A general computational framework for modeling cellular structure and function.

The "Virtual Cell" provides a general system for testing cell biological mechanisms and creates a framework for encapsulating the burgeoning knowledge base comprising the distribution and dynamics of intracellular biochemical processes. It approaches the problem by associating biochemical and electrophysiological data describing individual reactions with experimental microscopic image data describing their subcellular localizations. Individual processes are collected within a physical and computational infrastructure that accommodates any molecular mechanism expressible as rate equations or membrane fluxes. An illustration of the method is provided by a dynamic simulation of IP3-mediated Ca2+ release from endoplasmic reticulum in a neuronal cell. The results can be directly compared to experimental observations and provide insight into the role of experimentally inaccessible components of the overall mechanism.     

Mathematical framework for modeling tissue growth

A phenomenological continuum mechanics framework for modeling growth of living tissues is proposed. Tissue is considered as an open system where mass is not conserved. The momentum balance is completed with the full-scale mass balance. Constitutive equations define simple growing materials. 'Thermoelastic' formulation of a simple growing material is specified. Within this framework traction free growth of a cylinder is considered. It is shown that the theory accommodates the case where stresses are not generated in uniform volumetric growth. It is also found that surface growth corresponds to a boundary layer solution of the governing equations.     

A framework for whole-cell mathematical modeling

The default framework for modeling biochemical processes is that of a constant-volume reactor operating under steady-state conditions. This is satisfactory for many applications, but not for modeling growth and division of cells. In this study, a whole-cell modeling framework is developed that assumes expanding volumes and a cell-division cycle. A spherical newborn cell is designed to grow in volume during the growth phase of the cycle. After 80% of the cycle period, the cell begins to divide by constricting about its equator, ultimately affording two spherical cells with total volume equal to twice that of the original. The cell is partitioned into two regions or volumes, namely the cytoplasm (Vcyt) and membrane (Vmem), with molecular components present in each. Both volumes change during the cell cycle; Vcyt changes in response to osmotic pressure changes as nutrients enter the cell from the environment, while Vmem changes in response to this osmotic pressure effect such that membrane thickness remains invariant. The two volumes change at different rates; in most cases, this imposes periodic or oscillatory behavior on all components within the cell. Since the framework itself rather than a particular set of reactions and components is responsible for this behavior, it should be possible to model various biochemical processes within it, affording stable periodic solutions without requiring that the biochemical process itself generates oscillations as an inherent feature. Given that these processes naturally occur in growing and dividing cells, it is reasonable to conclude that the dynamics of component concentrations will be more realistic than when modeled within constant-volume and/or steady-state frameworks. This approach is illustrated using a symbolic whole cell model.     

A general framework for marker-assisted selection

Early simulation studies have showed that the inclusion of epistatic components (especially the additive-by-additive effects) into marker-assisted selection (MAS) can improve selection efficiency for a short-term breeding program. In this study I extend Lande and Thompson's theory to incorporate both additive and non-additive effects into MAS with reference to the mass selection case. Four different indices are analytically examined in terms of the type of genetic components involved in the marker scores: phenotype-, general combining ability (GCA)-, and GCA and reciprocal effects-based marker scores. The phenotype-based marker index is applicable to any population of non-random mating, while the other three indices are applicable to the synthetic population derived from diallel crosses. All these indices may have higher selection efficiencies than the index with solely additive effects-associated markers as long as the detectable transient non-additive effects are present. The improvement in selection efficiency depends on the magnitude of non-additive variances and the proportion of them explained by markers. The index with the phenotype-based marker scores operates on the whole of the additive and non-additive effects, and has the largest selection efficiency. The indices with the GCA-based marker scores operate only on additive and additive-by-additive genetic variation and have relatively small selection efficiencies. Inclusion of the markers from organelle genomes can also increase selection efficiency, depending upon the proportion of the total genetic variation attributable to organelle genomes and the proportion of them explained by organelle genomic markers. Sharing of markers among different marker scores does not facilitate the improvement of selection efficiency.     

How cells coordinate growth and division

Size is a fundamental attribute impacting cellular design, fitness, and function. Size homeostasis requires a doubling of cell mass with each division. In yeast, division is delayed until a critical size has been achieved. In metazoans, cell cycles can be actively coupled to growth, but in certain cell types extracellular signals may independently induce growth and division. Despite a long history of study, the fascinating mechanisms that control cell size have resisted molecular genetic insight. Recently, genetic screens in Drosophila and functional genomics approaches in yeast have macheted into the thicket of cell size control.     

A growth and division model for retinoblastoma

A stochastic growth and division model for studying a two hit cancer is developed and applied to retinoblastoma. Retinoblastoma occurs if both genes coding for a tumor suppressor protein on homologous chromosomes become defective. Germinal cases occur when a patient or carrier, born with one defective gene, suffers a second insult to any progeny retinal cell. Somatic cases are far less likely as two hits to the same cell during development are required. Details of the disease, germinal or somatic, unilateral or bilateral, in combination with case data allow for the estimation of the two parameters of the model: mutation rate, estimated at p=7x10(-7) per chromosome per cell division, and carrier frequency, estimated at f=40 per million. The model indicates that carriers of the disease arise from similar mutations to germ cells; in particular, heridary transmission can occur for only a generation or two before dying out. The results show that a stochastic simulation of a multi-hit cancer is feasible and may predict tumor growth dynamics. A simulation run will have to consist of a few million cells in order to observe even a small number of mutations. And several dozens such runs will have to be simulated.     

A general eco-evolutionary framework for understanding bioinvasions

Studies of bioinvasions have revealed various strategies of invasion, depending on the ecosystem invaded and the alien species concerned. Here, we consider how migration (as a demographic factor), as well as ecological and evolutionary changes, affect invasion success. We propose three main theoretical scenarios that depend on how these factors generate the match between an invader and its new environment. Our framework highlights the features that are common to, or differ among, observed invasion cases, and clarifies some general trends that have been previously highlighted in bioinvasions. We also suggest some new directions of research, such as the assessment of the time sequence of demographic, genetic and environmental changes, using detailed temporal surveys.     

A framework for modeling of juxtacrine signaling systems

Juxtacrine signaling is intercellular communication, in which the receptor of the signal (typically a protein) as well as the ligand (also typically a protein, responsible for the activation of the receptor) are anchored in the plasma membranes, so that in this type of signaling the activation of the receptor depends on direct contact between the membranes of the cells involved. Juxtacrine signaling is present in many important cellular events of several organisms, especially in the development process. We propose a generic formal model (a modeling framework) for juxtacrine signaling systems that is a class of discrete dynamic systems. It possesses desirable characteristics in a good modeling framework, such as: a) structural similarity with biological models, b) capacity of operating in different scales of time, and c) capacity of explicitly treating both the events and molecular elements that occur in the membrane, and those that occur in the intracellular environment and that are involved in the juxtacrine signaling process. We have implemented this framework and used it to develop a new three-level discrete model for the neurogenic network and its participation in neuroblast segregation. This paper presents the details of this framework and its current status.     

A framework for structured modeling of skeletal muscle

The aim of this study is to present a detailed continuum mechanics formulation, and the corresponding algorithms, to predict the deformation of skeletal muscle at different structural levels, starting from the muscle fiber level. The model is used to investigate force production and structural changes during isometric and dynamic contractions of the cat medial gastrocnemius. From a comparison with experimental data obtained in our own laboratories, we conclude that the model faithfully predicts all of the observations pertaining to force production, fascicle length and angle of pennation under various test conditions.     

A log-linear modeling framework for selective mixing.

Nonrandom mixing can significantly alter the diffusion path of an infectious disease such as AIDS that requires intimate contact. Recent attempts to model this effect have sought a general framework capable of representing both simple and arbitrarily complicated mixing structures, and of solving the balancing problem in a nonequilibrium multigroup population. Log-linear models are proposed here as a general framework for solving the first problem. This approach offers several additional benefits: The parameters used to govern the mixing have a simple, intuitive interpretation, the framework provides a statistically sound basis for the estimation of these parameters from mixing-matrix data, and the resulting estimates are easily integrated into compartmental models for diffusion. A modified selection model is proposed to solve the second problem of generalizing the selection process to nonequilibrium populations. The distribution of contacts under this model is derived and is found to satisfy the assumptions of statistical inference for log-linear models. Together these techniques provide an integrated and flexible framework for modeling the role of selective mixing in the spread of disease.     

A general framework for biclustering gene expression data

A large number of biclustering methods have been proposed to detect patterns in gene expression data. All these methods try to find some type of biclusters but no one can discover all the types of patterns in the data. Furthermore, researchers have to design new algorithms in order to find new types of biclusters/patterns that interest biologists. In this paper, we propose a novel approach for biclustering that, in general, can be used to discover all computable patterns in gene expression data. The method is based on the theory of Kolmogorov complexity. More precisely, we use Kolmogorov complexity to measure the randomness of submatrices as the merit of biclusters because randomness naturally consists in a lack of regularity, which is a common property of all types of patterns. On the basis of algorithmic probability measure, we develop a Markov Chain Monte Carlo algorithm to search for biclusters. Our method can also be easily extended to solve the problems of conventional clustering and checkerboard type biclustering. The preliminary experiments on simulated as well as real data show that our approach is very versatile and promising.     

A modeling framework for the study of protein glycosylation

The key step in the asparagine-linked glycosylation of secretory proteins is the transfer of oligosaccharide from a dolichol precursor to the polypeptide at an Asp-X-Ser/Thr (NXS/T) consensus sequence. It is often the case, both in cultured cells and in vivo, that this reaction does not occur for every molecule of a given protein. Thus, the cell may create two protein populations, one bearing and one lacking oligosaccharide, for each potential glycosylation site. We present a structured kinetic modeling framework of the initial glycosylation event based on a balance of available glycosylation sites through the region of endoplasmic reticulum lumen proximal to the membrane. Oligosaccharyltransferase, a multimeric protein complex, catalyzes the sugar transfer. This enzyme is integral to the endoplasmic reticulum membrane, and it is thought to act cotranslationally. The nascent polypeptide may also fold in such a way as to prevent glycosylation from occurring. The net result is a potentially complex spatial and temporal relationship among translation, glycosylation, and other cotranslational events. Model results predict how fractional glycosylation site occupancy may depend on protein synthesis rate, oligosaccharyldolichol availability, and mRNA elongation rate. Although we are currently unable to quantitatively compare predicted to experimentally obtained fractional site occupancy, we are able to determine qualitative trends which may be confirmed experimentally. (c) 1996 John Wiley & Sons, Inc.     

Dynamin-related protein Drp1 is required for mitochondrial division in mammalian cells

Mutations in the human dynamin-related protein Drp1 cause mitochondria to form perinuclear clusters. We show here that these mitochondrial clusters consist of highly interconnected mitochondrial tubules. The increased connectivity between mitochondria indicates that the balance between mitochondrial division and fusion is shifted toward fusion. Such a shift is consistent with a block in mitochondrial division. Immunofluorescence and subcellular fractionation show that endogenous Drp1 is localized to mitochondria, which is also consistent with a role in mitochondrial division. A direct role in mitochondrial division is suggested by time-lapse photography of transfected cells, in which green fluorescent protein fused to Drp1 is concentrated in spots that mark actual mitochondrial division events. We find that purified human Drp1 can self-assemble into multimeric ring-like structures with dimensions similar to those of dynamin multimers. The structural and functional similarities between dynamin and Drp1 suggest that Drp1 wraps around the constriction points of dividing mitochondria, analogous to dynamin collars at the necks of budding vesicles. We conclude that Drp1 contributes to mitochondrial division in mammalian cells.