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Biochemistry
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Biochemistry, sometimes called biological chemistry, is the study of chemical processes within and relating to living organisms. By controlling information flow through biochemical signaling and the flow of energy through metabolism. Biochemistry is closely related to biology, the study of the molecular mechanisms by which genetic information encoded in DNA is able to result in the processes of life. Depending on the definition of the terms used, molecular biology can be thought of as a branch of biochemistry, or biochemistry as a tool with which to investigate. The chemistry of the cell depends on the reactions of smaller molecules. These can be inorganic, for water and metal ions, or organic, for example the amino acids. The mechanisms by which cells harness energy from their environment via chemical reactions are known as metabolism, the findings of biochemistry are applied primarily in medicine, nutrition, and agriculture. In medicine, biochemists investigate the causes and cures of diseases, in nutrition, they study how to maintain health and study the effects of nutritional deficiencies. In agriculture, biochemists investigate soil and fertilizers, and try to discover ways to improve crop cultivation, crop storage and pest control. However, biochemistry as a scientific discipline has its beginning sometime in the 19th century, or a little earlier. Gowland Hopkins on enzymes and the nature of biochemistry. The term biochemistry itself is derived from a combination of biology, the German chemist Carl Neuberg however is often cited to have coined the word in 1903, while some credited it to Franz Hofmeister. Then, in 1828, Friedrich Wöhler published a paper on the synthesis of urea and these techniques allowed for the discovery and detailed analysis of many molecules and metabolic pathways of the cell, such as glycolysis and the Krebs cycle. Another significant historic event in biochemistry is the discovery of the gene and this part of biochemistry is often called molecular biology. In the 1950s, James D. Watson, Francis Crick, Rosalind Franklin, in 1958, George Beadle and Edward Tatum received the Nobel Prize for work in fungi showing that one gene produces one enzyme. In 1988, Colin Pitchfork was the first person convicted of murder with DNA evidence, mello received the 2006 Nobel Prize for discovering the role of RNA interference, in the silencing of gene expression. Around two dozen of the 92 naturally occurring elements are essential to various kinds of biological life. Most rare elements on Earth are not needed by life, while a few common ones are not used, most organisms share element needs, but there are a few differences between plants and animals

2.
Enzyme kinetics
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Enzyme kinetics is the study of the chemical reactions that are catalysed by enzymes. In enzyme kinetics, the rate is measured and the effects of varying the conditions of the reaction are investigated. Enzymes are usually protein molecules that manipulate other molecules — the enzymes substrates, kinetic studies on enzymes that only bind one substrate, such as triosephosphate isomerase, aim to measure the affinity with which the enzyme binds this substrate and the turnover rate. Some other examples of enzymes are phosphofructokinase and hexokinase, both of which are important for cellular respiration, when enzymes bind multiple substrates, such as dihydrofolate reductase, enzyme kinetics can also show the sequence in which these substrates bind and the sequence in which products are released. An example of enzymes that bind a single substrate and release multiple products are proteases, others join two substrates together, such as DNA polymerase linking a nucleotide to DNA. Although these mechanisms are often a series of steps, there is typically one rate-determining step that determines the overall kinetics. This rate-determining step may be a reaction or a conformational change of the enzyme or substrates. Knowledge of the structure is helpful in interpreting kinetic data. For example, the structure can suggest how substrates and products bind during catalysis, what changes occur during the reaction, not all biological catalysts are protein enzymes, RNA-based catalysts such as ribozymes and ribosomes are essential to many cellular functions, such as RNA splicing and translation. The main difference between ribozymes and enzymes is that RNA catalysts are composed of nucleotides, whereas enzymes are composed of amino acids, ribozymes also perform a more limited set of reactions, although their reaction mechanisms and kinetics can be analysed and classified by the same methods. The reaction catalysed by an enzyme uses exactly the same reactants, like other catalysts, enzymes do not alter the position of equilibrium between substrates and products. However, unlike uncatalysed chemical reactions, enzyme-catalysed reactions display saturation kinetics, the substrate concentration midway between these two limiting cases is denoted by KM. The two most important kinetic properties of an enzyme are how quickly the enzyme becomes saturated with a substrate. Knowing these properties suggests what an enzyme might do in the cell, Enzyme assays are laboratory procedures that measure the rate of enzyme reactions. Because enzymes are not consumed by the reactions they catalyse, enzyme assays usually follow changes in the concentration of substrates or products to measure the rate of reaction. There are many methods of measurement, spectrophotometric assays are most convenient since they allow the rate of the reaction to be measured continuously. Although radiometric assays require the removal and counting of samples they are extremely sensitive. An analogous approach is to use mass spectrometry to monitor the incorporation or release of stable isotopes as substrate is converted into product, the most sensitive enzyme assays use lasers focused through a microscope to observe changes in single enzyme molecules as they catalyse their reactions

3.
Reaction velocity
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The reaction rate or speed of reaction for a reactant or product in a particular reaction is intuitively defined as how quickly or slowly a reaction takes place. Chemical kinetics is the part of chemistry that studies reaction rates. The concepts of chemical kinetics are applied in many disciplines, such as engineering, enzymology. Consider a typical reaction, a A + b B → p P + q Q The lowercase letters represent stoichiometric coefficients, while the capital letters represent the reactants. Reaction rate usually has the units of mol L−1 s−1, the rate of a reaction is always positive. A negative sign is present to indicate that the reactant concentration is decreasing. )The IUPAC recommends that the unit of time should always be the second. The rate of reaction differs from the rate of increase of concentration of a product P by a constant factor and for a reactant A by minus the reciprocal of the stoichiometric number. The stoichiometric numbers are included so that the rate is independent of which reactant or product species is chosen for measurement. For example, if a =1 and b =3 then B is consumed three times more rapidly than A, but v = -d/dt = -d/dt is uniquely defined. The above definition is valid for a single reaction, in a closed system of constant volume. If water is added to a pot containing salty water, the concentration of salt decreases, although there is no chemical reaction. When applied to the system at constant volume considered previously, this equation reduces to, r = d d t. Here N0 is the Avogadro constant, for a single reaction in a closed system of varying volume the so-called rate of conversion can be used, in order to avoid handling concentrations. It is defined as the derivative of the extent of reaction with respect to time, also V is the volume of reaction and Ci is the concentration of substance i. When side products or reaction intermediates are formed, the IUPAC recommends the use of the rate of appearance and rate of disappearance for products and reactants. Reaction rates may also be defined on a basis that is not the volume of the reactor, when a catalyst is used the reaction rate may be stated on a catalyst weight or surface area basis. If the basis is a specific catalyst site that may be counted by a specified method. The nature of the reaction, Some reactions are faster than others

4.
J. B. S. Haldane
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His article on abiogenesis in 1929 introduced the Primordial Soup Theory, and it became the foundation to build physical models for the chemical origin of life. Haldane established human gene maps for haemophilia and colour blindness on the X chromosome and he correctly proposed that sickle-cell disease confers some immunity to malaria. In 1957 he articulated Haldanes dilemma, a limit on the speed of evolution which subsequently proved incorrect. He willed his body for medical studies, as he wanted to remain even in death. Arthur C. Clarke credited him as perhaps the most brilliant science populariser of his generation, nobel laureate Peter Medawar called Haldane the cleverest man I ever knew. Haldane was born in Oxford to John Scott Haldane, a physiologist, scientist, a philosopher and a Liberal, and Louisa Kathleen Trotter and his younger sister, Naomi Mitchison, became a writer, and his uncle was Viscount Haldane and his aunt the author Elizabeth Haldane. Descended from an aristocratic and secular family of the Clan Haldane and he grew up at 11 Crick Road, North Oxford. He learnt to read at the age of three, and at four, after injuring his forehead he asked the doctor, Is this oxyhaemoglobin or carboxyhaemoglobin. From age eight he worked with his father in their home laboratory where he experienced his first self-experimentation and he and his father became their own human guinea pigs, such as in their investigation on the effects of poison gases. In 1899 his family moved to Cherwell, a late Victorian house at the outskirts of Oxford having its private laboratory and his formal education began in 1897 at Oxford Preparatory School, where he gained a First Scholarship in 1904 to Eton. In 1905 he joined Eton, where he experienced severe abuse from senior students for allegedly being arrogant, the indifference of authority left him with a lasting hatred for the English education system. However, the ordeal did not stop him from becoming Captain of the school and he studied mathematics and classics at New College at the University of Oxford and obtained first-class honours in mathematical moderations in 1912 and a first-class honours in 1914. With his father he published his first scientific paper, age 20 and he became engrossed in genetics and presented a paper on gene linkage in vertebrates in the summer of 1912. His first technical paper, a 30-page long article on function, was published. He was promoted to lieutenant on 18 February 1915 and to temporary captain on 18 October. He served in France and Iraq, where he was wounded and he relinquished his commission on 1 April 1920, retaining his rank of captain. For his ferocity and aggressiveness in battles, his commander called him the bravest and dirtiest officer in my Army, between 1919 and 1922 he was a Fellow of New College, Oxford, where he researched physiology and genetics. He then moved to the University of Cambridge, where he accepted a readership in Biochemistry, from 1927 until 1937 he was also Head of Genetical Research at the John Innes Horticultural Institution

5.
Nonlinear regression
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The data are fitted by a method of successive approximations. The data consist of independent variables, x, and their associated observed dependent variables. Each y is modeled as a variable with a mean given by a nonlinear function f. Systematic error may be present but its treatment is outside the scope of regression analysis, if the independent variables are not error-free, this is an errors-in-variables model, also outside this scope. This function is nonlinear because it cannot be expressed as a combination of the two β s. Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions, Gaussian function, some functions, such as the exponential or logarithmic functions, can be transformed so that they are linear. When so transformed, standard linear regression can be performed but must be applied with caution, see Linearization, below, for more details. In general, there is no closed-form expression for the best-fitting parameters, usually numerical optimization algorithms are applied to determine the best-fitting parameters. Again in contrast to linear regression, there may be many local minima of the function to be optimized, in practice, estimated values of the parameters are used, in conjunction with the optimization algorithm, to attempt to find the global minimum of a sum of squares. For details concerning nonlinear data modeling see least squares and non-linear least squares, the assumption underlying this procedure is that the model can be approximated by a linear function. F ≈ f 0 + ∑ j J i j β j where J i j = ∂ f ∂ β j and it follows from this that the least squares estimators are given by β ^ ≈ −1 J T y. The nonlinear regression statistics are computed and used as in linear regression statistics, the linear approximation introduces bias into the statistics. Therefore more caution than usual is required in interpreting statistics derived from a nonlinear model, the best-fit curve is often assumed to be that which minimizes the sum of squared residuals. This is the least squares approach, however, in cases where the dependent variable does not have constant variance, a sum of weighted squared residuals may be minimized, see weighted least squares. Each weight should ideally be equal to the reciprocal of the variance of the observation, some nonlinear regression problems can be moved to a linear domain by a suitable transformation of the model formulation. For example, consider the nonlinear regression problem y = a e b x U with parameters a and b, however, use of a nonlinear transformation requires caution. The influences of the values will change, as will the error structure of the model. These may not be desired effects, for Michaelis–Menten kinetics, the linear Lineweaver–Burk plot 1 v =1 V max + K m V max of 1/v against 1/ has been much used

6.
Abscissa and ordinate
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In mathematics, an abscissa is the number whose absolute value is the perpendicular distance of a point from the vertical axis. Usually this is the coordinate of a point in a two-dimensional rectangular Cartesian coordinate system. The term can refer to the horizontal axis of a two-dimensional graph. An ordered pair consists of two terms—the abscissa and the ordinate —which define the location of a point in two-dimensional rectangular space and we know no earlier use of the word abscissa in Latin originals. Maybe the word descends from translations of the Apollonian conics, where in Book I, Chapter 20 there appears ἀποτεμνομέναις, for which there would hardly be as an appropriate Latin word as abscissa. In a somewhat obsolete variant usage, the abscissa of a point may refer to any number that describes the points location along some path. Used in this way, the abscissa can be thought of as an analog to the independent variable in a mathematical model or experiment. For the point,2 is called the abscissa and 3 the ordinate, for the point, −1.5 is called the abscissa and −2.5 the ordinate.3 or later. The dictionary definition of abscissa at Wiktionary

7.
Dependent and independent variables
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In mathematical modelling and statistical modelling, there are dependent and independent variables. The models investigate how the former depend on the latter, the dependent variables represent the output or outcome whose variation is being studied. The independent variables represent inputs or causes, i. e. potential reasons for variation, models test or explain the effects that the independent variables have on the dependent variables. Sometimes, independent variables may be included for other reasons, such as for their potential confounding effect, in mathematics, a function is a rule for taking an input and providing an output. A symbol that stands for an input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is x, and the most common symbol for the output is y and it is possible to have multiple independent variables and/or multiple dependent variables. For instance, in calculus, one often encounters functions of the form z = f. Functions with multiple outputs are often written as vector-valued functions. In Set Theory, a function between a set X and a set Y is a subset of the Cartesian product X × Y such that every element of X appears in a pair with exactly one element of Y. However, many advanced textbooks do not distinguish between dependent and independent variables, in an experiment, the dependent variable is the event expected to change when the independent variable is manipulated. In data mining tools, the variable is assigned a role as target variable, while a dependent variable may be assigned a role as regular variable. Known values for the target variable are provided for the data set and test data set. The target variable is used in supervised learning algorithms but not in non-supervised learning, in mathematical modelling, the dependent variable is studied to see if and how much it varies as the independent variables vary. In the simple stochastic linear model y i = a + b x i + e i the term y i is the i th value of the dependent variable and x i is i th value of the independent variable. The term e i is known as the error and contains the variability of the dependent variable not explained by the independent variable, with multiple independent variables, the expression is, y i = a + b x 1 + b x 2 +. + b x n + e i, where n is the number of independent variables, in simulation, the dependent variable is changed in response to changes in the independent variables. If the independent variable is referred to as an explanatory variable then the response variable is preferred by some authors for the dependent variable. Explained variable is preferred by some authors over dependent variable when the quantities treated as dependent variables may not be statistically dependent, if the dependent variable is referred to as an explained variable then the term predictor variable is preferred by some authors for the independent variable