{\displaystyle \mathbf {T} ^{n}=\underbrace {S^{1}\times \cdots \times S^{1}} _{n}.} The 1-torus is just the circle: T1 = S1. The torus discussed above is the 2-torus, T2. And similar to the 2-torus, the n-torus, Tn can be described as a quotient of Rn under integral shifts in any coordinate. That is, the n-torus is Rn modulo the action of the integer lattice Zn (with the action being taken as vector addition). Equivalently, the n-torus is obtained from the n-dimensional hypercube by gluing the opposite faces together. An n-torus in this sense is an example of an n-dimensional compact manifold. It is also an example of a compact abelian Lie group. This follows from the fact that the unit circle is a compact abelian Lie group (when identified with the unit complex numbers with multiplication). Group multiplication on the torus is then defined by coordinate-wise multiplication. Toroidal groups play an important part in the theory of compact Lie groups. This is due in part to the fact that in any compact Lie group G one can always find a maximal torus; that is, a closed subgroup which is a torus of the largest possible dimension. Such maximal tori T have a controlling role to play in theory of connected G. Toroidal groups are examples of protori, which (like tori) are compact connected abelian groups, which are not required to be manifolds.
Ecallantide (trade name Kalbitor) is a drug used for the treatment of hereditary angioedema (HAE) and in the prevention of blood loss in cardiothoracic surgery. It is an inhibitor of the protein kallikrein and a 60-amino acid polypeptide which was developed from a Kunitz domain through phage display to mimic antibodies inhibiting kallikrein. Medical uses
Angioedema
On November 27, 2009, ecallantide was approved by the FDA for the treatment of acute attacks of hereditary angioedema for persons over 16 years of age. A single dose requires three separate injections, which are given under the skin.Ecallantide does not appear to be efficacious for the treatment of angioedema due to ACE inhibitors. Adverse effects
The most common adverse effects are headache, nausea, fatigue and diarrhea. Less common, but observed in more than 5% of patients in clinical trials, are respiratory tract infections, fever, vomiting, itching and upper abdominal pain. Up to 4% of patients showed anaphylaxis, which led to a black box warning in the US. Interactions
As of 2011, no interaction studies have been conducted. Mechanism of action
HAE is caused by a mutation of the C1-inhibitor gene. Defective or missing C1-inhibitor permits activation of kallikrein, a protease that is responsible for liberating bradykinin from its precursor kininogen. An excess of bradykinin leads to fluid leakage from blood vessels, causing swelling of tissues typical of HAE. Ecallantide suppresses this pathogenetic mechanism by selectively and reversibly inhibiting the activity of plasma kallikrein. Ecallantides inhibitory constant (Ki) for kallikrein is 25 picoMolar, indicating high affinity.