It is difficult to provide a precise answer without seeing the raw data as a direct plot of rate versus substrate concentration. Kinetic parameters should not be determined using a Lineweaver-Burk plot, but using a non-linear fit to the Michaelis Menten equation. The reciprocal transformation introduces errors that are much higher at low substrate concentrations of substrate and linear regression should not be used to analyze the data. Assuming your data set is robust, then another possibility is non-M-M kinetics, e.g. allosteric activation or inhibition. There are sample plots of this in the venerable textbook "Enzymes" by Dixon and Webb.

It is difficult to provide a precise answer without seeing the raw data as a direct plot of rate versus substrate concentration. Kinetic parameters should not be determined using a Lineweaver-Burk plot, but using a non-linear fit to the Michaelis Menten equation. The reciprocal transformation introduces errors that are much higher at low substrate concentrations of substrate and linear regression should not be used to analyze the data. Assuming your data set is robust, then another possibility is non-M-M kinetics, e.g. allosteric activation or inhibition. There are sample plots of this in the venerable textbook "Enzymes" by Dixon and Webb.

Is there an irreversible inhibitor in the reaction medium?

Jozef makes a good point. Generally the ideal range of substrate concentrations range from 0.2 to 5 times the Km obtained from an inital experiment. Doubling dilutions generally provides a suitable rate versus substrate data set.

Hassan, sometimes the best way to answer a similar question is to do a little computer experiment.  If you have any kind of a spread sheet program available (for example MS Excel or Open Office), in a few seconds you can make up an artificial data set that represents a typical Lineweaver-Burk plot with a negative intercept.

Here is one:

1/S | 1/v

1 | 0.5

2 | 1.5

4 | 3.5

8 | 7.5

16 | 15.5

32 | 31.5

Note that the "1/v" values are all equal to the "1/S" values, minus 0.5.  That means that this line has a slope of 1.0 and intercept -0.5.   The intercept is negative, which is what we are trying to understand.

Now you can use your spreadsheet program to invert the 1/S and 1/v values, to produce the "original data" (i.e. the substrate concentrations, S, and the initial rates, v).  When you do that with the above L-B plot data, here is what you get:

S | v

1.000 | 2.000

0.500 | 0.667

0.250 | 0.286

0.125 | 0.133

0.063 | 0.065

0.031 | 0.032

And now  you can make a simple plot of this "raw data".  [Please see the attached screen shots from Excel.] What does the plot look like to you?  Does the plot suggest a possible mechanistic reason for the negative intercept?

Also, what does the plot say about the applicability of the Michaelis-Menten rate equation (and therefore, indirectly, about the applicability of the Lineweaver-Burk  transformation) for  the analysis of any data that show this behavior?

An an alternative to these essentially algebraic methods of analysis (dating back to the first half of the 20th century), you might wish to explore the symbolic/numerical method of kinetic analysis, as implemented in the software package DynaFit (free for academic users):

     http://www.biokin.com/dynafit/

In DynaFit, we could probably model the data I just simulated above by using the notation similar to this:

[mechanism]   ; "sigmoid",  "activation"

   E + S ES   :    Ks     dissoc

   ES + S ESS    :   Kss    dissoc

   ESS ---> E + P  :  kcat

I haven't tried it myself, but maybe you could try...  If so, let us know what you find  Hope this helps.

Are your LB plots linear ones)