Binding, specificity and molecular interactions: lessons from reproductive biology

My previous post on the sperm egg recognition molecules gave me some initial concerns. As a Biochemist brought up to believe that specificity of interactions goes hand in hand with high affinities (usually reflected in dissociation constants in the nano-molar range... which needs some explanation!). 

We measure the interaction between two molecules (such as two proteins, or a small molecule [a metabolite, a drug or an enzyme substrate]) using the simple relationship below, where A and B are two interacting molecules and the rate constant kon defines the binding or association step  and the rate of dissociation of the AB complex is given by koff. 

This is an equilibrium which is simply defined by an equilibrium constant under the experimental, or physiological conditions.The equilibrium constant (Ka) is directly related to the proportion of free A and B versus complexed AB and is given by the ratio of on and off rates:

Biochemists, often use the dissociation constant (Kd) which is the reciprocal of the equilibrium constant, and has units of concentration. Importantly the units of kon are M-1.sec-1 and koff units are sec-1. This means that the Ka is in units of M-1 and therefore Kd is expressed in molar terms and is used because it is possible to relate its significance to a concentration term. So we talk of Kds as being "in the nanomolar range" or "in the micromolar range". As a rule of thumb I think of protein:protein, or protein DNA interactions as nM; substrate interactions as mM; and cofactor interactions with enzymes as μM. These concentration units are also a reasonably good approximation to the physiological concentrations of proteins, substrates and cofactors respectively. So, the lower the (concentration) units of the dissociation constant, the higher the affinity. I shall defer a discussion here of the forces that underpin the interactions (hydrophobic, ionic, H-bonds etc.) until a later Blog.

The on rate of encounter

The association rate constant (kon) is largely determined by the rate of diffusion of two molecules (eg an enzyme and its substrate) and will therefore have units that express the rate of encounter of two molecules depending on their concentration. This is referred to as a bimolecular rate constant and has typical units of M-1.s-1. The off rate will be defined as per unit time (sec-1). What are the practical consequences? Well, an interaction characterised by a nanomolar Kd, will result from an encounter (or collision) that is generally the same for most interactions (weak or strong), but once contact is made, it will be very difficult to dissociate. Think of the fly landing on a Venus fly trap (left), where access to the interior is simple (on rate is diffusion limited), but once inside, the doors are shut (right): the off rate is very slow. The encounter between two molecules

A slow off rate!

with perfect fit (see the lock and key above) has been promoted for over 100 years (by the second Nobel laureate in Chemistry (Emil Fischer, who incidentally would have shared a platform in Stockholm with Ronald Ross from Liverpool, in 1902). We now see this as a simplification, since the intrinsic flexibility in molecular interactions is better described by a "hand in glove" phenomenon. There are occasions when the on rate is unusually low, in which case there is a barrier to interaction which must first be overcome before productive binding takes place, but the most common situation is a modified Venus fly trap where binding triggers a shape change which secures the ligand in the active site (or binding pocket).

Returning to Juno and Izumo! Why do some critical cellular interactions involve weak binding events? We must now move beyond the simple model I have described above, to consider the reproductive system. Male ejaculation releases on average 250 000 000 sperm, per egg. It is also know in humans that following a single productive encounter, no further sperm interactions lead to fusion. By comparison, consider the interaction between a bacterial repressor protein and its DNA target sequence: here encounter will block gene transcription, but eventually the repressor is likely to be released, often in response to ligand binding and the gene is expressed. Such systems are also intrinsically leaky and there may always be a level of transcription allowed to break through. However, in fertilisation the sperm egg interaction sets in motion an irreversible process and breakthrough is not acceptable!. Maybe we need to make sure this productive binding occurs therefore at a low frequency, but once it has occurred, the egg must prevent a second interaction. Weak binding can work when there is a massive excess of ligand (the sperm, in this case). But why not make a smaller number

of sperm and utilise high affinity recognition? Clearly this is not favoured in evolution. I want you to think about a system that has evolved to incorporate massive redundancy: 25m sperm, when just one would do! And then begin to calculate the dissociation constant that is likely to represent a system in which one egg (B) encounters 250 000 000 molecules of A to create an AB (fertilised egg) complex. You should assume 1000 sperm can bind to a single egg, but only one sperm triggers fusion. Think about the calculations and the problems in experimental challenges in detecting these interactions. I am glad I went back to basics and tried to appreciate the significance of this landmark discovery. I will discuss productive and non-productive binding in the context of enzymes later, but sperm egg recognition has made me think harder about specificity and binding phenomena in Biology.