Hi John, maybe the free cysteine is being S-nitrosylated.

http://www.jbc.org/content/282/27/19773.full

Cys is a semi-essential amino acid, which means that it can be biosynthesized in humans.[4] The thiol side chain in cysteine often participates in enzymatic reactions, serving as a nucleophile. The thiol is susceptible to oxidization to give the disulfide derivative cystine, which serves an important structural role in many proteins.

While free cysteine residues do occur in proteins, most are covalently bonded to other cysteine residues to form disulfide bonds. Disulfide bonds play an important role in the folding and stability of some proteins, usually proteins secreted to the extracellular medium.

This raises the possibility that hemoglobin thiols may play a role in the metabolism of RBC reactive species. Human hemoglobin has only one reactive cysteine, which is positioned at the 93rd codon of the β-chains (β93Cys). The β93 Cysteine residue of hemoglobin is conserved in vertebrates but its function in the red blood cell (RBC) remains unclear. Previous studies have shown that the reactivity of the β93Cys residues towards thiol-reactive agents is allosterically controlled by oxygen-dependent changes in hemoglobin conformation with the β93Cys in the R-state being more reactive towards nitrosating and alkylating agents and to mercurials than T-state hemoglobin. Moreover, the β93Cys can affect electron transfer reactions and limit ferrous heme-derived superoxide production and reactivity with other RBC components. Finally, a role for the β93Cys in the metabolism of reactive species has been implicated by the detection of β93Cys-thiyl radicals and oxidation products (mixed disulfides and cysteic acid) in this position after treatment of cell-free and intraerythrocytic hemoglobin with H2O2 and peroxynitrite

Also, the essential role of hemoglobin β93-cysteine in posthypoxia facilitation of breathing in conscious mice. 

Hi Masood, I think you should acknowledge the papers that you copied/pasted into your answer, including  

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3821075/

Also, John was asking about myoglobin, not hemoglobin.

Hi Steingrimur

Your mentioned article is completely true.

However, We can concluded that Hb structure comprise four Mb structure. Although this not completery true but can be used. This Cys in human Mb is a unique cysteine (Cys110).

You and other can be use the following article:

http://www.ncbi.nlm.nih.gov/pubmed/16042409

Thanks! This is some very current research going on!  I also found something in my readings:

The physiological significance of cysteine

residues in Mbs has only been indirectly addressed.

Marcinek et al. (2001) proposed that the cysteine

residue is located in a nonheme ligand interaction site,

whereas Suman et al. (2009) proposed that the

presence of the uniquely highly oxidizable cysteine

residue (Carbone et al. 2005; Fang and Holmgren

2006) leads to faster autoxidation of tuna Mb (Brown

and Mebine 1969) than in the livestock counterpart.

Point mutation studies on this nonconservative substitution

could provide data that are more conclusive in

the future.

Hasan, Muhammad Mehedi, Shugo Watabe, and Yoshihiro Ochiai. "Structural characterization of carangid fish myoglobins." Fish physiology and biochemistry 38.5 (2012): 1311-1322.

Cys is also present in tuna myoglobin as in other fishes. We used this cys to study the myoglobin unfolding and it was found always free, thus, was covalently labelled with I-AEDANS. I do not think of any physiological role. The cys role seems only structural.

In myoglobins, the evolution has changed all the possible amino acids except 1 specific histidine, however the globin fold is well retained.  I can imagine only a role of defense against ROS which are often produced in the presence of Fe and phenomena of oxygenation, but the molecular mechanism of myoglobin and its physiological role are different from those of Hb.

“Heme and cysteine microenvironments of tuna apomyoglobin. Evidence of two independent unfolding regions” Biochemistry. 1982 Jan 19;21(2):212-5.

Giovanni, as Steingrimur pointed out, an S-nitrosylated cystene increases heme O2 affinity and may promote hypoxia-induced nitric oxide (NO) delivery in the trout heart and improve myocardial efficiency.

I am not an expert on physiological problems of myoglobins, but it seems to me that the presence of cys is dispersed in myoglobins of various species. Cys residues are found in some mammals, fish, reptiles, and therefore a common physiological role for this mechanism is unlikely. In addition, it is unclear whether the SNO-dependent allosteric regulation of Mb is limited to trout or whether it is more widespread among fishes. It may be that cys has a potential functional significance only for groups of specific animals, but this is physiologically weird. Why only some organisms possess this mechanism (and cysteine ) and others not? This is my question.

Cys residues are present and concerved at specific positions in most fish species (either 1 or 2) and in most reptilian species, and a function in these groups therefore appears likely. Among mammals, only Mbs from humans, mice, rats and apes contain a cysteines, which suggests that is does not play an important role in these animals. For more discussion and data see these papers (including some of my own):

Article Human S-Nitroso Oxymyoglobin Is a Store of Vasoactive Nitric Oxide

Article Expression patterns and adaptive functional diversity of ver...

Article Oxygen-Linked S-Nitrosation in Fish Myoglobins: A Cysteine-S...