, if the complexity of the model is in balance with the amount and quality of the experimental data. If this is the case the model is said to be identifiable for the given data. If a model turns out to be unidentifiable, two steps can be taken. Either additional experiments need to be conducted, or the model has to be simplified.     

A binocular model for the simple cell

We authors propose a mathematical model for simple cell binocular response. It comprises two Gabor-type receptive fields (RF) having the same RF center, preferred spatial frequency, and preferred orientation. The model integrates the equally weighted signals from both eyes and performs a threshold operation. Poggio and Fischer (1977) classified binocular disparity cells in the striate cortex into four groups: tuned excitatory (TE), tuned inhibitory (TI), near, and far cells. They also found that most of the TE cells are ocularly balanced and that the other three types are usually unbalanced. This model can imitate these four types of disparity sensitivities and their ocular dominance tendency. We perform model fittings to Poggio's data using the “simulated annealing” method and discuss parameter dependence of the model's response. The model can also respond with exceptional disparity sensitivity: i.e., flat type, alternating type, and intermediate type.     

A simple model for calcium induced exocytosis

We have developed a simple model showing how the presence or absence of Ca²⁺ can determine whether an uncurved or curved membrane surface is favored energetically. The model shows why fusion of vesicles with the presynaptic membrane is favored in the presence of calcium and why the budding off of vesicles is favored in the absence of calcium inside of the presynaptic membrane. The model accurately predicts the radius of a synaptic vesicle using known properties of lipids and suggests consequences of temperature change, varied stimulation rate and addition of calcium by artificial means on rates of transmitter release.     

A simple model for a regulatory enzyme

A simple model for a regulatory enzyme is described which leads to relationships between the initial velocity of the catalysed reaction and the varied concentration of a substrate that are of the non-inflected or sigmoidal varieties without a maximum. The model assumes that the most relevant measure of protein configuration (itself determining the kinetic behaviour of the enzyme) is the apparent association constant, α_i, measured for the given fractional saturation of the ligand under investigation. It is further assumed that the original state of the protein in solution, α₀, is destabilized by an increment of energy, ΔG_p⁰, that is proportional to the fractional saturation of the enzyme by ligand so that the formation of a new configurational state, a,, can be represented by ?ΔG_p⁰ = RT ln $\text{α}{}_1\text{α}{}_0$. The rate or fractional saturation equation that can be derived from this model predicts both positive and negative cooperativity. Either equation can be transformed for linear representation, provided the maximum velocity or its equivalent maximum saturation is known, and estimates of α₀ and α_i (the apparent association constants at zero and complete saturation) can be obtained thereby. A procedure is also described by which an initial estimate of the maximum velocity or saturation can be improved. The model is tested by application to a range of data in the literature and it is shown to give fits to the data comparable in quality to those provided by the model of Monod, Wyman &; Changeux (1965).     

A simple model for the arterial system

We present a simple model for the arterial part of the cardiovascular system, based on Poiseuille flow constrained by the power dissipated into the cells lining the vessels. This, together with the assumption of a volume-filling network, leads to correct predictions for the evolution of vessel radii, vessel lengths and blood pressure in the human arterial system. The model can also be used to find exponents for allometric scaling, and gives good agreement with data on mammals.     

A simple model for multi-ion permeation. Single-vacancy conduction in a simple pore model.

Recent experimental evidence suggests that certain membrane channels operate in a nearly ion-saturated state. We therefore consider a "single-vacancy" model of ion permeation: if a channel has n conducting sites, it will contain either n or n-1 ions. Simple analytical expressions for the current, conductance, and reversal potential under bi-ionic conditions are derived. The results are compared with those of single ion models and recent experiments on Ca2(+)-activated K+ channels.     

Liver specification and early morphogenesis

The classically defined induction of the liver from the endoderm, elicited by the cardiac mesoderm, has recently been discovered to involve signaling by fibroblast growth factors (FGFs). Multiple FGFs induce hepatic gene expression independent of an effect on growth. A subset of these FGFs cooperates with other factors to promote morphogenesis of the newly specified hepatocytes. Subsequent to the formation of the liver bud, distinct mesenchymal signals and hepatic response pathways stimulate further growth and differentiation of the hepatic parenchymal cells and prevent apoptosis. The initial stages of hepatogenesis are therefore beginning to be understood, and serve as a paradigm for the development of other tissues from the endoderm.     

Some analytical results about a simple reaction-diffusion system for morphogenesis

Summary The reaction-diffusion system considered involves only one nonlinear term and is a gradient system. In a bifurcation analysis for the equilibrium states, the global existence of infinitely many solution branches can be shown by the method of Ljusternik-Schnirelmann. Their stability is studied. Using a Ljapunov functional it can be shown that the solutions of the time-dependent system converge to the equilibrium states.     

A simple kinetic model for dynein oscillatory activity

A kinetic model was proposed for dynein, a motor protein, complexed with microtubule fragments. The model explains the experimental observations of oscillatory movements in surprisingly simple axoneme fragments perfused with an ATP solution. This is the first model explaining the oscillatory activity of dynein as determined by a cooperative interaction of two dynein heads in the axoneme. The oscillation shape, frequency, and amplitude obtained for the model are close to the corresponding parameters determined experimentally.     

A simple kinetic model for dynein oscillatory activity

A kinetic model for dynein, a molecular motor, complexed with microtubule fragments, is considered. The model explains the experimental observations of oscillatory movements in surprisingly simple axonemal fragments perfused by the ATP solution. The model explains at first time the oscillatory dynein activity as a phenomenon induced by two dynein heads cooperative interaction in the axoneme. The oscillation form, frequency, and amplitude, observed for the model, are close to these experimental characteristics. Kinetic parameters, used in the model, are close to the known experimental parameters.     

A simple game-theoretic model for upstream fish migration

A simple game-theoretic model for upstream fish migration, which is a key element in life history of diadromous fishes, is proposed. Foundation of the model is a minimization problem on the cost of migration with the swimming speed and school size as the variables to be simultaneously optimized. Finding the optimizer ultimately reduces to solving a self-consistency equation without explicit solutions. Mathematical analytical results lead to the sufficient condition that the self-consistency equation has a unique solution, which turns out to be identified with the condition where the unique optimizer exists. Behavior of the optimizer is analyzed both mathematically and numerically to show its biophysical and ecological consequences. The analytical results demonstrate reasonable agreement between the present mathematical model and the theoretical and experimental results of upstream migration of fish schools reported in the past research.     

A simple mathematical model for Ebola in Africa

We deal with the following question: Can the consumption of contaminated bush meat, the funeral practices and the environmental contamination explain the recurrence and persistence of Ebola virus disease outbreaks in Africa? We develop an SIR-type model which, incorporates both the direct and indirect transmissions in such a manner that there is a provision of Ebola viruses. We prove that the full model has one (endemic) equilibrium which is locally asymptotically stable whereas, it is globally asymptotically stable in the absence of the Ebola virus shedding in the environment. For the sub-model without the provision of Ebola viruses, the disease dies out or stabilizes globally at an endemic equilibrium. At the endemic level, the number of infectious is larger for the full model than for the sub-model without provision of Ebola viruses. We design a nonstandard finite difference scheme, which preserves the dynamics of the model. Numerical simulations are provided.     

Epithelial-mesenchymal co-culture model for studying alveolar morphogenesis

Division of large, immature alveolar structures into smaller, more numerous alveoli increases the surface area available for gas exchange. Alveolar division requires precise epithelial-mesenchymal interactions. However, few experimental models exist for studying how these cell-cell interactions produce changes in 3-dimensional structure. Here we report an epithelial-mesenchymal cell co-culture model where 3-dimensional peaks form with similar cellular orientation as alveolar structures in vivo. Co-culturing fetal mouse lung mesenchyme with A549 epithelial cells produced tall peaks of cells covered by epithelia with cores of mesenchymal cells. These structures did not form when using adult lung fibroblasts. Peak formation did not require localized areas of cell proliferation or apoptosis. Mesenchymal cells co-cultured with epithelia adopted an elongated cell morphology closely resembling myofibroblasts within alveolar septa in vivo. Because inflammation inhibits alveolar formation, we tested the effects of E. coli lipopolysaccharide on 3-dimensional peak formation. Confocal and time-lapse imaging demonstrated that lipopolysaccharide reduced mesenchymal cell migration, resulting in fewer, shorter peaks with mesenchymal cells present predominantly at the base. This epithelial-mesenchymal co-culture model may therefore prove useful in future studies of mechanisms regulating alveolar morphogenesis.