Matrix exponentialIn mathematics, the matrix exponential is a matrix function on square matrices analogous to the ordinary exponential function. It is used to solve systems of linear differential equations. In the theory of Lie groups, the matrix exponential gives the exponential map between a matrix Lie algebra and the corresponding Lie group. Let X be an n×n real or complex matrix. The exponential of X, denoted by eX or exp(X), is the n×n matrix given by the power series where is defined to be the identity matrix with the same dimensions as .
Protein kinase BProtein kinase B (PKB), also known as Akt, is the collective name of a set of three serine/threonine-specific protein kinases that play key roles in multiple cellular processes such as glucose metabolism, apoptosis, cell proliferation, transcription, and cell migration. There are three different genes that encode isoforms of Protein kinase B. These three genes are referred to as AKT1, AKT2, and AKT3 and encode the RAC alpha, beta, and gamma serine/threonine protein kinases respectively.
Diagonal matrixIn linear algebra, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term usually refers to square matrices. Elements of the main diagonal can either be zero or nonzero. An example of a 2×2 diagonal matrix is , while an example of a 3×3 diagonal matrix is. An identity matrix of any size, or any multiple of it (a scalar matrix), is a diagonal matrix. A diagonal matrix is sometimes called a scaling matrix, since matrix multiplication with it results in changing scale (size).
Logarithm of a matrixIn mathematics, a logarithm of a matrix is another matrix such that the matrix exponential of the latter matrix equals the original matrix. It is thus a generalization of the scalar logarithm and in some sense an inverse function of the matrix exponential. Not all matrices have a logarithm and those matrices that do have a logarithm may have more than one logarithm. The study of logarithms of matrices leads to Lie theory since when a matrix has a logarithm then it is in an element of a Lie group and the logarithm is the corresponding element of the vector space of the Lie algebra.
3D bioprintingThree dimensional (3D) bioprinting is the utilization of 3D printing–like techniques to combine cells, growth factors, and/or biomaterials to fabricate biomedical parts, often with the aim of imitating natural tissue characteristics. Generally, 3D bioprinting can utilize a layer-by-layer method to deposit materials known as bio-inks to create tissue-like structures that are later used in various medical and tissue engineering fields. 3D bioprinting covers a broad range of bioprinting techniques and biomaterials.
Cell adhesion moleculeCell adhesion molecules (CAMs) are a subset of cell surface proteins that are involved in the binding of cells with other cells or with the extracellular matrix (ECM), in a process called cell adhesion. In essence, CAMs help cells stick to each other and to their surroundings. CAMs are crucial components in maintaining tissue structure and function. In fully developed animals, these molecules play an integral role in generating force and movement and consequently ensuring that organs are able to execute their functions normally.
Biochemical cascadeA biochemical cascade, also known as a signaling cascade or signaling pathway, is a series of chemical reactions that occur within a biological cell when initiated by a stimulus. This stimulus, known as a first messenger, acts on a receptor that is transduced to the cell interior through second messengers which amplify the signal and transfer it to effector molecules, causing the cell to respond to the initial stimulus. Most biochemical cascades are series of events, in which one event triggers the next, in a linear fashion.
Adjugate matrixIn linear algebra, the adjugate or classical adjoint of a square matrix A is the transpose of its cofactor matrix and is denoted by adj(A). It is also occasionally known as adjunct matrix, or "adjoint", though the latter term today normally refers to a different concept, the adjoint operator which for a matrix is the conjugate transpose. The product of a matrix with its adjugate gives a diagonal matrix (entries not on the main diagonal are zero) whose diagonal entries are the determinant of the original matrix: where I is the identity matrix of the same size as A.
Tissue engineeringTissue engineering is a biomedical engineering discipline that uses a combination of cells, engineering, materials methods, and suitable biochemical and physicochemical factors to restore, maintain, improve, or replace different types of biological tissues. Tissue engineering often involves the use of cells placed on tissue scaffolds in the formation of new viable tissue for a medical purpose but is not limited to applications involving cells and tissue scaffolds.
Focal adhesionIn cell biology, focal adhesions (also cell–matrix adhesions or FAs) are large macromolecular assemblies through which mechanical force and regulatory signals are transmitted between the extracellular matrix (ECM) and an interacting cell. More precisely, focal adhesions are the sub-cellular structures that mediate the regulatory effects (i.e., signaling events) of a cell in response to ECM adhesion. Focal adhesions serve as the mechanical linkages to the ECM, and as a biochemical signaling hub to concentrate and direct numerous signaling proteins at sites of integrin binding and clustering.
