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
Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, protein or non-coding RNA, and ultimately affect a phenotype, as the final effect. The ...
levels of
mRNA
In molecular biology, messenger ribonucleic acid (mRNA) is a single-stranded molecule of RNA that corresponds to the genetic sequence of a gene, and is read by a ribosome in the process of Protein biosynthesis, synthesizing a protein.
mRNA is ...
and proteins which, in turn, determine the function of the cell. GRN also play a central role in
morphogenesis
Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of devel ...
, the creation of body structures, which in turn is central to
evolutionary developmental biology
Evolutionary developmental biology (informally, evo-devo) is a field of biological research that compares the developmental processes of different organisms to infer how developmental processes evolved.
The field grew from 19th-century beginni ...
(evo-devo).
The regulator can be
DNA,
RNA
Ribonucleic acid (RNA) is a polymeric molecule essential in various biological roles in coding, decoding, regulation and expression of genes. RNA and deoxyribonucleic acid ( DNA) are nucleic acids. Along with lipids, proteins, and carbohydra ...
,
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
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 a specific protein (or set of proteins). In some cases this protein will be
structural
A structure is an arrangement and organization of interrelated elements in a material object or system, or the object or system so organized. Material structures include man-made objects such as buildings and machines and natural objects such a ...
, 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
Enzymes () are proteins that act as biological catalysts by accelerating chemical reactions. The molecules upon which enzymes may act are called substrates, and the enzyme converts the substrates into different molecules known as products. A ...
, 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 the
transcription factors
In molecular biology, a transcription factor (TF) (or sequence-specific DNA-binding factor) is a protein that controls the rate of transcription of genetic information from DNA to messenger RNA, by binding to a specific DNA sequence. The func ...
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 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 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
In biology, epigenetics is the study of stable phenotypic changes (known as ''marks'') that do not involve alterations in the DNA sequence. The Greek prefix '' epi-'' ( "over, outside of, around") in ''epigenetics'' implies features that are "o ...
by which
chromatin
Chromatin is a complex of DNA and protein found in eukaryotic cells. The primary function is to package long DNA molecules into more compact, denser structures. This prevents the strands from becoming tangled and also plays important roles in r ...
modification may provide cellular memory by blocking or allowing transcription. A major feature of multicellular animals is the use of
morphogen
A morphogen is a substance whose non-uniform distribution governs the pattern of tissue development in the process of morphogenesis or pattern formation, one of the core processes of developmental biology, establishing positions of the various ...
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 a new fate, and may even generate other
morphogens
A morphogen is a substance whose non-uniform distribution governs the pattern of tissue development in the process of morphogenesis or pattern formation, one of the core processes of developmental biology, establishing positions of the various ...
that signal back to the original cell. Over longer distances morphogens may use the active process of
signal transduction
Signal transduction is the process by which a chemical or physical signal is transmitted through a cell as a series of molecular events, most commonly protein phosphorylation catalyzed by protein kinases, which ultimately results in a cellula ...
. Such signalling controls
embryogenesis
An embryo is an initial stage of development of a multicellular organism. In organisms that reproduce sexually, embryonic development is the part of the life cycle that begins just after fertilization of the female egg cell by the male sperm ...
, the building of a
body plan
A body plan, ( ), or ground plan is a set of morphological features common to many members of a phylum of animals. The vertebrates share one body plan, while invertebrates have many.
This term, usually applied to animals, envisages a "blueprin ...
from scratch through a series of sequential steps. They also control and maintain adult bodies through
feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled ...
processes, and the loss of such feedback because of a mutation can be responsible for the cell proliferation that is seen in
cancer
Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body. These contrast with benign tumors, which do not spread. Possible signs and symptoms include a lump, abnormal b ...
. In parallel with this process of building structure, the gene cascade turns on genes that make
structural protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respond ...
s that give each cell the physical properties it needs.
Overview
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 the
messenger RNA
In molecular biology, messenger ribonucleic acid (mRNA) is a single-stranded molecule of RNA that corresponds to the genetic sequence of a gene, and is read by a ribosome in the process of synthesizing a protein.
mRNA is created during the p ...
s (mRNAs) and
protein
Proteins are large biomolecules and macromolecules that comprise one or more long chains of amino acid residues. Proteins perform a vast array of functions within organisms, including catalysing metabolic reactions, DNA replication, respo ...
s 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 membrane
The cell membrane (also known as the plasma membrane (PM) or cytoplasmic membrane, and historically referred to as the plasmalemma) is a biological membrane that separates and protects the interior of all cells from the outside environment ( ...
s, 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 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
Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical p ...
. Edges between nodes represent interactions between 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 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 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 the manual curation of GRNs, some recent efforts try to use
text mining
Text mining, also referred to as ''text data mining'', similar to text analytics, is the process of deriving high-quality information from text. It involves "the discovery by computer of new, previously unknown information, by automatically extract ...
, 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 factor
In molecular biology, a transcription factor (TF) (or sequence-specific DNA-binding factor) is a protein that controls the rate of transcription of genetic information from DNA to messenger RNA, by binding to a specific DNA sequence. The fu ...
s, and outputs being the level of
gene expression
Gene expression is the process by which information from a gene is used in the synthesis of a functional gene product that enables it to produce end products, protein or non-coding RNA, and ultimately affect a phenotype, as the final effect. The ...
. The value of the node depends on a function which depends on the value of its regulators in previous time steps (in the Boolean network described below these are
Boolean functions
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...
, typically AND, OR, and NOT). These functions have been interpreted as performing a kind of
information processing
Information processing is the change (processing) of information in any manner detectable by an observer. As such, it is a process that ''describes'' everything that happens (changes) in the universe, from the falling of a rock (a change in posit ...
within the cell, which determines cellular behavior. The basic drivers within cells are concentrations of some proteins, which determine both spatial (location within 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 model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
s of GRNs have been developed to capture 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 equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s (ODEs),
Boolean network
A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the stat ...
s,
Petri net
A Petri net, also known as a place/transition (PT) net, is one of several mathematical modeling languages for the description of distributed systems. It is a class of discrete event dynamic system. A Petri net is a directed bipartite graph that ...
s,
Bayesian network
A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). Bay ...
s, graphical
Gaussian network model
The Gaussian network model (GNM) is a representation of a biological macromolecule as an elastic mass-and-spring network to study, understand, and characterize the mechanical aspects of its long-time large-scale dynamics. The model has a wide ra ...
s,
Stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
, and
Process Calculi
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems. Process calculi provide a tool for the high-level description of interactions, communications, and ...
. Conversely, techniques have been proposed for generating models of GRNs that best explain a set of
time series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Exa ...
observations. Recently it has been shown that
ChIP-seq
ChIP-sequencing, also known as ChIP-seq, is a method used to analyze protein interactions with DNA. ChIP-seq combines chromatin immunoprecipitation (ChIP) with Massively parallel signature sequencing, massively parallel DNA sequencing to identify t ...
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.
Structure and evolution
Global feature
Gene regulatory networks are generally thought to be made up of a few highly connected
node
In general, a node is a localized swelling (a "knot") or a point of intersection (a vertex).
Node may refer to:
In mathematics
*Vertex (graph theory), a vertex in a mathematical graph
*Vertex (geometry), a point where two or more curves, lines, ...
s (
hubs) and many poorly connected nodes nested within a hierarchical regulatory regime. Thus gene regulatory networks approximate a
hierarchical
A hierarchy (from Greek: , from , 'president of sacred rites') is an arrangement of items (objects, names, values, categories, etc.) that are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important ...
scale free network
A scale-free network is a network whose degree distribution follows a power law, at least asymptotically. That is, the fraction ''P''(''k'') of nodes in the network having ''k'' connections to other nodes goes for large values of ''k'' as
:
P(k) ...
topology.
This is consistent with the view that most genes have limited
pleiotropy
Pleiotropy (from Greek , 'more', and , 'way') occurs when one gene influences two or more seemingly unrelated phenotypic traits. Such a gene that exhibits multiple phenotypic expression is called a pleiotropic gene. Mutation in a pleiotropic g ...
and operate within regulatory
modules
Broadly speaking, modularity is the degree to which a system's components may be separated and recombined, often with the benefit of flexibility and variety in use. The concept of modularity is used primarily to reduce complexity by breaking a sy ...
. This structure is thought to evolve due to the
preferential attachment
A preferential attachment process is any of a class of processes in which some quantity, typically some form of wealth or credit, is distributed among a number of individuals or objects according to how much they already have, so that those who ...
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 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
''Drosophila'' () is a genus of flies, belonging to the family Drosophilidae, whose members are often called "small fruit flies" or (less frequently) pomace flies, vinegar flies, or wine flies, a reference to the characteristic of many species ...
''
Hippo signaling pathway
The Hippo signaling pathway, also known as the Salvador-Warts-Hippo (SWH) pathway, is a signaling pathway that controls organ size in animals through the regulation of cell proliferation and apoptosis. The pathway takes its name from one of its k ...
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 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 a transcription factor may bind to a
cis-regulatory element
''Cis''-regulatory elements (CREs) or ''Cis''-regulatory modules (CRMs) are regions of non-coding DNA which regulate the transcription of neighboring genes. CREs are vital components of genetic regulatory networks, which in turn control morphoge ...
. Such variation in strength of network edges has been shown to underlie between species variation in vulva cell fate patterning of ''
Caenorhabditis
''Caenorhabditis'' is a genus of nematodes which live in bacteria-rich environments like compost piles, decaying dead animals and rotting fruit. The name comes from Greek: caeno- (καινός (caenos) = new, recent); rhabditis = rod-like (ῥά ...
'' worms.
Local feature
![Feed-forward motif](https://upload.wikimedia.org/wikipedia/commons/f/f2/Feed-forward_motif.GIF)
Another widely cited characteristic of gene regulatory network is their abundance of certain repetitive sub-networks known as
network motif
Network motifs are recurrent and statistically significant Subgraph (graph theory), subgraphs or patterns of a larger complex network, graph. All networks, including biological networks, social networks, technological networks (e.g., computer netw ...
s. Network motifs can be regarded as repetitive topological patterns when dividing 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 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
Convergent evolution is the independent evolution of similar features in species of different periods or epochs in time. Convergent evolution creates analogous structures that have similar form or function but were not present in the last com ...
, suggesting they are "optimal designs" for certain regulatory purposes. For example, modeling shows that feed-forward loops are able to coordinate 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
Galactose (, '' galacto-'' + '' -ose'', "milk sugar"), sometimes abbreviated Gal, is a monosaccharide sugar that is about as sweet as glucose, and about 65% as sweet as sucrose. It is an aldohexose and a C-4 epimer of glucose. A galactose molec ...
utilization system of ''
E. coli
''Escherichia coli'' (),Wells, J. C. (2000) Longman Pronunciation Dictionary. Harlow ngland Pearson Education Ltd. also known as ''E. coli'' (), is a Gram-negative, facultative anaerobic, rod-shaped, coliform bacterium of the genus ''Escher ...
'' contains a feed-forward loop which accelerates the activation of galactose utilization
operon
In genetics, an operon is a functioning unit of DNA containing a cluster of genes under the control of a single promoter. The genes are transcribed together into an mRNA strand and either translated together in the cytoplasm, or undergo splic ...
''galETK'', potentially facilitating the metabolic transition to galactose when glucose is depleted. The feed-forward loop in the
arabinose
Arabinose is an aldopentose – a monosaccharide containing five carbon atoms, and including an aldehyde (CHO) functional group.
For biosynthetic reasons, most saccharides are almost always more abundant in nature as the "D"-form, or structurally ...
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
''Xenopus'' () (Gk., ξενος, ''xenos''=strange, πους, ''pous''=foot, commonly known as the clawed frog) is a genus of highly aquatic frogs native to sub-Saharan Africa. Twenty species are currently described within it. The two best-known ...
'', the feed-forward loop acts as a fold-change detector that responses to the fold change, rather than the absolute change, in 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
In biology, adaptation has three related meanings. Firstly, it is the dynamic evolutionary process of natural selection that fits organisms to their environment, enhancing their evolutionary fitness. Secondly, it is a state reached by the po ...
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 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 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 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.
Bacterial regulatory networks
Regulatory networks allow
bacteria
Bacteria (; singular: bacterium) are ubiquitous, mostly free-living organisms often consisting of one biological cell. They constitute a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria were among ...
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, 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
Bacteria (; singular: bacterium) are ubiquitous, mostly free-living organisms often consisting of one biological cell. They constitute a large domain of prokaryotic microorganisms. Typically a few micrometres in length, bacteria were among ...
, such as ''
E. coli
''Escherichia coli'' (),Wells, J. C. (2000) Longman Pronunciation Dictionary. Harlow ngland Pearson Education Ltd. also known as ''E. coli'' (), is a Gram-negative, facultative anaerobic, rod-shaped, coliform bacterium of the genus ''Escher ...
.'' After this environmental change, thousands of genes change expression level. However, these changes are predictable from the topology and logic of the gene network
that is reported in
RegulonDB RegulonDB is a database of the regulatory network of gene expression in ''Escherichia coli'' K-12.{{Cite journal, last=Gama-Castro, first=Socorro, last2=Salgado, first2=Heladia, last3=Santos-Zavaleta, first3=Alberto, last4=Ledezma-Tejeida, first4 ...
. 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.
Modelling
Coupled ordinary differential equations
It is common to model such a network with a set of coupled
ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast w ...
s (ODEs) or
SDEs, describing the reaction kinetics of the constituent parts. Suppose that our regulatory network has
nodes, and let
represent the concentrations of the
corresponding substances at time
. Then the temporal evolution of the system can be described approximately by
:
where the functions
express the dependence of
on the concentrations of other substances present in the cell. The functions
are ultimately derived from basic
principles of chemical kinetics or simple expressions derived from these e.g.
Michaelis–Menten enzymatic kinetics. Hence, the functional forms of the
are usually chosen as low-order
polynomials
In mathematics, a polynomial is an expression (mathematics), expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtrac ...
or
Hill functions that serve as an
ansatz
In physics and mathematics, an ansatz (; , meaning: "initial placement of a tool at a work piece", plural Ansätze ; ) is an educated guess or an additional assumption made to help solve a problem, and which may later be verified to be part of the ...
for the real molecular dynamics. Such models are then studied using the mathematics of
nonlinear dynamics
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
. System-specific information, like
reaction rate
The reaction rate or rate of reaction is the speed at which a chemical reaction takes place, defined as proportional to the increase in the concentration of a product per unit time and to the decrease in the concentration of a reactant per unit ...
constants and sensitivities, are encoded as constant parameters.
By solving for the
fixed point of the system:
:
for all
, one obtains (possibly several) concentration profiles of proteins and mRNAs that are theoretically sustainable (though not necessarily
stable
A stable is a building in which livestock, especially horses, are kept. It most commonly means a building that is divided into separate stalls for individual animals and livestock. There are many different types of stables in use today; the ...
).
Steady state
In systems theory, a system or a Process theory, process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those p ...
s of kinetic equations thus correspond to potential cell types, and
oscillatory
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
solutions to the above equation to naturally cyclic cell types. Mathematical stability of these
attractor
In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain ...
s can usually be characterized by the sign of higher derivatives at critical points, and then correspond to
biochemical stability of the concentration profile.
Critical points and
bifurcation
Bifurcation or bifurcated may refer to:
Science and technology
* Bifurcation theory, the study of sudden changes in dynamical systems
** Bifurcation, of an incompressible flow, modeled by squeeze mapping the fluid flow
* River bifurcation, the for ...
s 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 the equations to short-term biological events. For a more mathematical discussion, see the articles on
nonlinearity
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
,
dynamical systems
In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a p ...
,
bifurcation theory
Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations. Mo ...
, and
chaos theory
Chaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have co ...
.
Boolean network
The following example illustrates how a
Boolean network
A Boolean network consists of a discrete set of boolean variables each of which has a Boolean function (possibly different for each variable) assigned to it which takes inputs from a subset of those variables and output that determines the stat ...
can model a GRN together with its gene products (the outputs) and the substances from the environment that affect it (the inputs).
Stuart Kauffman
Stuart Alan Kauffman (born September 28, 1939) is an American medical doctor, theoretical biologist, and complex systems researcher who studies the origin of life on Earth. He was a professor at the University of Chicago, University of Pennsylv ...
was amongst the first biologists to use the metaphor of Boolean networks to model genetic regulatory networks.
# Each gene, each input, and each output is represented by a node in a
directed graph
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is made up of a set of vertices connected by directed edges, often called arcs.
Definition
In formal terms, a directed graph is an ordered pa ...
in which there is an arrow from one node to another if and only if there is a causal link between the two nodes.
# Each node in the graph can be in one of two states: on or off.
# For a gene, "on" corresponds to the gene being expressed; for inputs and outputs, "off" corresponds to the substance being present.
# Time is viewed as proceeding in discrete steps. At each step, the new state of a node is a
Boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ( ...
of the prior states of the nodes with arrows pointing towards it.
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 the model.
Continuous networks
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 the Boolean model. Formally most of these approaches are similar to an
artificial neural network
Artificial neural networks (ANNs), usually simply called neural networks (NNs) or neural nets, are computing systems inspired by the biological neural networks that constitute animal brains.
An ANN is based on a collection of connected unit ...
, 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 is formally closer to a higher order
recurrent neural network
A recurrent neural network (RNN) is a class of artificial neural networks where connections between nodes can create a cycle, allowing output from some nodes to affect subsequent input to the same nodes. This allows it to exhibit temporal dynamic ...
. The same model has also been used to mimic the evolution of
cellular differentiation
Cellular differentiation is the process in which a stem cell alters from one type to a differentiated one. Usually, the cell changes to a more specialized type. Differentiation happens multiple times during the development of a multicellular ...
and even multicellular
morphogenesis
Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of devel ...
.
Stochastic gene networks
Recent 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 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 In probability theory, the Gillespie algorithm (or the Doob-Gillespie algorithm or ''Stochastic Simulation Algorithm'', the SSA) generates a statistically correct trajectory (possible solution) of a stochastic equation system for which the reactio ...
.
Since some processes, such as gene transcription, involve many reactions and could not be correctly modeled as an instantaneous reaction in 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 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, 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 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 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 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 the design of synthetic systems.
Prediction
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 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 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.
Applications
Multiple sclerosis
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 the disease mechanism across these three different multiple sclerosis classes.
See also
*
Body plan
A body plan, ( ), or ground plan is a set of morphological features common to many members of a phylum of animals. The vertebrates share one body plan, while invertebrates have many.
This term, usually applied to animals, envisages a "blueprin ...
*
Cis-regulatory module
''Cis''-regulatory elements (CREs) or ''Cis''-regulatory modules (CRMs) are regions of non-coding DNA which regulate the transcription of neighboring genes. CREs are vital components of genetic regulatory networks, which in turn control morphoge ...
*
Genenetwork
GeneNetwork is a combined database and open-source software, open-source bioinformatics data analysis software resource for systems genetics. This resource is used to study gene regulatory networks that link DNA sequence differences to correspon ...
(database)
*
Morphogen
A morphogen is a substance whose non-uniform distribution governs the pattern of tissue development in the process of morphogenesis or pattern formation, one of the core processes of developmental biology, establishing positions of the various ...
*
Operon
In genetics, an operon is a functioning unit of DNA containing a cluster of genes under the control of a single promoter. The genes are transcribed together into an mRNA strand and either translated together in the cytoplasm, or undergo splic ...
*
Synexpression {{refimprove, date=June 2012
Synexpression is a type of non-random eukaryotic gene organization. Genes in a synexpression group may not be physically linked, but they are involved in the same process and they are coordinately expressed. It is expe ...
*
Systems biology
Systems biology is the computational modeling, computational and mathematical analysis and modeling of complex biological systems. It is a biology-based interdisciplinary field of study that focuses on complex interactions within biological syst ...
*
Weighted gene co-expression network analysis
References
Further reading
*
*
External links
Plant Transcription Factor Database and Plant Transcriptional Regulation Data and Analysis PlatformOpen source web service for GRN analysisBIB: Yeast Biological Interaction Browser– Inference of gene association networks with GGMs
A bibliography on learning causal networks of gene interactions– regularly updated, contains hundreds of links to papers from bioinformatics, statistics, machine learning.
* https://web.archive.org/web/20060907074456/http://mips.gsf.de/proj/biorel/ BIOREL is a web-based resource for quantitative estimation of the gene network bias in relation to available database information about gene activity/function/properties/associations/interactio.
Evolving Biological Clocks using Genetic Regulatory Networks– Information page with model source code and Java applet.
Engineered Gene NetworksTutorial: Genetic Algorithms and their Application to the Artificial Evolution of Genetic Regulatory NetworksBEN: a web-based resource for exploring the connections between genes, diseases, and other biomedical entitiesGlobal protein-protein interaction and gene regulation network of Arabidopsis thaliana
{{DEFAULTSORT:Gene Regulatory Network
Gene expression
Networks
Systems biology
Evolutionary developmental biology