METAMorph (Model for Experimentation and Teaching in Artificial Morphogenesis)
Category Cross-Omics>Pathway Analysis/Gene Regulatory Networks/Tools and Cross-Omics>Agent-Based Modeling/Simulation/Tools
Abstract METAMorph (Model for Experimentation and Teaching in Artificial Morphogenesis) is an application that models the processes involved in morphogenesis, i.e. the growth of a multicellular organism from a single cell. Underlying the model are ‘genetic regulatory networks’ (GRNs) which exist within each cell.
The user is able to hand-design three-dimensional organisms by defining the genome, setting the properties of the various proteins expressed by the genes and specifying which proteins can trigger cell-level actions such as division or programmed death.
METAMorph is also an open source software platform for the experimental design of simulated ‘cellular development’ processes using genomes encoded as genetic regulatory networks (GRNs). METAMorph allows researchers to design GRNs by hand and to visualize the resulting morphological growth process. As such, it is a tool to aid researchers in developing an understanding of the expressive properties of GRNs.
Genetic Regulatory Networks (GRNs) --
GRNs model the interaction between genes, proteins, and the cellular environment. Each cell contains the same genome, but a potentially different set of active proteins, distributed across a fixed set of diffusion sites on the cell.
Each gene has a set of enhancer and inhibitor proteins, which increase or decrease its activation, respectively, and when activated, produces some protein, using some output function (which scales its protein output according to its activation) and some distribution function (which places produced proteins at the cell's diffusion sites).
Protein levels are also subject to attenuation (where protein levels decay) and diffusion (where proteins at diffusion sites move to other sites, in the same cell or on adjacent cells). Proteins can also be used as sensor mechanisms (where the cell produces them by itself under certain conditions), and as actuation mechanisms (where sufficient concentrations cause a cellular event, such as cell division, to occur).
In this way, genes form a network whereby the interaction of the elements they produce regulates further ‘gene expression’.
Variants of this basic abstract idea have been used in conjunction with an evolutionary process for a variety of applications, such as simulated ‘cellular development’, real-time robot control and for the control of groups of underwater robots.
GRNs are thus a ‘natural model’ for cellular development, and appear to possess desirable properties for acting as an evolutionary substrate (e.g., they show a strong tendency towards modularity).
However, evolved GRNs are difficult for humans to understand, and we do Not even have a qualitative measure of how difficult some natural structures are to achieve using them. METAMorph aims to facilitate the accumulation of such knowledge through experimentation.
METAMorph Model description --
1) Overview - The purpose of METAMorph (as stated above) is to model the processes involved in morphogenesis, albeit at a fairly high level of abstraction.
Multicellular artificial organisms are grown from a single cell. Within the cells exist genetic regulatory networks (GRNs), whereby a set of genes produce proteins, which in turn affect the expression of the genes. These proteins also trigger cell-level actions such as cell division or death.
2) Proteins - Proteins are defined by the following parameters:
- a) Name: a unique identifier for each protein;
- b) Type: internal or external;
- c) Decay constant; and d) Diffusion constant.
Internal proteins may only diffuse within a cell, whereas ‘external proteins’ pass through the cell ‘membrane’ and can hence be used for inter-cellular signaling. These two (2) types of protein differ considerably in their behavior.
3) Internal proteins - The ‘decay constant’ specifies the proportion of the protein that is lost due to decay at each time-step. So if the decay constant for a certain protein is 0.2, and its concentration is initially 1.0, then it will decrease to 0.8 after one time-step (assuming none is produced when the genome is expressed).
The concentrations of each protein at 12 ‘sites’ around the cell are stored; thus proteins may be unevenly distributed within the cytoplasm. The genome is expressed separately at each of these sub-cellular sites. The concentration of a protein at a given site can never exceed 100; this is taken to be the saturation level.
The diffusion constant specifies the proportion of the protein that diffuses to neighboring sites at each time-step. Due to the isospatial layout of the sites, each one has exactly four (4) equidistant neighbors between whom this diffused protein is equally shared. Note that as long as the concentration at the neighboring site is non-zero, this will be a two-way process with some diffusing back.
4) External proteins - Concentrations of external proteins are represented by isotropic 3D Gaussian distributions centred on the cell-site at which the protein originates. The diffusion constant specifies how much is added to the variance at each time-step in order to model the protein spreading out.
The decay constant determines how much the total concentration (equal to the integral of the Gaussian function) should be reduced at each time- step, in a similar manner to that of internal proteins. Note that the presence or absence of cells has No effect on the diffusion of external proteins, i.e. they pass straight through cells.
5) Genes - All the cells have the same genome comprising a number of genes. Each gene produces exactly one protein, although the same protein maybe produced by several genes. The amount produced by the gene depends on zero or more promoter sequences attached to that gene.
Each promoter sequence consists of a protein name and a weighting. If the weighting is positive then the presence of the corresponding protein enhances the expression of the gene, if negative it inhibits it.
6) Cells - Cells are, of course, the building blocks of morphogenesis. Cells are represented as spheres, all of the same radius. They occupy a position on an isospatial grid in three dimensions, meaning that each cell can potentially have 12 equidistant neighbors. The model begins with just one cell in the world (the ‘zygote’) for which the user may define the initial distribution of cytoplasmic proteins.
On each time-step, a cell first expresses its genome, producing various proteins. These proteins then diffuse, and subsequently decay. Finally, the concentrations of protein are checked to determine if any cell actions should be carried out (see below...).
Cells can perform a number of actions. An action is triggered when a specific protein's ‘mean concentration’ in the cell (over the 12 sites) exceeds a threshold value. In carrying out the action, an amount of the protein equal to the threshold is ‘consumed’.
Cells can perform the following actions:
- a) Cell division - When a cell divides it produces a daughter cell in the adjacent grid space in the direction of the mitotic spindle. The cells are placed with their centres 0.9 diameters apart, so that they appear to overlap slightly. Should the adjacent position already be occupied by a cell, nothing happens, although the trigger protein is still consumed in the attempt.
- When a cell splits, the internal proteins in its cytoplasm may be shared unequally between mother and daughter, if they were distributed unevenly to begin with. Note that the total amounts of protein in the two resulting cells are equal to that in the original one (minus the protein consumed in initiating the action); none is created or lost.
- b) Programmed cell death (apoptosis) - Quite simply, the cell vanishes. It is removed from the world leaving a vacant grid space. Note that any external proteins previously emitted by the cell will remain in the world until they decay away.
- c) Differentiation - Cells in the model can have various different types. The type of a cell has No effect on its functioning, but is visualized by its color. This feature is included to allow the investigation of how heterogeneous forms can potentially be created, e.g. in animals, cells specialize as skin cells, blood cells, neurons, etc. from an initially homogeneous embryo.
- Separate protein-thresholds are set for each type the cell can change to, although note that it will only change once per time-step, to the type whose threshold is exceeded by the greatest margin. When a new cell is created by division it inherits its mother's type, although obviously this may be switched later.
- d) Mitotic spindle movement - Each cell has a ‘mitotic spindle’ that points in one of the 12 grid directions at any given time (it is initialized to position 0 in the zygote, and then is inherited from mother to daughter cells). It defines the direction in which cell division takes place.
- Note that in ‘biological cells’ the mitotic spindle simply defines an axis along which division happens, with both cells moving outwards. Due to the model's grid representation of space, however, these spindles must be directional. This spindle may be moved ‘forwards’ or ‘backwards’ one step as a result of a protein threshold being reached.
- Alternatively, the spindle can be moved based on the distribution of protein around the cell. That is, the spindle is made to point in the direction of the sub-site where the concentration of a given protein is either highest or lowest.
- When this happens, the current orbit and direction of ‘forward’ and ‘backward’ are set arbitrarily. As with cell differentiation (see above...), at most one protein-relative ‘spindle movement’ (of either type) may occur per time-step. The one which exceeds its triggering threshold by the greatest margin will be chosen.
System Requirements
Web-based.
Manufacturer
- Institute of Perception, Action and Behaviour (IPAB)
- School of Informatics
- University of Edinburgh
- United Kingdom
Manufacturer Web Site METAMorph
Price Contact manufacturer.
G6G Abstract Number 20566
G6G Manufacturer Number 104173