A genetically modified mouse (Mus musculus) is a mouse that has had its genome altered through the use of genetic engineering techniques. Genetically modified mice are commonly used for research or as animal models of human diseases, and are also used for research on genes.
In 1974 Rudolf Jaenisch created the first genetically modified animal by inserting a DNA virus into an early-stage mouse embryo and showing that the inserted genes were present in every cell.  However, the mice did not pass the transgene to their offspring, and the impact and applicability of this experiment were, therefore, limited. In 1981 the laboratories of Frank Ruddle  from Yale University, Frank Costantini and Elizabeth Lacy from Oxford, and Ralph Brinster and Richard Palmiter in collaboration from the University of Pennsylvania and the University of Washington injected purified DNA into a single-cell mouse embryo utilizing techniques developed by Brinster in the 1960s and 1970s, showing transmission of the genetic material to subsequent generations for the first time.    During the early eighties, Palmiter and Brinster developed and led the field of transgenesis, refining methods of germline modification and using these techniques to elucidate the activity and function of genes in a way never possible before their unique approach. 
There are two basic technical approaches to produce genetically modified mice. The first involves pronuclear injection into a single cell of the mouse embryo, where it will randomly integrate into the mouse genome.  This method creates a transgenic mouse and is used to insert new genetic information into the mouse genome or to over-express endogenous genes. The second approach, pioneered by Oliver Smithies and Mario Capecchi, involves modifying embryonic stem cells with a DNA construct containing DNA sequences homologous to the target gene. Embryonic stem cells that recombine with the genomic DNA are selected for and they are then injected into the mice blastocysts.  This method is used to manipulate a single gene, in most cases "knocking out" the target gene, although more subtle genetic manipulation can occur (e.g. only changing single nucleotides).
Genetically modified mice are used extensively in research as models of human disease.  Mice are a useful model for genetic manipulation and research, as their tissues and organs are similar to that of a human and they carry virtually all the same genes that operate in humans.  They also have advantages over other mammals, in regards to research, in that they are available in hundreds of genetically homogeneous strains.  Also, due to their size, they can be kept and housed in large numbers, reducing the cost of research and experiments.  The most common type is the knockout mouse, where the activity of a single (or in some cases multiple) genes are removed. They have been used to study and model obesity, heart disease, diabetes, arthritis, substance abuse, anxiety, aging and Parkinson disease.  Transgenic mice generated to carry cloned oncogenes and knockout mice lacking tumor suppressing genes have provided good models for human cancer. Hundreds of these oncomice have been developed covering a wide range of cancers affecting most organs of the body and they are being refined to become more representative of human cancer.  The disease symptoms and potential drugs or treatments can be tested against these mouse models.
A mouse has been genetically engineered to have increased muscle growth and strength by overexpressing the insulin-like growth factor I (IGF-I) in differentiated muscle fibers.   Another mouse has had a gene altered that is involved in glucose metabolism and runs faster, lives longer, is more sexually active and eats more without getting fatter than the average mouse (see Metabolic supermice).  
Great care should be taken when deciding how to use genetically modified mice in research.  Even basic issues like choosing the correct "wild-type" control mouse to use for comparison are sometimes overlooked. 
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