A generegulatory 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, the creation of body structures, which in turn is central to evolutionary developmental biology (evo-devo).
Chemical kinetics, also known as reaction kinetics, is the branch of physical chemistry that is concerned with understanding the rates of chemical reactions. It is to be contrasted with thermodynamics, which deals with the direction in which a process occurs but in itself tells nothing about its rate. Chemical kinetics includes investigations of how experimental conditions influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that also can describe the characteristics of a chemical reaction.
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 and behavior of the systems, as opposed to experimental biology which deals with the conduction of experiments to prove and validate the scientific theories. The field is sometimes called mathematical biology or biomathematics to stress the mathematical side, or theoretical biology to stress the biological side. Theoretical biology focuses more on the development of theoretical principles for biology while mathematical biology focuses on the use of mathematical tools to study biological systems, even though the two terms are sometimes interchanged.
In physics, chemistry and related fields, master equations are used to describe the time evolution of a system that can be modelled as being in a probabilistic combination of states at any given time and the switching between states is determined by a transition rate matrix. The equations are a set of differential equations – over time – of the probabilities that the system occupies each of the different states.
Stochastic resonance (SR) is a phenomenon in which a signal that is normally too weak to be detected by a sensor, can be boosted by adding white noise to the signal, which contains a wide spectrum of frequencies. The frequencies in the white noise corresponding to the original signal's frequencies will resonate with each other, amplifying the original signal while not amplifying the rest of the white noise – thereby increasing the signal-to-noise ratio, which makes the original signal more prominent. Further, the added white noise can be enough to be detectable by the sensor, which can then filter it out to effectively detect the original, previously undetectable signal.
Enzyme kinetics is the study of the rates of enzyme-catalysed chemical reactions. In enzyme kinetics, the reaction rate is measured and the effects of varying the conditions of the reaction are investigated. Studying an enzyme's kinetics in this way can reveal the catalytic mechanism of this enzyme, its role in metabolism, how its activity is controlled, and how a drug or a modifier might affect the rate.
Neuronal noise or neural noise refers to the random intrinsic electrical fluctuations within neuronal networks. These fluctuations are not associated with encoding a response to internal or external stimuli and can be from one to two orders of magnitude. Most noise commonly occurs below a voltage-threshold that is needed for an action potential to occur, but sometimes it can be present in the form of an action potential; for example, stochastic oscillations in pacemaker neurons in suprachiasmatic nucleus are partially responsible for the organization of circadian rhythms.
In probability theory, the Gillespie algorithm generates a statistically correct trajectory of a stochastic equation system for which the reaction rates are known. It was created by Joseph L. Doob and others, presented by Dan Gillespie in 1976, and popularized in 1977 in a paper where he uses it to simulate chemical or biochemical systems of reactions efficiently and accurately using limited computational power. As computers have become faster, the algorithm has been used to simulate increasingly complex systems. The algorithm is particularly useful for simulating reactions within cells, where the number of reagents is low and keeping track of the position and behaviour of individual molecules is computationally feasible. Mathematically, it is a variant of a dynamic Monte Carlo method and similar to the kinetic Monte Carlo methods. It is used heavily in computational systems biology.
A stochastic simulation is a simulation of a system that has variables that can change stochastically (randomly) with individual probabilities.
Systems immunology is a research field under systems biology that uses mathematical approaches and computational methods to examine the interactions within cellular and molecular networks of the immune system. The immune system has been thoroughly analyzed as regards to its components and function by using a "reductionist" approach, but its overall function can't be easily predicted by studying the characteristics of its isolated components because they strongly rely on the interactions among these numerous constituents. It focuses on in silico experiments rather than in vivo.
Daniel Thomas Gillespie was a physicist who is best known for his derivation in 1976 of the stochastic simulation algorithm (SSA), also called the Gillespie algorithm. Gillespie's broader research has produced articles on cloud physics, random variable theory, Brownian motion, Markov process theory, electrical noise, light scattering in aerosols, and quantum mechanics.
Creating a cellular model has been a particularly challenging task of systems biology and mathematical biology. It involves developing efficient algorithms, data structures, visualization and communication tools to orchestrate the integration of large quantities of biological data with the goal of computer modeling.
Super-resolution microscopy is a series of techniques in optical microscopy that allow such images to have resolutions higher than those imposed by the diffraction limit, which is due to the diffraction of light. Super-resolution imaging techniques rely on the near-field or on the far-field. Among techniques that rely on the latter are those that improve the resolution only modestly beyond the diffraction-limit, such as confocal microscopy with closed pinhole or aided by computational methods such as deconvolution or detector-based pixel reassignment, the 4Pi microscope, and structured-illumination microscopy technologies such as SIM and SMI.
The system size expansion, also known as van Kampen's expansion or the Ω-expansion, is a technique pioneered by Nico van Kampen used in the analysis of stochastic processes. Specifically, it allows one to find an approximation to the solution of a master equation with nonlinear transition rates. The leading order term of the expansion is given by the linear noise approximation, in which the master equation is approximated by a Fokker–Planck equation with linear coefficients determined by the transition rates and stoichiometry of the system.
In dynamics, probability, physics, chemistry and related fields, a heterogeneous random walk in one dimension is a random walk in a one dimensional interval with jumping rules that depend on the location of the random walker in the interval.
Cellular noise is random variability in quantities arising in cellular biology. For example, cells which are genetically identical, even within the same tissue, are often observed to have different expression levels of proteins, different sizes and structures. These apparently random differences can have important biological and medical consequences.
Johan Paulsson is a Swedish mathematician and systems biologist at Harvard Medical School. He is a leading researcher in systems biology and stochastic processes, specializing in stochasticity in gene networks and plasmid reproduction.
Virtual Cell (VCell) is an open-source software platform for modeling and simulation of living organisms, primarily cells. It has been designed to be a tool for a wide range of scientists, from experimental cell biologists to theoretical biophysicists.
Multi-state modeling of biomolecules refers to a series of techniques used to represent and compute the behaviour of biological molecules or complexes that can adopt a large number of possible functional states.
Hybrid stochastic simulations are a sub-class of stochastic simulations. These simulations combine existing stochastic simulations with other stochastic simulations or algorithms. Generally they are used for physics and physics-related research. The goal of a hybrid stochastic simulation varies based on context, however they typically aim to either improve accuracy or reduce computational complexity. The first hybrid stochastic simulation was developed in 1985.
