Biochemical relationship definition math

Enzyme structure and function (article) | Khan Academy

biochemical relationship definition math

Biochemical systems theory (BST) is a mathematical and computational framework for . On the surface, one is faced with a simple cause-effect relationship. . Second, the result of a canonical model design is by definition a. Biochemical compounds sound very impressive, but what are they? Learn about biochemical compounds, the classes of biochemical compounds, and how. Biochemistry, sometimes called biological chemistry, is the study of chemical processes within 5 Relationship to other "molecular-scale" biological sciences; 6 See also .. Historical Encyclopedia of Natural and Mathematical Sciences.

Most population geneticists consider the appearance of new alleles by mutationthe appearance of new genotypes by recombinationand changes in the frequencies of existing alleles and genotypes at a small number of gene loci.

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When infinitesimal effects at a large number of gene loci are considered, together with the assumption of linkage equilibrium or quasi-linkage equilibriumone derives quantitative genetics. Ronald Fisher made fundamental advances in statistics, such as analysis of variancevia his work on quantitative genetics. Another important branch of population genetics that led to the extensive development of coalescent theory is phylogenetics. Phylogenetics is an area that deals with the reconstruction and analysis of phylogenetic evolutionary trees and networks based on inherited characteristics [14] Traditional population genetic models deal with alleles and genotypes, and are frequently stochastic.

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Many population genetics models assume that population sizes are constant. Variable population sizes, often in the absence of genetic variation, are treated by the field of population dynamics. Work in this area dates back to the 19th century, and even as far as when Thomas Malthus formulated the first principle of population dynamics, which later became known as the Malthusian growth model.

The Lotka—Volterra predator-prey equations are another famous example. Population dynamics overlap with another active area of research in mathematical biology: As an example, the important blood serum protein albumin contains amino acid residues.

A schematic of hemoglobin. The red and blue ribbons represent the protein globin ; the green structures are the heme groups. For instance, movements of the proteins actin and myosin ultimately are responsible for the contraction of skeletal muscle. One property many proteins have is that they specifically bind to a certain molecule or class of molecules—they may be extremely selective in what they bind.

Antibodies are an example of proteins that attach to one specific type of molecule. Antibodies are composed of heavy and light chains. Two heavy chains would be linked to two light chains through disulfide linkages between their amino acids.

Antibodies are specific through variation based on differences in the N-terminal domain. Probably the most important proteins, however, are the enzymes. Virtually every reaction in a living cell requires an enzyme to lower the activation energy of the reaction.

These molecules recognize specific reactant molecules called substrates ; they then catalyze the reaction between them. By lowering the activation energythe enzyme speeds up that reaction by a rate of or more; a reaction that would normally take over 3, years to complete spontaneously might take less than a second with an enzyme.

The enzyme itself is not used up in the process, and is free to catalyze the same reaction with a new set of substrates. Using various modifiers, the activity of the enzyme can be regulated, enabling control of the biochemistry of the cell as a whole.

The primary structure of a protein consists of its linear sequence of amino acids; for instance, "alanine-glycine-tryptophan-serine-glutamate-asparagine-glycine-lysine-…". Secondary structure is concerned with local morphology morphology being the study of structure.

Tertiary structure is the entire three-dimensional shape of the protein. This shape is determined by the sequence of amino acids. In fact, a single change can change the entire structure. The alpha chain of hemoglobin contains amino acid residues; substitution of the glutamate residue at position 6 with a valine residue changes the behavior of hemoglobin so much that it results in sickle-cell disease.

Finally, quaternary structure is concerned with the structure of a protein with multiple peptide subunits, like hemoglobin with its four subunits. Not all proteins have more than one subunit. They can then be joined to make new proteins. Intermediate products of glycolysis, the citric acid cycle, and the pentose phosphate pathway can be used to make all twenty amino acids, and most bacteria and plants possess all the necessary enzymes to synthesize them.

Humans and other mammals, however, can synthesize only half of them. They cannot synthesize isoleucineleucinelysinemethioninephenylalaninethreoninetryptophanand valine. These are the essential amino acidssince it is essential to ingest them. Mammals do possess the enzymes to synthesize alanineasparagineaspartatecysteineglutamateglutamineglycineprolineserineand tyrosinethe nonessential amino acids.

While they can synthesize arginine and histidinethey cannot produce it in sufficient amounts for young, growing animals, and so these are often considered essential amino acids. The amino acids may then be linked together to make a protein.

It is first hydrolyzed into its component amino acids. At the same time, he recognized that general nonlinear theory was too complicated for any streamlined analysis [ ]. The only realistic, feasible strategy had to be a compromise between generality and tractability, and this compromise had to be an approximation.

Indeed, it became clear later that all nonlinearities that can be formulated as ordinary differential equations can also be represented, with complete exactness, in BST [ ].

biochemical relationship definition math

Expanding the scope beyond biochemistry and metabolism, one might address this question by looking at the nascent field of systems biology. And indeed, the often declared goals and purposes of systems biology are not fundamentally different from those of early BST.

The first goal is the creation of large-scale models of an entire cell or organism. Such models would clearly be very useful in a vast array of applications, from metabolic engineering to drug targeting and the development of personalized disease simulators. The second type of understanding is the discovery of design and operating principles, which rationalize why a particular structure or process in nature outcompeted alternatives during evolution [ 343578 ].

biochemical relationship definition math

For instance, why does end product inhibition almost always target the first step in a linear chain of processes? Why are some genes controlled by inducers and others by repressors? Attaining the first goal of realistic simulators clearly requires very large models with many processes and parameters, while the second goal suggests the peeling away of any extraneous information, until the essence of a structure or process is revealed in a relatively small model.

biochemical relationship definition math

Nonetheless, at a deep organizational level, the goals are two sides of the same issue, because most large systems in biology are modular and exhibit possibly generic design features at different levels. They are organized and controlled in a hierarchical manner so that a true understanding of ever smaller functional modules greatly enhances the understanding of the system as a whole.

Biochemical Systems Theory: A Review

Thus, the core goals and aspirations of BST are still valid, with an extension in scope toward biological systems in general. The methods of analysis have of course evolved, and it is now possible, for instance, to assesS-systems with Monte-Carlo simulations of millions of runs, a feat that, a few decades ago, could only be accomplished on a few computers worldwide.

Of equal importance is the rapidly expanding availability of biological technologies, along with the enormous amounts of useful quantitative data they bring forth. Combined with a much enhanced appreciation for computational approaches among experimental biologists, there is an unprecedented exuberance that we might indeed be able to formulate and parameterize very large models of biological systems in the foreseeable future and use these models for the betterment of humankind.

The true holy grail of systems biology will be a theory of biology. It is easy to see what such a theory could do, when we study the transition of physics from an experimental to a theory-based science. Instead of studying one application at a time, we could make and prove general statements about entire classes of biological phenomena. Some biological laws and partial theories have already been proposed, but they are scarce and isolated in certain niches.

For instance, the almost universal law of correspondence between amino acids and codons has had tremendous ramifications for the interpretation of genomic information, and the theory of evolution has helped us explain the relatedness and differences among species. Demand theory [] explains different modes of gene regulation, and the theory of multiple equilibria and of concordance [] addresses certain phenomena in metabolism.

Nonetheless, while some inroads have been made, general theories of larger biological domains seem out of reach at this point. BST and Other Canonical Modeling Approaches The key to understanding large-scale systems in biology through modeling is an effective compromise between applicability, accuracy of representation, mathematical tractability, and efficient computational tools.

It is not difficult to realize though that models consisting of vastly heterogeneous mixtures of functions and submodels, while possibly quite accurate, are not likely to permit streamlined formulations and analyses or crisp interpretations.

By contrast, homogeneous model structures provide a high potential level of tractability and elegance, especially if powerful tools like linear algebra can be brought to bear on these structures. These consist of mathematically homogeneous structures that are the result of strict construction rules which, in turn, are rigorously derived from mathematical theory.

The best-understood canonical model is the linear representation. When setting up a linear model, it is clear from the beginning that every process in the model is to be represented with a linear function and that the ultimate result will consist entirely of such linear functions.

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The reward of this severe constraint to model choice and construction is that a vast repertoire of effective methods is available for analysis.

It is this wealth of methods that, for instance, has propelled engineering to the enormous level of sophistication we discussed before. As soon as one component of the model is made nonlinear, the homogeneity is lost, and streamlined analyses are hampered, if not precluded.

While linear models are rightfully the first choice for modeling, they obviously do not account for nonlinearities, and because biological phenomena are predominantly nonlinear, linear models are not directly applicable to biological systems.

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We will see, however, that some nonlinear canonical models possess linear features that allow analyses of certain aspects of nonlinear systems. Two questions thus arise: Let us begin with the second question of why is it beneficial to accept the constraints of canonical models.

Several complementary answers may be given. First, canonical models directly address the fundamental question of how to get started with the design of a model. As indicated above, we usually do not know the biophysical processes and mathematical functions that are optimal for describing complex processes in biology. One response of the modeling community has been the use of default models or ad hoc formulations that for some reason appear beneficial, even though they might not have a biophysical or chemical foundation and even if the necessary assumptions are not really valid.

For instance, the standard representation of enzyme-catalyzed reactions is the Michaelis-Menten function [ — ], although the biochemical assumptions underlying the use of this function are typically not satisfied for metabolic pathways in vivo [ 41213 ].