[Nescafe]

Can someone please explain this subject to me. I have been reading on it for hours and I am still so lost. I came across this http://www.pearsonhighered.com/mathews/ch07/fi7p8.htm

 which even further confused me.


Nescafe.

[Babcock_Hall]

This topic might fit better in biochemistry.  The Hill coefficient measures the cooperativity of binding.  Hemoglobin (Hb) binds four oxygen molecules at four separate sites.  If it binds them noncooperatively (binding at one site has no effect on binding at another site), the Hill coefficient will be one; if it binds them with infinite cooperativity (all-or-nothing binding), the Hill coefficient will be 4.  For Hb the actual Hill coefficient is near three.  Myoglobin (Mb) has only one oxygen binding site; therefore, it cannot engage in cooperative binding.

When the Hill coefficient is large, it only takes a small change in concentration or partial pressure to bring about a large change in fractional saturation (which is usually given the symbol Y or θ).  That is desirable in a transport protein, because the larger the change in fractional saturation, ΔY or Δθ, under physiological conditions, the greater the amount of ligand that can be transported.  I don't entirely like the diagrams in your link, but they have some useful information, nevertheless.  Maybe you can formulate some questions and supply your best answers to them now.

[Yggdrasil]

Many proteins have multiple identical binding sites for a particular ligand.  As mentioned by Babcock_Hall, hemoglobin is a good example as it contains four binding sites for oxygen.  These binding sites are all characterized by a certain binding affinity for the ligand (i.e. how strongly do these sites bind the ligand), and binding affinities are usually expressed as the concentration of ligand required for the site to be occupied 50% of the time (the dissociation constant K_D).

Now for proteins with multiple binding sites, the question arises as to whether ligand binding at one site will affect ligand binding at the other sites.  For example, when hemoglobin binds the first oxygen molecule, does it bind the second oxygen molecule with the same affinity, a stronger affinity, or a weaker affinity?  If binding of the first ligand molecule does not affect the binding of subsequent ligand molecules, the protein is said to display no cooperativity.  However, if binding of the first ligand molecule make binding subsequent ligand molecules more difficult, the protein is said to exhibit negative cooperativity.  On the other hand, if binding the first ligand molecule makes subsequent binding events occur more readily, the protein is said to display positive cooperativity.  An extreme case of positive cooperativity is the all-or-nothing binding that Babcock_Hall mentioned: in the case of all or none binding, either all of the binding sites in the protein are occupied or none of the binding sites are occupied.  In this case, binding the first ligand molecule would greatly increase the affinity at the other sites, such that binding at the other sites occurs instantaneously after ligand binding at the first site.

To determine whether a protein exhibits no cooperativity, positive cooperativity, or negative cooperativity, one performs an experiment to measure the binding of the ligand to the protein at various concentrations of ligand.  Plotting these data on a Hill plot (or fitting the data to the Hill equation) allows one to determine the Hill coefficient for the protein.  A Hill coefficient of one indicates no cooperativity, a Hill coefficient of less than one indicates negative cooperativity, and a Hill coefficient of greater than one indicates positive cooperativity.

[Nescafe]

For Hb the actual Hill coefficient is near three

Does this mean that binding of one oxygen leads to the cooperative binding of another two but not a fourth?

When the Hill coefficient is large, it only takes a small change in concentration or partial pressure to bring about a large change in fractional saturation (which is usually given the symbol Y or θ).  That is desirable in a transport protein, because the larger the change in fractional saturation, ΔY or Δθ, under physiological conditions, the greater the amount of ligand that can be transported.  I don't entirely like the diagrams in your link, but they have some useful information, nevertheless.  Maybe you can formulate some questions and supply your best answers to them now.

I am a bit confused about this paragraph because I am really new to this topic. So thanks to our friends at wiki, theta is defined as "fraction of occupied sites where the ligand can bind to the active site of the receptor protein". Are you saying, hypothetically speaking, if the hill coefficient is large (positive cooperativity?) and we apply pressure (Like actual pressure, a bit confused by this) this will bring about a large change in the fraction of sites that are occupied before and after the pressure is applied. And since we want to transport things this indicates that sites are opening/or being occupied and therefore we have an active transporter. I am really trying to understand this but I don't think I am getting it.


Thanks Babcock, now I am going to bug Yggdrasil with a question or two regarding what he wrote

To determine whether a protein exhibits no cooperativity, positive cooperativity, or negative cooperativity, one performs an experiment to measure the binding of the ligand to the protein at various concentrations of ligand.  Plotting these data on a Hill plot (or fitting the data to the Hill equation) allows one to determine the Hill coefficient for the protein.  A Hill coefficient of one indicates no cooperativity, a Hill coefficient of less than one indicates negative cooperativity, and a Hill coefficient of greater than one indicates positive cooperativity.

What kind of experiment do they usually do to determine the binding of the ligand for the protein? (fluorescene polarization, ITC, or SPR?)  I am just curious as how these experiments are usually conduced. What you are saying makes sense. So one always looks for the hill coefficient to get any clues regarding cooperativity. And this only applies to proteins that have more than just one binding site cause, well, that makes sense this does not apply to myoglobin as Babcok mentioned.

Thank you good sir and I look forward to hearing back from you guys to help me understand this!

[Babcock_Hall]

Qualitatively, a Hill coefficient of three means that binding at one site makes binding at other sites stronger, but not infinitely stronger.  If binding at the other sites became infinitely stronger, the Hill coefficient would be 4 for hemoglobin.  Y = (number of occupied sites)/(total number of sites).  So Y is always between 0 and 1.  It might be easiest to think of the partial pressure of oxygen as being proportional to the concentration of oxygen in solution, in other words just use your knowledge of how concentration affects the position of any chemical equilibrium.

In the lungs, the concentration of oxygen is higher, and hemoglobin loads up most of its binding sites.  In muscle the concentration of oxygen is lower, and this favors dissociation of oxygen away from hemoglobin.  Given reasonable estimates for these two oxygen concentrations (as in your diagram), it is fairly simple algebra to show that a protein with a Hill coefficient of three will pick up and drop off more oxygen than a protein with a Hill coefficient of one, all else held equal.

[Yggdrasil]

I am a bit confused about this paragraph because I am really new to this topic. So thanks to our friends at wiki, theta is defined as "fraction of occupied sites where the ligand can bind to the active site of the receptor protein". Are you saying, hypothetically speaking, if the hill coefficient is large (positive cooperativity?) and we apply pressure (Like actual pressure, a bit confused by this) this will bring about a large change in the fraction of sites that are occupied before and after the pressure is applied. And since we want to transport things this indicates that sites are opening/or being occupied and therefore we have an active transporter. I am really trying to understand this but I don't think I am getting it.

An important concept when thinking about the regulation of enzyme activity is the concept of dynamic range or sensitivity.  Basically, for substrate concentration to regulate enzyme activity, varying the substrate concentration has to have an effect on enzyme activity.  At very low substrate concentrations, the enzyme activity is essentially zero, so varying the substrate concentration will not have much of an effect on an enzyme's activity.  At very high substrate concentrations, the enzyme is saturated (i.e. working at V_max), so increasing the substrate concentration will not increase the enzyme's activity any further.  Only at intermediate substrate concentrations will variations in the concentration of substrate have an appreciable effect on the enzyme's activity.  Another way of thinking about this is the range of concentrations where the enzyme goes from inactive to fully active (say going from 10% of V_max to 90% of V_max).

For a non-cooperative enzyme, enzyme activity is most sensitive to substrate concentration when the substrate concentration is near the K_M of the substrate.  The dynamic range (the range of concentrations where the enzyme goes from inactive to fully active) extends from ~0.1K_M to  ~10K_M.  

Enzymes that display cooperative behavior, however, display a much reduced dynamic range.  As a result, for most substrate concentrations, the enzyme will be either inactive or fully active, but in the small range around the K_M of the enzyme, smaller changes in concentration will have larger effects on enzyme activity.  As a result, enzymes or processes that display positive cooperativity are often called ultrasensitive or switch-like in their activity (an enzyme that exhibits infinite cooperativity would be completely inactive below a certain concentration of substrate and fully active above that concentration).

Negative cooperativity has the opposite effect: it makes the dynamic range of the enzyme larger.  Enzyme activity varies over a larger range of concentration values, but in this region, changes to the concentration of substrate do not cause very large changes in enzyme activity.

Thus, one reason enzymes have evolved cooperative behavior has been to tune their sensitivity of their activity to substrate concentrations.

What kind of experiment do they usually do to determine the binding of the ligand for the protein? (fluorescene polarization, ITC, or SPR?)  I am just curious as how these experiments are usually conduced. What you are saying makes sense. So one always looks for the hill coefficient to get any clues regarding cooperativity. And this only applies to proteins that have more than just one binding site cause, well, that makes sense this does not apply to myoglobin as Babcok mentioned.

Any type of binding experiment would work as long as you can get a reliable estimate of the free ligand concentration and the fraction of binding sites occupied.  The details of how you would back out these numbers, of course, depend on the exact method by which they are measured.

For enzymes with only one binding site, you would expect to see non-cooperative behavior (i.e. a Hill coefficient of one).  Observing a non-unity Hill coefficient could indicate that the protein you are studying is not monomeric, which could be investigated using techniques such as gel filtration chromatography.