On integrating experimental and theoretical models to determine physical mechanisms of morphogenesis

Researchers in developmental biology are increasingly recognizing the value of theoretical models in studies of morphogenesis. However, creating and testing realistic quantitative models for morphogenetic processes can be an extremely challenging task. The focus of this paper is on models for the mechanics of morphogenesis. Models for these problems often must include large changes in geometry, leading to highly nonlinear problems with the possibility of multiple solutions that must be sorted out using experimental data. Here, we illustrate our approach to these problems using the specific example of head fold formation in the early chick embryo. The interplay between experimental and theoretical results is emphasized throughout, as the model is gradually refined. Some of the limitations inherent in theoretical/computational modeling of biological systems are also discussed.     

Models of epileptic seizures in immature rats

Models of basic types of epileptic seizures are elaborated not only in adult but also in immature rodents. It is important because at least half of human epilepsies starts during infancy and childhood. This paper presents a review of chemically and electrically induced models of generalized convulsive and nonconvulsive (absence) seizures as well as models of partial simple (neocortical) and complex (limbic) seizures in immature rats. These models can also serve as a tool for study the development of central nervous system and motor abilities because the level of maturation is reflected in seizure semiology. Age-dependent models of epileptic seizures (absences and flexion seizures) are discussed. Models of seizures in immature animals should be used for testing of potential antiepileptic drugs.     

Mechanisms of platelet production

The precise mechanism by which platelets are formed from megakaryocytes (MK) remains unclear, despite numerous studies which have been performed during this century. Models have been proposed that attempt to account for platelet formation from disruption of elongated processes of MK cytoplasm, designated proplatelets, or by fragmentation of MK cytoplasm. MK demarcation membranes are hypothesized by some investigators to delineate platelet territories in the MK cytoplasm, and by others to act as a membrane reservoir for MK process formation. Platelet production has been variously speculated to occur primarily in the bone marrow or lung. Each theory or model has attempted to elucidate the phenomenon of size heterogeneity of circulating platelets and the changes that occur under conditions of altered thrombopoiesis. In this article, we have analyzed and compared the characteristics of previously proposed models for platelet production and suggested additional techniques for future studies of thrombopoiesis.     

Pattern formation models and developmental constraints

Most schemes for embryonic pattern formation are built around the notion of lateral inhibition. Models of this type arise in many settings, and all share some common characteristics. In this paper we examine a number of pattern formation models and show how the phenomenon of lateral inhibition constrains the possible geometries that can arise.     

Orientations of transfer RNA in the ribosomal A and P sites.

In protein synthesis, peptide bond formation requires that the tRNA carrying the amino acid (A site tRNA) contact the tRNA carrying the growing peptide chain (P site tRNA) at their 3' termini. Two models have been proposed for the orientations of two tRNAs as they would be bound to the mRNA in the ribosome. Viewing the tRNA as an upside down L, anticodon loop pointing down, acceptor stem pointing right, and calling this the front view, the R (Rich) model would have the back of the P site tRNA facing the front of the A site tRNA. In the S (Sundaralingam) model the front of the P site tRNA faces the back of the A site tRNA. Models of two tRNAs bound to mRNA as they would be positioned in the ribosomal A and P sites have been created using MC-SYM, a constraint satisfaction search program designed to build nucleic acid structures. The models incorporate information from fluorescence energy transfer experiments and chemical crosslinks. The models that best answer the constraints are of the S variety, with no R conformations produced consistent with the constraints.     

Using models to enhance the intellectual content of learning in developmental biology

Models have been particularly useful in developmental biology over the last 30 years. At first, underlying control mechanisms were poorly understood, but over time a wealth of detailed information became available to provide an increasingly detailed knowledge of underlying mechanisms, at levels from genes through cells to organs, organisms and populations. Models are also of great value in teaching developmental biology, as they allow students to explore phenomena hard to perceive directly because of their scale, accessibility, expense or other considerations. A model may allow students to "experiment" in ways which would be impractical in real life, as well as give them a deep understanding of competing hypotheses of development. Lastly, students can be challenged to produce models of their own, whereas only rarely are they able to carry out original experiments. I discuss two main kinds of models and their uses in generating, testing and expounding hypotheses and point out dangers in the use of models in education. Models may draw upon and reflect the consensus paradigm in the field: a researcher may be able to appreciate that models are interim conditional statements of probability and use them to generate new knowledge. A student may be less able to do so and may fail to appreciate where new knowledge will come from. And unlike physics, biology is stochastic and contingent and can never be entirely deduced from first principles, implying that models can never be as perfect in any biological field as they can be in some other fields.     

Models for organizer and notochord formation

In the development of higher organisms, small groups of cells can play an important role by directing the fate of the surrounding cells. Models are discussed that account for the generation of such organizing regions. The generation of local high concentrations of signalling substances was proposed to depend on local self-enhancement combined with a long-range inhibition. The model accounts for pattern regulation, for instance, for the formation of multiple embryos after fragmentation of the early blastodisc in chickens or for head regeneration in the fresh water polyp Hydra. The model has found support from more recently discovered interactions involved in organizer formation. The mutual down-regulation of noggin/chordin and BMP-4 is proposed to function as an indirect self-enhancement, establishing in this way an essential prerequisite for primary pattern formation. Self-enhancement and long-range inhibition is also crucial for the generation of substructures such as bristles or tracheae. A poisoning of an organizing region by a second antagonistic reaction of a short range but a long time constant can lead to its displacement. Long extended structures can be formed as a trace behind the moving organizer. The notochord and the tracheae of insects are discussed as examples.     

Assignment of segments of the bacteriorhodopsin sequence to positions in the structural map.

Specific amino acid sequence segments have been assigned to locations in the structural map of bacteriorhodopsin using two-dimensional neutron diffraction data and a model building analysis. Models are constructed computationally by building specific regions of the amino acid sequence as alpha helices and then positioning the helices on axes indicated by the density map of Henderson and Unwin (Nature [Lond.]. 1975, 257:28-32). Neutron diffraction data were collected from samples of stacked, oriented "native" purple membranes as well as purple membranes containing different kinds of deuterated amino acids. Models differing in the assignments of helices to specific axes and in rotations of the helices about those axes were tested against the neutron data using a weighted residual factor to rank the models. This residual factor was calculated between observed and predicted intensity differences for pairs of data sets. Using this approach, a small set of related models has been found that predicts the observed intensity changes between five independent data sets. These models are inconsistent with the proposed locations of the retinal chromophore and the carboxyl terminus and with any of the previously proposed models for bacteriorhodopsin.     

Models for the 3(10)-helix/coil,pi-helix/coil,and alpha-helix/3(10)-helix/coil transitions in isolated peptides.

Models for the 3(10)-helix/coil and pi-helix/coil equilibria have been derived. The theory is based on classifying residues into helical or nonhelical (coil) conformations. Statistical weights are assigned to residues in a helical conformation with an associated helical hydrogen bond, a helical conformation with no hydrogen bond, an N-cap position, a C-cap position, or the reference coil conformation. The models for alpha-helix formation and 3(10)-helix formation have also been combined to describe a three-state equilibrium in which alpha-helical, 3(10)-helical, and coil conformations are populated. The results are compared with the modified Lifson-Roig theory for the alpha-helix/coil equilibrium. The comparison accounts for the experimental observations that 3(10)-helices tend to be short and pi-helices are not favored for any length. This work may provide a framework for quantitatively rationalizing experimental work on isolated 3(10)-helices and mixed 3(10)-/alpha-helices.     

Relating coupled map lattices to integro-difference equations: dispersal-driven instabilities in coupled map lattices

Recently there has been a great deal of interest within the ecological community about the interactions of local populations that are coupled only by dispersal. Models have been developed to consider such scenarios but the theory needed to validate model outcomes has been somewhat lacking. In this paper, we present theory which can be used to understand these types of interaction when population exhibit discrete time dynamics. In particular, we consider a spatial extension to discrete-time models, known as coupled map lattices (CMLs) which are discrete in space. We introduce a general form of the CML and link this to integro-difference equations via a special redistribution kernel. General conditions are then derived for dispersal-driven instabilities. We then apply this theory to two discrete-time models; a predator-prey model and a host-pathogen model.     

石膏样毛癣菌LZY8905株所致体癣模型及其在药物研究中应用探讨

石膏样毛癣菌ＬＺＹ８９０５株是从临床分离的强毒株,将其接种到豚鼠背部皮肤上,造成实验性体癣模型,其发病过程和病变特点与国外报告基本一致。用克霉唑癣药水对其进行治疗实验,证明对其具有较好的疗效。由于目前国内尚乏对动物致病性较强的菌株用于动物造模,所以该菌株可用于动物体癣模型的造模,用于抗皮肤癣菌药物等方面的研究。     

Phenomenological and molecular models of biological proton transfers

In this paper, the main models describing the transfer of a proton in a molecular system are presented. Models valid when the intersite coupling is weak (non-adiabatic and electronically adiabatic regimes) and strong (adiabatic regime) are described. We distinguish molecular models in which the rate constant is obtained by considering explicitly various degrees of freedom of the system and simpler, phenomenological models built to account for the kinetic isotope effect. The relations between the various models are discussed. Their application to specific systems is illustrated by several studies reported in the literature, with a special emphasis on biological systems.     

Models of the Transmembrane Domains of the Yeast Mitochondrial CitrateTransport Protein

We have used cysteine scanning, hydropathy analysis and molecular modeling to construct four possible models of the transmembrane helical domains of the yeast mitochondrial citrate transport protein. Models 1 and 2 invoke the formation of a translocation pathway by the six membrane-spanning alpha-helical domains that comprise each citrate transport protein monomer. Thus the homodimeric CTP (the functional form of the CTP) would contain two separate translocation pathways. Models 3 and 4 explore a novel way in which dimerization might take place, in which transmembrane domain 3 would form part of the dimer interface. This would lead to the formation of two seven-helix translocation pathways within the transporter dimer. Importantly, these studies have led to the construction of the first detailed structural models for any of the mitochondrial anion transport proteins, a family of proteins which is essential to cellular bioenergetics. Furthermore, these models suggest numerous experiments which can be carried out to further elucidate the structure of the translocation pathway through the membrane.     

A population genetical model for sequence evolution under multiple types of mutation

DNA sequencing and restriction mapping provide us with information on DNA sequence evolution within populations, from which the phylogenetic relationships among the sequences can be inferred. Mutations such as base substitutions, deletions, insertions and transposable element insertions can be identified in each sequence. Theoretical study of this type of sequence evolution has been initiated recently. In this paper, population genetical models for sequence evolution under multiple types of mutation are developed. Models of infinite population size with neutral mutation, infinite population size with deleterious mutation and finite population size with neutral mutation are considered.     

The Role of Flower Inclination, Depth, and Height in the Preferences of a Pollinating Beetle (Coleoptera: Glaphyridae)

Amphicoma (Glaphyridae) beetles are important pollinators of red bowl-shaped flowers in the Mediterranean. The role of color and shape in flower choice is well studied but the roles of inclination, depth, and height have seldom been investigated. Under field conditions, models were used to experimentally manipulate these three characters and visitation rates of beetles were recorded. Models with red horizontal surfaces were visited significantly more often than models with red vertical surfaces. Shallow flower models were visited significantly more than deeper equivalents. Models below or at the height of natural flower populations elicited significantly more landings than models above the height of flowers. Inclination, depth, and height characteristics are all likely to be important components in the flower preferences exhibited by pollinating beetles.     

The pore domain of the nicotinic acetylcholine receptor: molecular modeling, pore dimensions, and electrostatics.

The pore domain of the nicotinic acetylcholine receptor has been modeled as a bundle of five kinked M2 helices. Models were generated via molecular dynamics simulations incorporating restraints derived from 9-A resolution cryoelectron microscopy data (Unwin, 1993; 1995), and from mutagenesis data that identify channel-lining side chains. Thus, these models conform to current experimental data but will require revision as higher resolution data become available. Models of the open and closed states of a homopentameric alpha 7 pore are compared. The minimum radius of the closed-state model is less than 2 A; the minimum radius of the open-state models is approximately 6 A. It is suggested that the presence of "bound" water molecules within the pore may reduce the effective minimum radii below these values by up to approximately 3 A. Poisson-Boltzmann calculations are used to obtain a first approximation to the potential energy of a monovalent cation as it moves along the pore axis. The differences in electrostatic potential energy profiles between the open-state models of alpha 7 and of a mutant of alpha 7 are consistent with the experimentally observed change in ion selectivity from cationic to anionic. Models of the open state of the heteropentameric Torpedo nicotinic acetylcholine receptor pore domain are also described. Relatively small differences in pore radius and electrostatic potential energy profiles are seen when the Torpedo and alpha 7 models are compared.     

Growth of newly established alien populations: comparison of North American gypsy moth colonies with invasion theory

A common characteristic observed in many biological invasions is the existence of a lag between the time of arrival by the alien population and the time when established populations are noticed. Considerable advances have been made in modeling the expansion of invading species, and there is often remarkable congruence between the behavior of these models with spread of actual populations. While these models have been used to characterize expansion of very newly founded colonies, there have been few attempts to compare the behavior predicted from theory with spread in actual newly founded populations, largely due to the difficulty of sampling sparse populations. Models predict that time lags in the radial expansion of newly invaded populations may be due to time requirements for the population to grow from founding to detectable levels. Models also indicate that these time lags can be predicted based upon population parameters such as the intrinsic rate of population growth and diffusion coefficient. In this paper, we compared the behavior of these models with historical data on gypsy moth, Lymantria dispar, establishment and spread to show similarities between model predictions and observed population spread, both of which exhibited temporal lags of expansion. However, actual populations exhibited certain behaviors that were not predicted, and this could be due, in part, to the existence of Allee effects and stochasticity. Further work that incorporates these effects is needed to more fully understand the growth of incipient colonies of invading species. Ultimately, this information can be of critical importance in the selection of effective strategies for their detection and eradication.     

Algorithmic specification as a technique for computing with informal biological models

Conceptual biological models can sometimes be usefully expressed in algorithmic form. Models expressed in this way are often capable of capturing more aspects of the complete system than could be captured by other modeling approaches, though in general each aspect is captured in a highly simplified way. Two examples are given. The first involves algorithmic specification of the theory of evolution. The second involves a recently implemented computational model of the brain. Work with such models has, to some extent, the style of experimental work. It often suggests interesting problems or exposes subtle features of the system whose importance has been overlooked.     

Holliday intermediates and reaction by-products in FLP protein-promoted site-specific recombination.

Holliday structures are formed and resolved by FLP protein during site-specific recombination. These structures have been isolated and are visualized in both native and partially denatured states by electron microscopy. No single-strand breaks are found within the junction, indicating that the structure results from a reciprocal exchange of strands. These structures have properties consistent with being reaction intermediates. Double-strand cleavage products and "Y structures" are also detected and appear to be by-products of the reaction. The Y structures are three-armed branched molecules with a covalently closed junction located at the FLP recombination target site. Models are discussed, suggesting that both of these novel structures are made by aberrant cleavages during formation and resolution of the Holliday intermediate.