BiofilmA biofilm comprises any syntrophic consortium of microorganisms in which cells stick to each other and often also to a surface. These adherent cells become embedded within a slimy extracellular matrix that is composed of extracellular polymeric substances (EPSs). The cells within the biofilm produce the EPS components, which are typically a polymeric conglomeration of extracellular polysaccharides, proteins, lipids and DNA. Because they have three-dimensional structure and represent a community lifestyle for microorganisms, they have been metaphorically described as "cities for microbes".
Matrix (mathematics)In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.
Extracellular polymeric substanceExtracellular polymeric substances (EPSs) are natural polymers of high molecular weight secreted by microorganisms into their environment. EPSs establish the functional and structural integrity of biofilms, and are considered the fundamental component that determines the physicochemical properties of a biofilm. EPS in the matrix of biofilms provides compositional support and protection of microbial communities from the harsh environments. Components of EPS can be of different classes of polysaccharides, lipids, nucleic acids, proteins, lipopolysaccharides, and minerals.
Extracellular matrixIn biology, the extracellular matrix (ECM), also called intercellular matrix, is a network consisting of extracellular macromolecules and minerals, such as collagen, enzymes, glycoproteins and hydroxyapatite that provide structural and biochemical support to surrounding cells. Because multicellularity evolved independently in different multicellular lineages, the composition of ECM varies between multicellular structures; however, cell adhesion, cell-to-cell communication and differentiation are common functions of the ECM.
Triangular matrixIn mathematics, a triangular matrix is a special kind of square matrix. A square matrix is called if all the entries above the main diagonal are zero. Similarly, a square matrix is called if all the entries below the main diagonal are zero. Because matrix equations with triangular matrices are easier to solve, they are very important in numerical analysis. By the LU decomposition algorithm, an invertible matrix may be written as the product of a lower triangular matrix L and an upper triangular matrix U if and only if all its leading principal minors are non-zero.
Show more