Some confusion is exactly what you're going to find, since the answer to your question is not truly known. Here's what is known:

1) In rigor, both heads can bind, each to an adjacent binding site on actin

2) In vitro, the two heads appear to go through rapid, successive power strokes.

3) Even if one head is hydrolytically inactive, it "helps" the second head presumably by tethering it to the actin.

4) Despite all this, the duty ratio is low overall, so the motor is non-processive in the truest sense in that it cannot "walk" along filaments.

So what is probably going on here is "micro-processivity" (my own made-up word). While a power stroke by one head is immediately followed by a power stroke by the paired head, neither head remains attached for long; the average duty ratio for the entire hydrolytic cycle is still low.

Large Subject which for me is still controversial.

Imagine a rower with two oars, the bulbous portion of each oar represents the myosin heads. Is it more efficient to row both oars simultaneously or one then the other?

No matter what the method implies that the two heads of myosin are equivalent.

So my answer is the two heads of myosin are equivalent.

But, sometimes there is a possibility of modulation for this, In fact there is a possibility to associate one myosin heavy chain with one regulatory light chain (A2) but also with only one of the two types of alkaline myosin light chains , either type A1 or type A3. Thereby the myosin monomeric complex could be with A1 or with A3. The final hexameric form of myosin could result from the assembly of homodimer or heterodimer. This situation has been demonstrated using specific monoclonal antibodies (directed against each alkali light chains specificaly) and applied on isolated myosin in electronic microscopy. This result can drive to imagine that a difference between the two heads exist in specific conditions and that may indicate any adaptation in some specific muscle.

This is not my area of research, but to Dr Guilfords insightful comments above, I would like to add that there was a study published in 2007 by Brunello and colleagues, who proposed that the second myosin head binds to actin during eccentric/lengthening contractions (thus resulting in both of the heads being attached to actin), while only one head is attached to actin during concentric and isometric contractions.

http://www.ncbi.nlm.nih.gov/pubmed/18077437

This would probably at least in part explain why muscles can generate markedly higher forces during eccentric contractions than during isometric and concentric contractions.

The binding of the second myosin head only during ecentric contractions as cited by Mathias Wernborn from Brunello's paper might be important for the energy need for this form of contraction, as only one ATP is split. See my recent editorial in the German Journal of Sports Medicine (Dtsch Z Sportmed 62 (3): 55-56 (2011), open access under www.zeitschrift-sportmedizin.de).

some old paper have also considered the situation as follows:

http://www.pnas.org/content/96/8/4402.full.pdf

Two heads of myosin are better than one for generating

force and motion

http://www.ncbi.nlm.nih.gov/pubmed/12417762

Coordination of the two heads of myosin during muscle contraction.

Thanks for all that great informations, I didn´t expected that the function of the 2nd s1 head remains somehow uncertain. Found also:

http://www.plosone.org/article/info:doi%2F10.1371%2Fjournal.pone.0012643

How do thick filaments assemble and get incooperated into the muscle sarcomers (Titin?) Is there any biochemical evidence?

Just now I am retired but probably you will find some interesting references (all in English) in the following link about “Titine” that is written in French, and that I try to maintained up to date in these research fields.

http://www.univ-montp1.fr/recherche/unites_de_recherche/physiologie_medecine_experimentale_du_caeur_et_des_muscles_inserm_u1046/equipes_teams/pour_en_savoir_plus_more_details/titine

More on the associated panel of muscle proteins (see links).

http://www.univ-montp1.fr/recherche/unites_de_recherche/physiologie_medecine_experimentale_du_caeur_et_des_muscles_inserm_u1046/equipes_teams/pour_en_savoir_plus_more_details

One possible function could be that of solely increasing friction during the sliding portion of muscle-fiber force generation, thereby making muscle function more efficient.

Maria, thanks for the link. While I'm no researcher, I've been considering for a while that these features all have a mechanical model answer that is reflected in Hill's Force-Velocity curve (http://en.wikipedia.org/wiki/File:Muscle_Force_Velocity_relationship.png).

In particular the behavior of the second Myosin head would nicely explain the irregularity of the Force-Velocity curve when V approaches zero. The parameters a and b of Hill's curve would in my opinion represent respectively the friction force of the sliding filament, and the speed of sliding of the filament (after the main Myosin head has already acted).

It's been a while since the last answer to this question.

In a recent paper (2016, below) we propose a theory that relates the muscle fibre structure to function. A by-product of this theory is a suggested function of the second myosin head. It may damp the concentric muscle contraction when the sarcomere contracts to lengths below myosin filament length.

A model of this theory can explain the whole force-length relationship (including strange behaviour of muscle fibers at short lengths) as well as the steep decline of maximal contraction velocity at short sarcomere lengths.

The key idea is that myosin heads have opposite polarity and hence the second myosin head interacts with actin filaments of opposite polarity. How this comes about within a sarcomere, please see the publication below :).

Article Myosin filament sliding through the Z-disc relates striated ...