A cellular model is a

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, ...

of aspects of a

biological cell The cell is the basic structural and functional unit of life forms. Every cell consists of a cytoplasm enclosed within a membrane, and contains many biomolecules such as proteins, DNA and RNA, as well as many small molecules of nutrients an ...

, for the purposes of

in silico In biology and other experimental sciences, an ''in silico'' experiment is one performed on computer or via computer simulation. The phrase is pseudo-Latin for 'in silicon' (correct la, in silicio), referring to silicon in computer chips. It ...

research. Developing such models has been a task of

systems biology Systems biology is the 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 systems, using a holistic ...

and

mathematical biology Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development a ...

. It involves developing efficient

algorithms In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific problems or to perform a computation. Algorithms are used as specifications for performing ...

data structures In computer science, a data structure is a data organization, management, and storage format that is usually chosen for efficient access to data. More precisely, a data structure is a collection of data values, the relationships among them, ...

visualization Visualization or visualisation may refer to: * Visualization (graphics), the physical or imagining creation of images, diagrams, or animations to communicate a message * Data visualization, the graphic representation of data * Information visuali ...

and communication tools to orchestrate the integration of large quantities of biological data with the goal of

computer modeling Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be dete ...

. It involves the use of

computer simulation Computer simulation is the process of mathematical modelling, performed on a computer, which is designed to predict the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be deter ...

s of cellular subsystems, such as the networks of metabolites and

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 ...

s which comprise

metabolism Metabolism (, from el, μεταβολή ''metabolē'', "change") is the set of life-sustaining chemical reactions in organisms. The three main functions of metabolism are: the conversion of the energy in food to energy available to run ...

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 ...

pathways and gene regulatory networks.It is the preminary research of biology cells

Overview

The eukaryotic

cell cycle The cell cycle, or cell-division cycle, is the series of events that take place in a cell that cause it to divide into two daughter cells. These events include the duplication of its DNA (DNA replication) and some of its organelles, and sub ...

is very complex and is one of the most studied topics, since its misregulation leads to

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 ...

s. It is possibly a good example of a mathematical model as it deals with simple calculus but gives valid results. Two research groups have produced several models of the cell cycle simulating several organisms. They have recently produced a generic eukaryotic cell cycle model which can represent a particular eukaryote depending on the values of the parameters, demonstrating that the idiosyncrasies of the individual cell cycles are due to different protein concentrations and affinities, while the underlying mechanisms are conserved (Csikasz-Nagy et al., 2006). By means of a system of

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 ...

s these models show the change in time (

dynamical system 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 i ...

) of the protein inside a single typical cell; this type of model is called a deterministic process (whereas a model describing a statistical distribution of protein concentrations in a population of cells is called a

stochastic process In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that ap ...

). To obtain these equations an iterative series of steps must be done: first the several models and observations are combined to form a consensus diagram and the appropriate kinetic laws are chosen to write the differential equations, such as rate kinetics for stoichiometric reactions, Michaelis-Menten kinetics for enzyme substrate reactions and

Goldbeter–Koshland kinetics The Goldbeter–Koshland kinetics Zoltan Szallasi, Jörg Stelling, Vipul Periwal: ''System Modeling in Cellular Biology''. The MIT Press. p 108. describe a steady-state solution for a 2-state biological system. In this system, the interconversi ...

for ultrasensitive transcription factors, afterwards the parameters of the equations (rate constants, enzyme efficiency coefficients and Michaelis constants) must be fitted to match observations; when they cannot be fitted the kinetic equation is revised and when that is not possible the wiring diagram is modified. The parameters are fitted and validated using observations of both wild type and mutants, such as protein half-life and cell size. In order to fit the parameters the differential equations need to be studied. This can be done either by simulation or by analysis. In a simulation, given a starting

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

(list of the values of the variables), the progression of the system is calculated by solving the equations at each time-frame in small increments. In analysis, the properties of the equations are used to investigate the behavior of the system depending on the values of the parameters and variables. A system of differential equations can be represented as a vector field, where each vector described the change (in concentration of two or more protein) determining where and how fast the trajectory (simulation) is heading. Vector fields can have several special points: a

stable point In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper in class ...

, called a sink, that attracts in all directions (forcing the concentrations to be at a certain value), an unstable point, either a source or a

saddle point In mathematics, a saddle point or minimax point is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point), but which is not a local extremum of the functi ...

which repels (forcing the concentrations to change away from a certain value), and a limit cycle, a closed trajectory towards which several trajectories spiral towards (making the concentrations oscillate). A better representation which can handle the large number of variables and parameters is called a

bifurcation diagram In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the sy ...

(

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. ...

): the presence of these special steady-state points at certain values of a parameter (e.g. mass) is represented by a point and once the parameter passes a certain value, a qualitative change occurs, called a bifurcation, in which the nature of the space changes, with profound consequences for the protein concentrations: the cell cycle has phases (partially corresponding to G1 and G2) in which mass, via a stable point, controls cyclin levels, and phases (S and M phases) in which the concentrations change independently, but once the phase has changed at a bifurcation event (

cell cycle checkpoint Cell cycle checkpoints are control mechanisms in the eukaryotic cell cycle which ensure its proper progression. Each checkpoint serves as a potential termination point along the cell cycle, during which the conditions of the cell are assessed, wi ...

), the system cannot go back to the previous levels since at the current mass the vector field is profoundly different and the mass cannot be reversed back through the bifurcation event, making a checkpoint irreversible. In particular the S and M checkpoints are regulated by means of special bifurcations called a

Hopf bifurcation In the bifurcation theory, mathematical theory of bifurcations, a Hopf bifurcation is a Critical point (mathematics), critical point where a system's stability switches and a Periodic function, periodic solution arises. More accurately, it is a lo ...

and an infinite period bifurcation.

Molecular level simulations

Cell Collective is a modeling software that enables one to house dynamical biological data, build computational models, stimulate, break and recreate models. The development is led by Tomas Helikar, a researcher within the field of computational biology. It is designed for biologists, students learning about computational biology, teachers focused on teaching life sciences, and researchers within the field of life science. The complexities of math and computer science are built into the backend and one can learn about the methods used for modeling biological species, but complex math equations, algorithms, programming are not required and hence won't impede model building. The mathematical framework behind Cell Collective is based on a common qualitative (discrete) modeling technique where the regulatory mechanism of each node is described with a logical function or more comprehensive information on logical modeling, see In the July 2012 issue of ''Cell'', a team led by Markus Covert at Stanford published the most complete computational model of a cell to date. The model of the roughly 500-gene ''

Mycoplasma genitalium ''Mycoplasma genitalium'' (''MG'', commonly known as Mgen) is a sexually transmitted, small and pathogenic bacterium that lives on the mucous epithelial cells of the urinary and genital tracts in humans. Medical reports published in 2007 and 2 ...

'' contains 28 algorithmically-independent components incorporating work from over 900 sources. It accounts for interactions of the complete

genome In the fields of molecular biology and genetics, a genome is all the genetic information of an organism. It consists of nucleotide sequences of DNA (or RNA in RNA viruses). The nuclear genome includes protein-coding genes and non-coding ...

transcriptome The transcriptome is the set of all RNA transcripts, including coding and non-coding, in an individual or a population of cells. The term can also sometimes be used to refer to all RNAs, or just mRNA, depending on the particular experiment. The t ...

proteome The proteome is the entire set of proteins that is, or can be, expressed by a genome, cell, tissue, or organism at a certain time. It is the set of expressed proteins in a given type of cell or organism, at a given time, under defined conditions. ...

, and

metabolome The metabolome refers to the complete set of Small molecule, small-molecule chemicals found within a biological sample. The biological sample can be a Cell (biology), cell, a cellular organelle, an Organ (anatomy), organ, a Tissue (biology), tiss ...

of the organism, marking a significant advancement for the field. Most attempts at modeling cell cycle processes have focused on the broad, complicated molecular interactions of many different chemicals, including several

cyclin Cyclin is a family of proteins that controls the progression of a cell through the cell cycle by activating cyclin-dependent kinase (CDK) enzymes or group of enzymes required for synthesis of cell cycle. Etymology Cyclins were originally disco ...

and

cyclin-dependent kinase Cyclin-dependent kinases (CDKs) are the families of protein kinases first discovered for their role in regulating the cell cycle. They are also involved in regulating transcription, mRNA processing, and the differentiation of nerve cells. They ...

molecules as they correspond to the S, M, G1 and G2 phases of the

. In a 2014 published article in PLOS computational biology, collaborators at

University of Oxford , mottoeng = The Lord is my light , established = , endowment = £6.1 billion (including colleges) (2019) , budget = £2.145 billion (2019–20) , chancellor ...

Virginia Tech Virginia Tech (formally the Virginia Polytechnic Institute and State University and informally VT, or VPI) is a public land-grant research university with its main campus in Blacksburg, Virginia. It also has educational facilities in six re ...

and Institut de Génétique et Développement de Rennes produced a simplified model of the cell cycle using only one cyclin/CDK interaction. This model showed the ability to control totally functional

cell division Cell division is the process by which a parent cell divides into two daughter cells. Cell division usually occurs as part of a larger cell cycle in which the cell grows and replicates its chromosome(s) before dividing. In eukaryotes, there ...

through regulation and manipulation only the one interaction, and even allowed researchers to skip phases through varying the concentration of CDK. This model could help understand how the relatively simple interactions of one chemical translate to a cellular level model of cell division.

Projects

Multiple projects are in progress.{{Cite journal , url=http://www.nature.com/naturejobs/2002/020627/full/nj6892-04a.html , doi=10.1038/nj6892-04a, pmid=12087360, title=Silicon dreams in the biology lab, journal=Nature, volume=417, issue=6892, pages=4–5, year=2002, last1=Gershon, first1=Diane, bibcode=2002Natur.417....4G, s2cid=10737442
CytoSolveSynthecell

Karyote
-

Indiana University Indiana University (IU) is a system of public universities in the U.S. state of Indiana. Campuses Indiana University has two core campuses, five regional campuses, and two regional centers under the administration of IUPUI. *Indiana Universi ...

E-Cell ProjectVirtual Cell
-

University of Connecticut Health Center UConn Health (formerly known as the UConn Health Center) is the branch of the University of Connecticut that oversees clinical care, advanced biomedical research, and academic education in medicine. The main branch is located in Farmington, Connec ...

Silicon CellWholeCell
-

Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is conside ...

MCell

National Center for Multiscale Modeling of Biological Systems (MMBioS)

References

Bioinformatics Systems biology Scientific models

Overview

Molecular level simulations

Projects

See also

References