Mechanical model of geometric cell and topological algorithm for cell dynamics from single-cell to formation of monolayered tissues with pattern.

Geometric and mechanical properties of individual cells and interactions among neighboring cells are the basis of formation of tissue patterns. Understanding the complex interplay of cells is essential for gaining insight into embryogenesis, tissue development, and other emerging behavior. Here we describe a cell model and an efficient geometric algorithm for studying the dynamic process of tissue formation in 2D (e.g. epithelial tissues). Our approach improves upon previous methods by incorporating properties of individual cells as well as detailed description of the dynamic growth process, with all topological changes accounted for. Cell size, shape, and division plane orientation are modeled realistically. In addition, cell birth, cell growth, cell shrinkage, cell death, cell division, cell collision, and cell rearrangements are now fully accounted for. Different models of cell-cell interactions, such as lateral inhibition during the process of growth, can be studied in detail. Cellular pattern formation for monolayered tissues from arbitrary initial conditions, including that of a single cell, can also be studied in detail. Computational efficiency is achieved through the employment of a special data structure that ensures access to neighboring cells in constant time, without additional space requirement. We have successfully generated tissues consisting of more than 20,000 cells starting from 2 cells within 1 hour. We show that our model can be used to study embryogenesis, tissue fusion, and cell apoptosis. We give detailed study of the classical developmental process of bristle formation on the epidermis of D. melanogaster and the fundamental problem of homeostatic size control in epithelial tissues. Simulation results reveal significant roles of solubility of secreted factors in both the bristle formation and the homeostatic control of tissue size. Our method can be used to study broad problems in monolayered tissue formation. Our software is publicly available.

Mechanisms of regulating tissue elongation in Drosophila wing: impact of oriented cell divisions, oriented mechanical forces, and reduced cell size.

Regulation of cell growth and cell division plays fundamental roles in tissue morphogenesis. However, the mechanisms of regulating tissue elongation through cell growth and cell division are still not well understood. The wing imaginal disc of Drosophila provides a model system that has been widely used to study tissue morphogenesis. Here we use a recently developed two-dimensional cellular model to study the mechanisms of regulating tissue elongation in Drosophila wing. We simulate the effects of directional cues on tissue elongation. We also computationally analyze the role of reduced cell size. Our simulation results indicate that oriented cell divisions, oriented mechanical forces, and reduced cell size can all mediate tissue elongation, but they function differently. We show that oriented cell divisions and oriented mechanical forces act as directional cues during tissue elongation. Between these two directional cues, oriented mechanical forces have a stronger influence than oriented cell divisions. In addition, we raise the novel hypothesis that reduced cell size may significantly promote tissue elongation. We find that reduced cell size alone cannot drive tissue elongation. However, when combined with directional cues, such as oriented cell divisions or oriented mechanical forces, reduced cell size can significantly enhance tissue elongation in Drosophila wing. Furthermore, our simulation results suggest that reduced cell size has a short-term effect on cell topology by decreasing the frequency of hexagonal cells, which is consistent with experimental observations. Our simulation results suggest that cell divisions without cell growth play essential roles in tissue elongation.

Dynamic mechanical finite element model of biological cells for studying cellular pattern formation.

Understanding the geometric, topologic, and mechanical properties of cells and their interactions is critical for studying tissue pattern formation and organ development. Computational model and tools for simulating cell pattern formation have broad implications in studying embryogenesis, blood-vessel development, tissue regeneration, and tumor growth. Although a number of cell modeling methods exist, they do not simultaneously account for detailed cellular shapes as well as dynamic changes in cell geometry and topology. Here we describe a dynamic finite element cell model (dFEMC) for studying populations of cells and tissue development. By incorporating details of cell shape, cell growth and shrinkage, cell birth and death, cell division and fusion, our method can model realistically a variety problems of cell pattern formation. We give two examples of applying our method to the study of cell fusion and cell apoptosis. The dFEMC model developed here provides a general computational framework for studying dynamics pattern formation of tissue.

Mechanisms of regulating cell topology in proliferating epithelia: impact of division plane, mechanical forces, and cell memory.

Regulation of cell growth and cell division has a fundamental role in tissue formation, organ development, and cancer progression. Remarkable similarities in the topological distributions were found in a variety of proliferating epithelia in both animals and plants. At the same time, there are species with significantly varied frequency of hexagonal cells. Moreover, local topology has been shown to be disturbed on the boundary between proliferating and quiescent cells, where cells have fewer sides than natural proliferating epithelia. The mechanisms of regulating these topological changes remain poorly understood. In this study, we use a mechanical model to examine the effects of orientation of division plane, differential proliferation, and mechanical forces on animal epithelial cells. We find that regardless of orientation of division plane, our model can reproduce the commonly observed topological distributions of cells in natural proliferating animal epithelia with the consideration of cell rearrangements. In addition, with different schemes of division plane, we are able to generate different frequency of hexagonal cells, which is consistent with experimental observations. In proliferating cells interfacing quiescent cells, our results show that differential proliferation alone is insufficient to reproduce the local changes in cell topology. Rather, increased tension on the boundary, in conjunction with differential proliferation, can reproduce the observed topological changes. We conclude that both division plane orientation and mechanical forces play important roles in cell topology in animal proliferating epithelia. Moreover, cell memory is also essential for generating specific topological distributions.

Accuracy of functional surfaces on comparatively modeled protein structures.

Identification and characterization of protein functional surfaces are important for predicting protein function, understanding enzyme mechanism, and docking small compounds to proteins. As the rapid speed of accumulation of protein sequence information far exceeds that of structures, constructing accurate models of protein functional surfaces and identify their key elements become increasingly important. A promising approach is to build comparative models from sequences using known structural templates such as those obtained from structural genome projects. Here we assess how well this approach works in modeling binding surfaces. By systematically building three-dimensional comparative models of proteins using MODELLER: , we determine how well functional surfaces can be accurately reproduced. We use an alpha shape based pocket algorithm to compute all pockets on the modeled structures, and conduct a large-scale computation of similarity measurements (pocket RMSD and fraction of functional atoms captured) for 26,590 modeled enzyme protein structures. Overall, we find that when the sequence fragment of the binding surfaces has more than 45% identity to that of the template protein, the modeled surfaces have on average an RMSD of 0.5 Å, and contain 48% or more of the binding surface atoms, with nearly all of the important atoms in the signatures of binding pockets captured.

Mechanical forces mediate localized topological change in epithelia.

Regulation of cell growth and proliferation has a fundamental role in tissue development, organogenesis, and disease progression. Conserved distribution of the number of sides of cells with a mean value of six was found in a variety of proliferating epithelia. Previous studies have shown that clones of proliferating cells bounded by quiescent cells have fewer sides than normal epithelia. However, the mechanisms for mediating such localized topological change remain poorly understood. In this study, we use a two-dimensional vertex model with consideration of mechanical forces to investigate how differential proliferation and forces can influence cell shape and tissue morphogenesis, and how they may lead to distorted topological change. We find that differential proliferation alone is insufficient to affect the topology of boundary proliferating cells. Rather, increased surface tension on the boundary, in addition to differential proliferation, can significantly decrease the average number of cell sides. Our results are consistent with experimental observations. We conclude that mechanical forces in addition to localized differential proliferation are required to produce the distorted topological change which significantly impacts the overall cell shape and tissue morphogenesis.

Geometric order in proliferating epithelia: impact of rearrangements and cleavage plane orientation.

Regulation of proliferation is required for normal development of tissues and prevention of cancer formation. Continuous control of proliferation leads to regular shaped cells forming characteristic tissue patterns. Epithelial tissues serve as a model system for studying tissue morphogenesis. Several groups have studied epithelial morphogenesis using topological or geometric models, with various assumptions. In this study, we have developed a method to simulate the dynamic process of proliferating epithelia using an off-lattice cellular model. Our method realistically models the shape, size, geometry, lineage, cleavage plane orientation as well as topological properties of individual cells. We find that cellular rearrangements and cleavage plane orientation are critical in the formation of the observed cellular pattern of epithelia, including a high percentage of hexagons in proliferating epithelial cells. It is likely that the rearrangements and orientation of the cleavage plane reduces the overall stress on the cell. We show that a high percentage of hexagons in proliferating epithelia can be obtained using uniform growth rates, which was considered unlikely in previous studies. Our off-lattice cellular model provides an improvement over existing topological for studying the dynamics of proliferating epithelium.

NET-SYNTHESIS: a software for synthesis, inference and simplification of signal transduction networks.

UNLABELLED: We present a software for combined synthesis, inference and simplification of signal transduction networks. The main idea of our method lies in representing observed indirect causal relationships as network paths and using techniques from combinatorial optimization to find the sparsest graph consistent with all experimental observations. We illustrate the biological usability of our software by applying it to a previously published signal transduction network and by using it to synthesize and simplify a novel network corresponding to activation-induced cell death in large granular lymphocyte leukemia. AVAILABILITY: NET-SYNTHESIS is freely downloadable from http://www.cs.uic.edu/~dasgupta/network-synthesis/

A novel method for signal transduction network inference from indirect experimental evidence.

In this paper, we introduce a new method of combined synthesis and inference of biological signal transduction networks. A main idea of our method lies in representing observed causal relationships as network paths and using techniques from combinatorial optimization to find the sparsest graph consistent with all experimental observations. Our contributions are twofold: (a) We formalize our approach, study its computational complexity and prove new results for exact and approximate solutions of the computationally hard transitive reduction substep of the approach (Sections 2 and 5). (b) We validate the biological usability of our approach by successfully applying it to a previously published signal transduction network by Li et al. (2006) and show that our algorithm for the transitive reduction substep performs well on graphs with a structure similar to those observed in transcriptional regulatory and signal transduction networks.

Protein folding dynamics via quantification of kinematic energy landscape.

We study folding dynamics of proteinlike sequences on a square lattice using a physical move set that exhausts all possible conformational changes. By analytically solving the master equation, we follow the time-dependent probabilities of occupancy of all 802 075 conformations of 16 mers over 7 orders of time span. We find that (i) folding rates of these proteinlike sequences of the same length can differ by 4 orders of magnitude, (ii) folding rates of sequences of the same conformation can differ by a factor of 190, and (iii) parameters of the native structures, designability, and thermodynamic properties are weak predictors of the folding rates; rather, a basin analysis of the kinematic energy landscape defined by the moves can provide an excellent account of the observed folding rates.

Protein folding dynamics in lattice model with physical movement.

We study folding dynamics of protein-like sequences on square lattice by constructing a physically realizable move set that exhausts all possible conformational changes for a structure. By solving the master equation of 16-mer characterized by a 802,075times802,075 transition matrix, we monitor the time-dependent probabilities of occupancy of all conformations over 9-orders of time scale from the first kinetic move until reaching Boltzmann equilibrium. We find that folding rates of protein-like sequences adopting the same ground state conformation differ as much as 200 times, and parameters of the native structures, designability, and thermodynamic properties are weak predictors of the folding rates in our model systems. Instead, we show that properties of the kinetic energy landscape defined by the connection graph of physical moves can provide excellent account for observed folding rates. Without the approximation of macrostates, we show how transiently accumulating intermediate states can be identified by basin analysis of the kinetic energy landscape.