Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
KinetochoreA kinetochore (kᵻˈnɛtəkɔər, -ˈniːtəkɔər) is a disc-shaped protein structure associated with duplicated chromatids in eukaryotic cells where the spindle fibers attach during cell division to pull sister chromatids apart. The kinetochore assembles on the centromere and links the chromosome to microtubule polymers from the mitotic spindle during mitosis and meiosis. The term kinetochore was first used in a footnote in a 1934 Cytology book by Lester W. Sharp and commonly accepted in 1936.
Cell growthCell growth refers to an increase in the total mass of a cell, including both cytoplasmic, nuclear and organelle volume. Cell growth occurs when the overall rate of cellular biosynthesis (production of biomolecules or anabolism) is greater than the overall rate of cellular degradation (the destruction of biomolecules via the proteasome, lysosome or autophagy, or catabolism). Cell growth is not to be confused with cell division or the cell cycle, which are distinct processes that can occur alongside cell growth during the process of cell proliferation, where a cell, known as the mother cell, grows and divides to produce two daughter cells.
Cell biologyCell biology (also cellular biology or cytology) is a branch of biology that studies the structure, function, and behavior of cells. All living organisms are made of cells. A cell is the basic unit of life that is responsible for the living and functioning of organisms. Cell biology is the study of the structural and functional units of cells. Cell biology encompasses both prokaryotic and eukaryotic cells and has many subtopics which may include the study of cell metabolism, cell communication, cell cycle, biochemistry, and cell composition.
CytokinesisCytokinesis (ˌsaɪtoʊkɪˈniːsɪs) is the part of the cell division process during which the cytoplasm of a single eukaryotic cell divides into two daughter cells. Cytoplasmic division begins during or after the late stages of nuclear division in mitosis and meiosis. During cytokinesis the spindle apparatus partitions and transports duplicated chromatids into the cytoplasm of the separating daughter cells. It thereby ensures that chromosome number and complement are maintained from one generation to the next and that, except in special cases, the daughter cells will be functional copies of the parent cell.
Verlet integrationVerlet integration (vɛʁˈlɛ) is a numerical method used to integrate Newton's equations of motion. It is frequently used to calculate trajectories of particles in molecular dynamics simulations and computer graphics. The algorithm was first used in 1791 by Jean Baptiste Delambre and has been rediscovered many times since then, most recently by Loup Verlet in the 1960s for use in molecular dynamics. It was also used by P. H. Cowell and A. C. C.
Asymmetric cell divisionAn asymmetric cell division produces two daughter cells with different cellular fates. This is in contrast to symmetric cell divisions which give rise to daughter cells of equivalent fates. Notably, stem cells divide asymmetrically to give rise to two distinct daughter cells: one copy of the original stem cell as well as a second daughter programmed to differentiate into a non-stem cell fate. (In times of growth or regeneration, stem cells can also divide symmetrically, to produce two identical copies of the original cell.
EukaryogenesisEukaryogenesis, the process which created the eukaryotic cell and lineage, is a milestone in the evolution of life, since eukaryotes include all complex cells and almost all multicellular organisms. The process is widely agreed to have involved symbiogenesis, in which archaea and bacteria came together to create the first eukaryotic common ancestor (FECA). This cell had a new level of complexity and capability, with a nucleus, at least one centriole and cilium, facultatively aerobic mitochondria, sex (meiosis and syngamy), a dormant cyst with a cell wall of chitin and/or cellulose and peroxisomes.
Spindle pole bodyThe spindle pole body (SPB) is the microtubule organizing center in yeast cells, functionally equivalent to the centrosome. Unlike the centrosome the SPB does not contain centrioles. The SPB organises the microtubule cytoskeleton which plays many roles in the cell. It is important for organising the spindle and thus in cell division. The molecular mass of a diploid SPB, including microtubules and microtubule associated proteins, is estimated to be 1–1.5 GDa whereas a core SPB is 0.3–0.5 GDa.
TelophaseTelophase () is the final stage in both meiosis and mitosis in a eukaryotic cell. During telophase, the effects of prophase and prometaphase (the nucleolus and nuclear membrane disintegrating) are reversed. As chromosomes reach the cell poles, a nuclear envelope is re-assembled around each set of chromatids, the nucleoli reappear, and chromosomes begin to decondense back into the expanded chromatin that is present during interphase. The mitotic spindle is disassembled and remaining spindle microtubules are depolymerized.
Bifurcation theoryBifurcation 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. Most commonly applied to the mathematical study of dynamical systems, a bifurcation occurs when a small smooth change made to the parameter values (the bifurcation parameters) of a system causes a sudden 'qualitative' or topological change in its behavior.
Overlapping geneAn overlapping gene (or OLG) is a gene whose expressible nucleotide sequence partially overlaps with the expressible nucleotide sequence of another gene. In this way, a nucleotide sequence may make a contribution to the function of one or more gene products. Overlapping genes are present and a fundamental feature of both cellular and viral genomes. The current definition of an overlapping gene varies significantly between eukaryotes, prokaryotes, and viruses.
