Total least squares fitting Michaelis–Menten enzyme kinetic model function

The Michaelis–Menten enzyme kinetic model f(x;a,b)=ax/(b+x)f(x;a,b)=ax/(b+x), a,b>0a,b>0, is widely used in biochemistry, pharmacology, biology and medical research.Given the data (pi,xi,yi)(pi,xi,yi), i=1,…,mi=1,…,m, m⩾3m⩾3, we consider the total least squares (TLS) problem for the Michaelis–Menten model. We show that it is possible that the TLS estimate does not exist. As the main result, we show that the TLS estimate exists if the data satisfy some natural conditions. Some numerical examples are included.