Inference of a haploid biosynthetic pathway

X, Y and Z are metabolites in a biochemical pathway;
    A, B, & C are enzymes that convert a precursor metabolite to X, X to Y, and Y to Z, respectively.
        A fully functional pathway permits growth.

Mutant strains are unable to grow:
    Some enzymatic block prevents synthesis of some metabolite from its precursor
    Growth occurs if any downstream metabolite is added (the mutant is "cured").
    If the addition of a metabolite enables growth of a mutant strain,
        then the block occurs before synthesis of that metabolite,
        or, the metabolite occurs in the pathway after the block.

Consider seven arg^- mutant strains of Neurospora that cannot grow on minimal medium:
     some of them can grow when supplied with the amino acids arginine, citrulline, and/or ornithine

    arg^-4 mutant strain grows with addition of any of arg, cit, or orn:
        block must precede all three,
            => block affects metabolism of precursor substance

    arg^-1 mutant strain has a specific requirement for arginine:
        block must occur immediately before arg, after both orn & cit
            => arg is last product in pathway

    arg^-2 mutant strain is 'cured' by citrulline, and not by ornithine:
        block must occur before cit, and after orn
        block prevents conversion of orn to cit
           => cit occurs after orn

Arginine biosynthesis  as inferred from preceding data [an alternative presentation]:

Homework: Are arg4, arg2, and arg1 different alleles of the same gene, arg? Explain why or why not?