# What are the typical values of probabilities for nonspecific binding to an antibody?

I'm physicist by training, so please excuse me if I don't use the proper terminology.

I think there is a way to make a sensor that detects if a single antibody has caught something from the flow. So I'm trying to figure out if this would be a useful sensor, but this depends on how specific the antibodies really are.

When I ask biologists "How specific are antibodies?", they reply: "Very-very specific", but provide no values that I understand on microscopic level. But I am trying to make a quantitative estimation, e.g. for the following thought experiment:

Suppose I have attached an antibody to inorganic surface. It's an antibody for catching object X. And I flow blood over the surface, slowly. Suppose there's no X in this blood at all. But there are lots (maybe 1017, or some crazy number like that) of other stray particles flowing by this antibody every second, right? So, when one of these particles bumps into this one antibody, what is the probability that it would stick to this antibody? Is it really 10-17 ? Is it really so small?

And, in any case, how do I estimate this probability at least to 1-2 orders of magnitude?

Also, how do I estimate the "collision cross section area" through which an object has to fly to make an attempt to bind to an antibody? In other words, does it only have to touch it slightly, or bump into antibody in a hard and messy collision?

Does the probability of successful bind depend on the flow speed?

How would the values change if I take serum instead of blood?

Could you please point to some relevant papers, books or just keywords? I would very much appreciate any help.

• You have to keep in mind antibody structures are complex as well as the antigens they bind to. I think it really depends on an antibody with a specific structure (the binding site of the antibody, the sequences in its hypervariable site) that's being measured. This is an older paper that touches on anitbody binding specificity. pellegrini.mcdb.ucla.edu/Lab/publication_pdfs/… Commented Apr 3, 2015 at 13:40
• The specificity of antibodies can vary. Also, the binding/unbinding rates can be different. You can look at 1977 Gillespie's paper on how to convert deterministic rate constants to reaction probabilities. For incorporating flows you need to formulate partial differential equations or corresponding stochastic models. Commented Apr 3, 2015 at 13:42

TL;DR Specificity of antibody can be not superb. It can give false-positive results in up to 90% of experiments. However, some essay are 90% specific.

That is an interesting question and there sure a lot of research done to understand specificity and strength of binding of antibody to its target.

First of all, let me say that antibody-epitope interaction is, as many biological processes, probabilistic process, which means it can go either way, however, after binding antibody need a lot more energy or time to "fall off". Direct contact is always required for establishment of non-covalent bond between antibody and epitope, because characteristic length of that interaction is very low (order or angstroms, 0.1nm and less). Point here is that you don't need to run antibody in stream, rather let is sit in solution with your sample or mix gently, random thermal motion will take care of them finding each other. In flow you will waste a lot of antibody, which is expensive.

I think that you can estimate probability of given antibody binding given molecule from their 3D structures, but this is extremely burdensome calculation. What you can do experimentally, I suppose, is label "right" epitope with red fluorescent tag, and every other molecule in your solution with green tag. Then run solution through column with antibody sitting on beads (as in chromatography), elute everything and compare green to red signal. Measuring accurately, this will tell you how much "junk" antibody picked out of solution.

Now, to numbers. Here Abcam talks about its antibody for progesterone. Molecules, closely related to progesterone, are recognized with 40-90% efficiency, compared to true-positive target (progesterone). But this is absolute-worst case scenario, because those molecules are so closely related.

On other note, antibody specificity is very important when essay is used, e.g. for HIV diagnosis. Here is nice page from U Penn, that discusses issues with specificity:

For example, in one study of 290,000 asymptomatic Minnesota blood donors donating 630,000 blood units, the false positive rate when both the screening and confirmatory assays were positive was was 0% per donation (95% confidence interval 0% to 0.0006%).

...

For example, in one study of asymptomatic Italian blood donors, only about 13% of donors with repeatedly-reactive EIA tests were confirmed to be HIV-infected on the basis of positive immunoblot. However, in a high risk population the false-positive rate can be much lower, as low as 1-3%.

I couldn't find any more precise data or studies. In biological imaging (my field) antibodies are split into "works" and "don't work, drop it" (aka high background) groups.

• Your first statement is not always true: the specificity of antibodies can vary; some can be extremely specific. Also, in antibody based chromatography there is flow, however, the antibody is immobilized and it is the antigen that is flowing. Commented Apr 4, 2015 at 6:08
• 1) Specificity of antibody can be not superb 2) I could not find data :-( My antibodies are working nice for imaging. 3) In chromatography flow is pretty slow, I think. But yes, if you fish antigen out of solution, you don't waste precious antibodies Commented Apr 4, 2015 at 6:13
1. Clarify, when you say "antibody" do you mean a monoclonal antibody (where every antibody is identical, and therefore a pure population), or do you mean a polyclonal antibody (which is a mixture of antibodies that all recognize the same antigen, but may each be recognizing different epitopes on the antigen)? A monoclonal Ab (mAb) recognizes a single epitope.

2. Textbooks and supplier catalogs often act like Ab binding is absolute, as if you could not measure the three quantities: molar concentration of free antigen, molar concentration of free mAb, and molar concentration of bound antibody antigen complex. In other words, as if every antibody is fully occupied all the time, once the Ab encounters a molecule of free antigen. But I think you can discern from the discussions and answers above that not all Ab are created equally.

In cases where people have measured this Kd (the dissociation constant) for a "tight" binding antibody the value is in the order of 10EE-14 or smaller (as I recall). When we say tight binding we usually mean that the so-called off-rate is very slow, with a t1/2 on the order of hours. In a typical reaction the on-rate is usually limited by the rate of diffusion, and cannot be faster (but search for discussions of lac Repressor DNA binding protein finding its targets with kinetics that are faster than the rate of diffusion!)

1. The device you are describing (that detects binding events using fixed proteins on a surface and target proteins in solution) measures surface plasmon resonance, and at one point was available for purchase under then brand name BIAcore. It was developed by Mel Simon, at CalTech.

2. Finally, if your goal is an automated way to use antibody reagents to detect vanishingly small quantities of antigen in a complex mixture of fluid, you would do well to familiarize yourself with the radioimmunoassay (RIA), it can be exquisitely sensitive. Keep in mind that all of these different techniques will have a lower limit of detection such that a negative result ("We could not measure any of protein X in the sample from this patient") always has to be considered with the proviso of "using this particular detection assay". So it is a type of confidence level.

• I understand that you talk about false-negative binding. $K_d$ is about probability of false-negative binding — antigen is present, but antibody doesn't bind it despite being specific to it. What I'm asking is the probability of a false-positive binding — a probability that non-target particle will bind to this antibody. That is, a particle that is not the antigen this antibody is specific for. Commented Apr 6, 2015 at 16:10
• Thanks for the links about BIAcore, but their methods don't count individual single particles. They measure the average signal over entire sensor surface, in an ensemble-averaging way. I'm talking about seeing a single bound particle - as in the detection scheme by Zybin et al. Commented Apr 6, 2015 at 16:14