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75-453: Aridity is the condition of a region that severely lacks available water, to the extent of hindering or preventing the growth and development of plant and animal life. Regions with arid climates tend to lack vegetation and are called xeric or desertic . Most arid climates are located in the subtropics ; these regions include parts of Africa , Asia , South America , North America , and Australia . The distribution of aridity at any time

150-416: A gene regulatory network . A typical gene regulatory network looks something like this: The nodes of this network can represent genes, proteins, mRNAs, protein/protein complexes or cellular processes. Nodes that are depicted as lying along vertical lines are associated with the cell/environment interfaces, while the others are free-floating and can diffuse . Edges between nodes represent interactions between

225-641: A big network into small blocks. Previous analysis found several types of motifs that appeared more often in gene regulatory networks than in randomly generated networks. As an example, one such motif is called feed-forward loops, which consist of three nodes. This motif is the most abundant among all possible motifs made up of three nodes, as is shown in the gene regulatory networks of fly, nematode, and human. The enriched motifs have been proposed to follow convergent evolution , suggesting they are "optimal designs" for certain regulatory purposes. For example, modeling shows that feed-forward loops are able to coordinate

300-465: A binary representation of the genes. Also, artificial neural networks omit using a hidden layer so that they can be interpreted, losing the ability to model higher order correlations in the data. Using a model that is not constrained to be interpretable, a more accurate model can be produced. Being able to predict gene expressions more accurately provides a way to explore how drugs affect a system of genes as well as for finding which genes are interrelated in

375-427: A bistable organelle at the apical end of each cell. The organelle consists of microtubules and microfilaments in mechanical opposition. It responds to local mechanical perturbations caused by morphogenetic movements. These then trigger traveling embryonic differentiation waves of contraction or expansion over presumptive tissues that determine cell type and is followed by cell differentiation. The cell state splitter

450-444: A cell divides, two cells result which, although they contain the same genome in full, can differ in which genes are turned on and making proteins. Sometimes a 'self-sustaining feedback loop' ensures that a cell maintains its identity and passes it on. Less understood is the mechanism of epigenetics by which chromatin modification may provide cellular memory by blocking or allowing transcription. A major feature of multicellular animals

525-462: A consequence of changes in cell adhesive and contractile properties. Following epithelial-mesenchymal transition, cells can migrate away from an epithelium and then associate with other similar cells in a new location. In plants, cellular morphogenesis is tightly linked to the chemical composition and the mechanical properties of the cell wall. During embryonic development, cells are restricted to different layers due to differential affinities. One of

600-663: A few highly connected nodes ( hubs ) and many poorly connected nodes nested within a hierarchical regulatory regime. Thus gene regulatory networks approximate a hierarchical scale free network topology. This is consistent with the view that most genes have limited pleiotropy and operate within regulatory modules . This structure is thought to evolve due to the preferential attachment of duplicated genes to more highly connected genes. Recent work has also shown that natural selection tends to favor networks with sparse connectivity. There are primarily two ways that networks can evolve, both of which can occur simultaneously. The first

675-481: A function which depends on the value of its regulators in previous time steps (in the Boolean network described below these are Boolean functions , typically AND, OR, and NOT). These functions have been interpreted as performing a kind of information processing within the cell, which determines cellular behavior. The basic drivers within cells are concentrations of some proteins, which determine both spatial (location within

750-557: A like-to-like manner: E-cadherin (found on many epithelial cells) binds preferentially to other E-cadherin molecules. Mesenchymal cells usually express other cadherin types such as N-cadherin. The extracellular matrix (ECM) is involved in keeping tissues separated, providing structural support or providing a structure for cells to migrate on. Collagen , laminin , and fibronectin are major ECM molecules that are secreted and assembled into sheets, fibers, and gels. Multisubunit transmembrane receptors called integrins are used to bind to

825-430: A mutation can be responsible for the cell proliferation that is seen in cancer . In parallel with this process of building structure, the gene cascade turns on genes that make structural proteins that give each cell the physical properties it needs. At one level, biological cells can be thought of as "partially mixed bags" of biological chemicals – in the discussion of gene regulatory networks, these chemicals are mostly

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900-415: A new fate, and may even generate other morphogens that signal back to the original cell. Over longer distances morphogens may use the active process of signal transduction . Such signalling controls embryogenesis , the building of a body plan from scratch through a series of sequential steps. They also control and maintain adult bodies through feedback processes, and the loss of such feedback because of

975-457: A process. This has been encouraged by the DREAM competition which promotes a competition for the best prediction algorithms. Some other recent work has used artificial neural networks with a hidden layer. There are three classes of multiple sclerosis: relapsing-remitting (RRMS), primary progressive (PPMS) and secondary progressive (SPMS). Gene regulatory network (GRN) plays a vital role to understand

1050-458: A set of time series observations. Recently it has been shown that ChIP-seq signal of histone modification are more correlated with transcription factor motifs at promoters in comparison to RNA level. Hence it is proposed that time-series histone modification ChIP-seq could provide more reliable inference of gene-regulatory networks in comparison to methods based on expression levels. Gene regulatory networks are generally thought to be made up of

1125-465: A short spurious signal, supporting adaptive evolution, but for non-idealized noise, a dynamics-based system of feed-forward regulation with different topology was instead favored. Regulatory networks allow bacteria to adapt to almost every environmental niche on earth. A network of interactions among diverse types of molecules including DNA, RNA, proteins and metabolites, is utilised by the bacteria to achieve regulation of gene expression. In bacteria,

1200-468: A single step, it was proposed to model these reactions as single step multiple delayed reactions in order to account for the time it takes for the entire process to be complete. From here, a set of reactions were proposed that allow generating GRNs. These are then simulated using a modified version of the Gillespie algorithm, that can simulate multiple time delayed reactions (chemical reactions where each of

1275-419: A specific protein (or set of proteins). In some cases this protein will be structural , and will accumulate at the cell membrane or within the cell to give it particular structural properties. In other cases the protein will be an enzyme , i.e., a micro-machine that catalyses a certain reaction, such as the breakdown of a food source or toxin. Some proteins though serve only to activate other genes, and these are

1350-408: A technique which has been highly optimized in recent years due to its use in machine learning . This model was limited to the generation of pictures, and is thus bi-dimensional. A similar model to the one described above was subsequently extended to generate three-dimensional structures, and was demonstrated in the video game Minecraft , whose block-based nature made it particularly expedient for

1425-502: A tissue level, ignoring the means of control, morphogenesis arises because of cellular proliferation and motility. Morphogenesis also involves changes in the cellular structure or how cells interact in tissues. These changes can result in tissue elongation, thinning, folding, invasion or separation of one tissue into distinct layers. The latter case is often referred as cell sorting . Cell "sorting out" consists of cells moving so as to sort into clusters that maximize contact between cells of

1500-445: A transcription factor may bind to a cis-regulatory element . Such variation in strength of network edges has been shown to underlie between species variation in vulva cell fate patterning of Caenorhabditis worms. Another widely cited characteristic of gene regulatory network is their abundance of certain repetitive sub-networks known as network motifs . Network motifs can be regarded as repetitive topological patterns when dividing

1575-437: A yeast cell, finding itself in a sugar solution, will turn on genes to make enzymes that process the sugar to alcohol. This process, which we associate with wine-making, is how the yeast cell makes its living, gaining energy to multiply, which under normal circumstances would enhance its survival prospects. In multicellular animals the same principle has been put in the service of gene cascades that control body-shape. Each time

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1650-471: Is a stub . You can help Misplaced Pages by expanding it . Morphogenesis The process controls the organized spatial distribution of cells during the embryonic development of an organism . Morphogenesis can take place also in a mature organism, such as in the normal maintenance of tissue by stem cells or in regeneration of tissues after damage. Cancer is an example of highly abnormal and pathological tissue morphogenesis. Morphogenesis also describes

1725-522: Is called dysmorphogenesis . Some of the earliest ideas and mathematical descriptions on how physical processes and constraints affect biological growth, and hence natural patterns such as the spirals of phyllotaxis , were written by D'Arcy Wentworth Thompson in his 1917 book On Growth and Form and Alan Turing in his The Chemical Basis of Morphogenesis (1952). Where Thompson explained animal body shapes as being created by varying rates of growth in different directions, for instance to create

1800-405: Is created from a graph with the desired topology, imposing in-degree and out-degree distributions. Gene promoter activities are affected by other genes expression products that act as inputs, in the form of monomers or combined into multimers and set as direct or indirect. Next, each direct input is assigned to an operator site and different transcription factors can be allowed, or not, to compete for

1875-547: Is driven by a stochastic simulation algorithm (SSA) able to deal with multiple time delayed events. The time delays can be drawn from several distributions and the reaction rates from complex functions or from physical parameters. SGNSim can generate ensembles of GRNs within a set of user-defined parameters, such as topology. It can also be used to model specific GRNs and systems of chemical reactions. Genetic perturbations such as gene deletions, gene over-expression, insertions, frame shift mutations can also be modeled as well. The GRN

1950-453: Is formally closer to a higher order recurrent neural network . The same model has also been used to mimic the evolution of cellular differentiation and even multicellular morphogenesis . Experimental results have demonstrated that gene expression is a stochastic process. Thus, many authors are now using the stochastic formalism, after the work by Arkin et al. Works on single gene expression and small synthetic genetic networks, such as

2025-547: Is largely the result of the general circulation of the atmosphere . The latter does change significantly over time through climate change . For example, temperature increase by 1.5–2.1 percent across the Nile Basin over the next 30–40 years could change the region from semi-arid to arid, significantly reducing the land usable for agriculture . In addition, changes in land use can increase demands on soil water and thereby increase aridity. This climatology -related article

2100-517: Is that network topology can be changed by the addition or subtraction of nodes (genes) or parts of the network (modules) may be expressed in different contexts. The Drosophila Hippo signaling pathway provides a good example. The Hippo signaling pathway controls both mitotic growth and post-mitotic cellular differentiation. Recently it was found that the network the Hippo signaling pathway operates in differs between these two functions which in turn changes

2175-424: Is the so-called French flag model , developed in the sixties. Improvements in computer performance in the twenty-first century enabled the simulation of relatively complex morphogenesis models. In 2020, such a model was proposed where cell growth and differentiation is that of a cellular automaton with parametrized rules. As the rules' parameters are differentiable, they can be trained with gradient descent ,

2250-405: Is the use of morphogen gradients, which in effect provide a positioning system that tells a cell where in the body it is, and hence what sort of cell to become. A gene that is turned on in one cell may make a product that leaves the cell and diffuses through adjacent cells, entering them and turning on genes only when it is present above a certain threshold level. These cells are thus induced into

2325-460: The arabinose utilization systems of E.coli delays the activation of arabinose catabolism operon and transporters, potentially avoiding unnecessary metabolic transition due to temporary fluctuations in upstream signaling pathways. Similarly in the Wnt signaling pathway of Xenopus , the feed-forward loop acts as a fold-change detector that responses to the fold change, rather than the absolute change, in

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2400-503: The bacteriophage (phage) T4 virion , the morphogenetic proteins encoded by the phage genes interact with each other in a characteristic sequence. Maintaining an appropriate balance in the amounts of each of these proteins produced during viral infection appears to be critical for normal phage T4 morphogenesis. Phage T4 encoded proteins that determine virion structure include major structural components, minor structural components and non-structural proteins that catalyze specific steps in

2475-472: The fixed point of the system: for all j {\displaystyle j} , one obtains (possibly several) concentration profiles of proteins and mRNAs that are theoretically sustainable (though not necessarily stable ). Steady states of kinetic equations thus correspond to potential cell types, and oscillatory solutions to the above equation to naturally cyclic cell types. Mathematical stability of these attractors can usually be characterized by

2550-442: The messenger RNAs (mRNAs) and proteins that arise from gene expression. These mRNA and proteins interact with each other with various degrees of specificity. Some diffuse around the cell. Others are bound to cell membranes , interacting with molecules in the environment. Still others pass through cell membranes and mediate long range signals to other cells in a multi-cellular organism. These molecules and their interactions comprise

2625-412: The spiral shell of a snail , Turing correctly predicted a mechanism of morphogenesis, the diffusion of two different chemical signals, one activating and one deactivating growth, to set up patterns of development, decades before the formation of such patterns was observed. The fuller understanding of the mechanisms involved in actual organisms required the discovery of the structure of DNA in 1953, and

2700-435: The transcription factors that are the main players in regulatory networks or cascades. By binding to the promoter region at the start of other genes they turn them on, initiating the production of another protein, and so on. Some transcription factors are inhibitory. In single-celled organisms, regulatory networks respond to the external environment, optimising the cell at a given time for survival in this environment. Thus

2775-480: The Boolean model. Formally most of these approaches are similar to an artificial neural network , as inputs to a node are summed up and the result serves as input to a sigmoid function , e.g., but proteins do often control gene expression in a synergistic, i.e. non-linear, way. However, there is now a continuous network model that allows grouping of inputs to a node thus realizing another level of regulation. This model

2850-615: The ECM. Integrins bind extracellularly to fibronectin, laminin, or other ECM components, and intracellularly to microfilament -binding proteins α-actinin and talin to link the cytoskeleton with the outside. Integrins also serve as receptors to trigger signal transduction cascades when binding to the ECM. A well-studied example of morphogenesis that involves ECM is mammary gland ductal branching. Tissues can change their shape and separate into distinct layers via cell contractility. Just as in muscle cells, myosin can contract different parts of

2925-567: The alveoli. Branching morphogenesis is also evident in the ductal formation of the mammary gland . Primitive duct formation begins in development , but the branching formation of the duct system begins later in response to estrogen during puberty and is further refined in line with mammary gland development. Cancer can result from disruption of normal morphogenesis, including both tumor formation and tumor metastasis . Mitochondrial dysfunction can result in increased cancer risk due to disturbed morphogen signaling. During assembly of

3000-443: The behavior of the Hippo signaling pathway. This suggests that the Hippo signaling pathway operates as a conserved regulatory module that can be used for multiple functions depending on context. Thus, changing network topology can allow a conserved module to serve multiple functions and alter the final output of the network. The second way networks can evolve is by changing the strength of interactions between nodes, such as how strongly

3075-675: The behavior of the system being modeled, and in some cases generate predictions corresponding with experimental observations. In some other cases, models have proven to make accurate novel predictions, which can be tested experimentally, thus suggesting new approaches to explore in an experiment that sometimes wouldn't be considered in the design of the protocol of an experimental laboratory. Modeling techniques include differential equations (ODEs), Boolean networks, Petri nets , Bayesian networks , graphical Gaussian network models , Stochastic , and Process Calculi . Conversely, techniques have been proposed for generating models of GRNs that best explain

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3150-473: The cell or tissue) and temporal (cell cycle or developmental stage) coordinates of the cell, as a kind of "cellular memory". The gene networks are only beginning to be understood, and it is a next step for biology to attempt to deduce the functions for each gene "node", to help understand the behavior of the system in increasing levels of complexity, from gene to signaling pathway, cell or tissue level. Mathematical models of GRNs have been developed to capture

3225-416: The change in node A (in terms of concentration and activity) and the expression dynamics of node C, creating different input-output behaviors. The galactose utilization system of E. coli contains a feed-forward loop which accelerates the activation of galactose utilization operon galETK , potentially facilitating the metabolic transition to galactose when glucose is depleted. The feed-forward loop in

3300-426: The concentration of one leading to an increase in the other, inhibitory (represented with filled circles, blunt arrows or the minus sign), with an increase in one leading to a decrease in the other, or dual, when depending on the circumstances the regulator can activate or inhibit the target node. The nodes can regulate themselves directly or indirectly, creating feedback loops, which form cyclic chains of dependencies in

3375-491: The constituent parts. Suppose that our regulatory network has N {\displaystyle N} nodes, and let S 1 ( t ) , S 2 ( t ) , … , S N ( t ) {\displaystyle S_{1}(t),S_{2}(t),\ldots ,S_{N}(t)} represent the concentrations of the N {\displaystyle N} corresponding substances at time t {\displaystyle t} . Then

3450-455: The creation of body structures, which in turn is central to evolutionary developmental biology (evo-devo). The regulator can be DNA , RNA , protein or any combination of two or more of these three that form a complex, such as a specific sequence of DNA and a transcription factor to activate that sequence. The interaction can be direct or indirect (through transcribed RNA or translated protein). In general, each mRNA molecule goes on to make

3525-421: The cytoplasm to change its shape or structure. Myosin-driven contractility in embryonic tissue morphogenesis is seen during the separation of germ layers in the model organisms Caenorhabditis elegans , Drosophila and zebrafish . There are often periodic pulses of contraction in embryonic morphogenesis. A model called the cell state splitter involves alternating cell contraction and expansion, initiated by

3600-431: The design of synthetic systems. Other work has focused on predicting the gene expression levels in a gene regulatory network. The approaches used to model gene regulatory networks have been constrained to be interpretable and, as a result, are generally simplified versions of the network. For example, Boolean networks have been used due to their simplicity and ability to handle noisy data but lose data information by having

3675-436: The development of molecular biology and biochemistry . Several types of molecules are important in morphogenesis. Morphogens are soluble molecules that can diffuse and carry signals that control cell differentiation via concentration gradients. Morphogens typically act through binding to specific protein receptors . An important class of molecules involved in morphogenesis are transcription factor proteins that determine

3750-407: The development of unicellular life forms that do not have an embryonic stage in their life cycle. Morphogenesis is essential for the evolution of new forms. Morphogenesis is a mechanical process involving forces that generate mechanical stress, strain, and movement of cells, and can be induced by genetic programs according to the spatial patterning of cells within tissues. Abnormal morphogenesis

3825-402: The equations to short-term biological events. For a more mathematical discussion, see the articles on nonlinearity , dynamical systems , bifurcation theory , and chaos theory . The following example illustrates how a Boolean network can model a GRN together with its gene products (the outputs) and the substances from the environment that affect it (the inputs). Stuart Kauffman was amongst

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3900-622: The evolution of gene regulatory networks by randomly rewiring nodes may suggest that the enrichment of feed-forward loops is a side-effect of evolution. In another model of gene regulator networks evolution, the ratio of the frequencies of gene duplication and gene deletion show great influence on network topology: certain ratios lead to the enrichment of feed-forward loops and create networks that show features of hierarchical scale free networks. De novo evolution of coherent type 1 feed-forward loops has been demonstrated computationally in response to selection for their hypothesized function of filtering out

3975-865: The fate of cells by interacting with DNA . These can be coded for by master regulatory genes , and either activate or deactivate the transcription of other genes; in turn, these secondary gene products can regulate the expression of still other genes in a regulatory cascade of gene regulatory networks . At the end of this cascade are classes of molecules that control cellular behaviors such as cell migration , or, more generally, their properties, such as cell adhesion or cell contractility. For example, during gastrulation , clumps of stem cells switch off their cell-to-cell adhesion, become migratory, and take up new positions within an embryo where they again activate specific cell adhesion proteins and form new tissues and organs. Developmental signaling pathways implicated in morphogenesis include Wnt , Hedgehog , and ephrins . At

4050-411: The first biologists to use the metaphor of Boolean networks to model genetic regulatory networks. The validity of the model can be tested by comparing simulation results with time series observations. A partial validation of a Boolean network model can also come from testing the predicted existence of a yet unknown regulatory connection between two particular transcription factors that each are nodes of

4125-424: The functional forms of the f j {\displaystyle f_{j}} are usually chosen as low-order polynomials or Hill functions that serve as an ansatz for the real molecular dynamics. Such models are then studied using the mathematics of nonlinear dynamics . System-specific information, like reaction rate constants and sensitivities, are encoded as constant parameters. By solving for

4200-510: The genetic toggle switch of Tim Gardner and Jim Collins , provided additional experimental data on the phenotypic variability and the stochastic nature of gene expression. The first versions of stochastic models of gene expression involved only instantaneous reactions and were driven by the Gillespie algorithm . Since some processes, such as gene transcription, involve many reactions and could not be correctly modeled as an instantaneous reaction in

4275-527: The level of β-catenin, potentially increasing the resistance to fluctuations in β-catenin levels. Following the convergent evolution hypothesis, the enrichment of feed-forward loops would be an adaptation for fast response and noise resistance. A recent research found that yeast grown in an environment of constant glucose developed mutations in glucose signaling pathways and growth regulation pathway, suggesting regulatory components responding to environmental changes are dispensable under constant environment. On

4350-399: The manual curation of GRNs, some recent efforts try to use text mining , curated databases, network inference from massive data, model checking and other information extraction technologies for this purpose. Genes can be viewed as nodes in the network, with input being proteins such as transcription factors , and outputs being the level of gene expression . The value of the node depends on

4425-411: The model. Continuous network models of GRNs are an extension of the Boolean networks described above. Nodes still represent genes and connections between them regulatory influences on gene expression. Genes in biological systems display a continuous range of activity levels and it has been argued that using a continuous representation captures several properties of gene regulatory networks not present in

4500-448: The morphogenesis sequence. Phage T4 morphogenesis is divided into three independent pathways: the head, the tail and the long tail fibres as detailed by Yap and Rossman. An approach to model morphogenesis in computer science or mathematics can be traced to Alan Turing 's 1952 paper, "The chemical basis of morphogenesis", a model now known as the Turing pattern . Another famous model

4575-430: The nodes, that can correspond to individual molecular reactions between DNA, mRNA, miRNA, proteins or molecular processes through which the products of one gene affect those of another, though the lack of experimentally obtained information often implies that some reactions are not modeled at such a fine level of detail. These interactions can be inductive (usually represented by arrowheads or the + sign), with an increase in

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4650-408: The other hand, some researchers hypothesize that the enrichment of network motifs is non-adaptive. In other words, gene regulatory networks can evolve to a similar structure without the specific selection on the proposed input-output behavior. Support for this hypothesis often comes from computational simulations. For example, fluctuations in the abundance of feed-forward loops in a model that simulates

4725-559: The principal function of regulatory networks is to control the response to environmental changes, for example nutritional status and environmental stress. A complex organization of networks permits the microorganism to coordinate and integrate multiple environmental signals. One example stress is when the environment suddenly becomes poor of nutrients. This triggers a complex adaptation process in bacteria , such as E. coli . After this environmental change, thousands of genes change expression level. However, these changes are predictable from

4800-474: The products is provided a time delay that determines when will it be released in the system as a "finished product"). For example, basic transcription of a gene can be represented by the following single-step reaction (RNAP is the RNA polymerase, RBS is the RNA ribosome binding site, and Pro   i is the promoter region of gene i ): Furthermore, there seems to be a trade-off between the noise in gene expression,

4875-644: The same operator site, while indirect inputs are given a target. Finally, a function is assigned to each gene, defining the gene's response to a combination of transcription factors (promoter state). The transfer functions (that is, how genes respond to a combination of inputs) can be assigned to each combination of promoter states as desired. In other recent work, multiscale models of gene regulatory networks have been developed that focus on synthetic biology applications. Simulations have been used that model all biomolecular interactions in transcription, translation, regulation, and induction of gene regulatory networks, guiding

4950-412: The same type. The ability of cells to do this has been proposed to arise from differential cell adhesion by Malcolm Steinberg through his differential adhesion hypothesis . Tissue separation can also occur via more dramatic cellular differentiation events during which epithelial cells become mesenchymal (see Epithelial–mesenchymal transition ). Mesenchymal cells typically leave the epithelial tissue as

5025-423: The sign of higher derivatives at critical points, and then correspond to biochemical stability of the concentration profile. Critical points and bifurcations in the equations correspond to critical cell states in which small state or parameter perturbations could switch the system between one of several stable differentiation fates. Trajectories correspond to the unfolding of biological pathways and transients of

5100-404: The simulation of 3D cellular automatons. Gene regulatory network A gene (or genetic ) regulatory network ( GRN ) is a collection of molecular regulators that interact with each other and with other substances in the cell to govern the gene expression levels of mRNA and proteins which, in turn, determine the function of the cell. GRN also play a central role in morphogenesis ,

5175-494: The speed with which genes can switch, and the metabolic cost associated their functioning. More specifically, for any given level of metabolic cost, there is an optimal trade-off between noise and processing speed and increasing the metabolic cost leads to better speed-noise trade-offs. A recent work proposed a simulator (SGNSim, Stochastic Gene Networks Simulator ), that can model GRNs where transcription and translation are modeled as multiple time delayed events and its dynamics

5250-594: The strongest adhesion move to the center of a mixed aggregates of cells. Moreover, cell-cell adhesion is often modulated by cell contractility, which can exert forces on the cell-cell contacts so that two cell populations with equal levels of the same adhesion molecule can sort out. The molecules responsible for adhesion are called cell adhesion molecules (CAMs). Several types of cell adhesion molecules are known and one major class of these molecules are cadherins . There are dozens of different cadherins that are expressed on different cell types. Cadherins bind to other cadherins in

5325-544: The temporal evolution of the system can be described approximately by where the functions f j {\displaystyle f_{j}} express the dependence of S j {\displaystyle S_{j}} on the concentrations of other substances present in the cell. The functions f j {\displaystyle f_{j}} are ultimately derived from basic principles of chemical kinetics or simple expressions derived from these e.g. Michaelis–Menten enzymatic kinetics. Hence,

5400-413: The topological network. The network structure is an abstraction of the system's molecular or chemical dynamics, describing the manifold ways in which one substance affects all the others to which it is connected. In practice, such GRNs are inferred from the biological literature on a given system and represent a distillation of the collective knowledge about a set of related biochemical reactions. To speed up

5475-462: The topology and logic of the gene network that is reported in RegulonDB . Specifically, on average, the response strength of a gene was predictable from the difference between the numbers of activating and repressing input transcription factors of that gene. It is common to model such a network with a set of coupled ordinary differential equations (ODEs) or SDEs , describing the reaction kinetics of

5550-428: The ways this can occur is when cells share the same cell-to- cell adhesion molecules . For instance, homotypic cell adhesion can maintain boundaries between groups of cells that have different adhesion molecules. Furthermore, cells can sort based upon differences in adhesion between the cells, so even two populations of cells with different levels of the same adhesion molecule can sort out. In cell culture cells that have

5625-431: Was first proposed to explain neural plate morphogenesis during gastrulation of the axolotl and the model was later generalized to all of morphogenesis. In the development of the lung a bronchus branches into bronchioles forming the respiratory tree . The branching is a result of the tip of each bronchiolar tube bifurcating, and the process of branching morphogenesis forms the bronchi, bronchioles, and ultimately

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