AntibodyAn antibody (Ab), also known as an immunoglobulin (Ig), is a large, Y-shaped protein used by the immune system to identify and neutralize foreign objects such as pathogenic bacteria and viruses. The antibody recognizes a unique molecule of the pathogen, called an antigen. Each tip of the "Y" of an antibody contains a paratope (analogous to a lock) that is specific for one particular epitope (analogous to a key) on an antigen, allowing these two structures to bind together with precision.
Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.
Dynamical systems theoryDynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.
Immunoglobulin GImmunoglobulin G (IgG) is a type of antibody. Representing approximately 75% of serum antibodies in humans, IgG is the most common type of antibody found in blood circulation. IgG molecules are created and released by plasma B cells. Each IgG antibody has two paratopes. It is the most common antibody. Antibodies are major components of humoral immunity. IgG is the main type of antibody found in blood and extracellular fluid, allowing it to control infection of body tissues.
LipopolysaccharideLipopolysaccharides (LPS) are large molecules consisting of a lipid and a polysaccharide that are bacterial toxins. They are composed of an O-antigen, an outer core, and an inner core all joined by covalent bonds, and are found in the outer membrane of Gram-negative bacteria. Today, the term endotoxin is often used synonymously with LPS, although there are a few endotoxins (in the original sense of toxins that are inside the bacterial cell that are released when the cell disintegrates) that are not related to LPS, such as the so-called delta endotoxin proteins produced by Bacillus thuringiensis.
Dynamical billiardsA dynamical billiard is a dynamical system in which a particle alternates between free motion (typically as a straight line) and specular reflections from a boundary. When the particle hits the boundary it reflects from it without loss of speed (i.e. elastic collisions). Billiards are Hamiltonian idealizations of the game of billiards, but where the region contained by the boundary can have shapes other than rectangular and even be multidimensional.
Hadamard's dynamical systemIn physics and mathematics, the Hadamard dynamical system (also called Hadamard's billiard or the Hadamard–Gutzwiller model) is a chaotic dynamical system, a type of dynamical billiards. Introduced by Jacques Hadamard in 1898, and studied by Martin Gutzwiller in the 1980s, it is the first dynamical system to be proven chaotic. The system considers the motion of a free (frictionless) particle on the Bolza surface, i.e, a two-dimensional surface of genus two (a donut with two holes) and constant negative curvature; this is a compact Riemann surface.
Humoral immunityHumoral immunity is the aspect of immunity that is mediated by macromolecules - including secreted antibodies, complement proteins, and certain antimicrobial peptides - located in extracellular fluids. Humoral immunity is named so because it involves substances found in the humors, or body fluids. It contrasts with cell-mediated immunity. Humoral immunity is also referred to as antibody-mediated immunity. The study of the molecular and cellular components that form the immune system, including their function and interaction, is the central science of immunology.
Monoclonal antibodyA monoclonal antibody (mAb, more rarely called moAb) is an antibody produced from a cell lineage made by cloning a unique white blood cell. All subsequent antibodies derived this way trace back to a unique parent cell. Monoclonal antibodies can have monovalent affinity, binding only to the same epitope (the part of an antigen that is recognized by the antibody). In contrast, polyclonal antibodies bind to multiple epitopes and are usually made by several different antibody-secreting plasma cell lineages.
Measure-preserving dynamical systemIn mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.
