Given a one-atom nanowire in the presence of an electrochemical potential, a novel formulation is presented so that the sensitivity to this potential of the number of conducting off-resonant channels is evaluated from defining a Suitable parameter which can be viewed as a normalized gradient of the above number with respect to the electrochemical potential. The range of values taken on by this parameter is determined in terms of the electrochemical potential which is assumed to take on strictly positive values only. in fact, sufficiently large strictly positive values of that potential are considered. In addition, a linear operator associated with the sensitivity parameter is introduced and discussed within a commutative semigroup structure. (C) 2009 Elsevier B.V. All rights reserved.