Why Affinity and Potency Must Be Compared Separately
A compound can bind a target more tightly in one species yet produce a stronger functional response in another. Binding affinity describes the interaction between a ligand and its target under specified binding conditions. Functional potency describes the concentration required to produce a specified response in a particular biological system. They are related, but they are not interchangeable measures.
This distinction matters when animal concentration-effect data are used to inform human projections. If species differ in target binding, a concentration that engages the target in one species may not do so to the same extent in another. Even when binding is similar, differences in receptor abundance, coupling, or downstream biology can produce different functional concentration-response relationships. Comparing the two types of data helps identify whether a species difference is consistent with target pharmacology or requires a broader explanation.
These quantities depend on what was measured. Binding results may be reported as \(K_d\), or as \(K_i\) estimated from a competition experiment. A competition assay often reports an \(IC_{50}\): the inhibitor concentration that reduces a measured binding signal by half. That value is not generally equal to \(K_i\). Functional \(EC_{50}\) values depend on the response being measured and the biological system, as well as on the compound-target interaction.
Assumptions and Interpretation of Binding Comparisons
For a simple reversible one-site interaction, let \(R\) denote unbound target, \(L\) unbound ligand, and \(RL\) the ligand-target complex. The equilibrium definition is:
Under this model, half of the target is bound when the free ligand concentration equals \(K_d\). The interpretation assumes that binding has reached equilibrium, the measured signal reflects the binding of interest, and the system is adequately represented by a single binding site with no important cooperative effects. Comparisons across species also require that the target identity, assay conditions, and concentration basis be sufficiently comparable. A difference in nominal concentration is not necessarily a difference in free concentration available to bind.
For competitive binding, the Cheng-Prusoff relation converts an observed \(IC_{50}\) to \(K_i\):
where \([L]\) is the free concentration of the labeled tracer and \(K_{d,L}\) is its dissociation constant. This relation assumes reversible competition at the same binding site, equilibrium, and the standard one-site binding model. If those assumptions do not hold, the conversion may not be valid; the measured \(IC_{50}\) should not simply be relabeled as \(K_i\).
Worked Example: Converting Competitive-Binding Results to Ki
In a hypothetical study, a competitive binding assay uses a tracer with \(K_{d,L}=2.0\) nM at a free tracer concentration of 6.0 nM. The inhibitor \(IC_{50}\) is 48 nM for a rodent target preparation and 12 nM for a human target preparation. Assume reversible competition at one site and equilibrium. Calculate each \(K_i\) and compare the inferred affinities.
Rodent preparation. The tracer term is \(1+[L]/K_{d,L}=1+6.0/2.0=4.0\). Therefore:
Human preparation. Using the same tracer term:
The ratio is \(12/3.0=4.0\). Under the stated model and comparable conditions, the compound has fourfold higher affinity for the human target, as indicated by its fourfold smaller \(K_i\). This is an affinity comparison; it does not establish a fourfold difference in functional potency or in vivo response.
Affinity is sometimes expressed as \(pK_d=-\log_{10}(K_d\text{ in M})\), or similarly as \(pK_i\). Larger pK values indicate higher affinity. For example, a tenfold decrease in \(K_d\) corresponds to an increase of one pK unit. Fold ratios are often easier to interpret directly, provided the numerator and denominator are clearly identified.
Functional Potency Is a System-Level Quantity
A functional assay measures a response, such as enzyme activity or a cellular signal, as concentration changes. For an illustrative concentration-response relationship with Hill coefficient fixed at 1, baseline \(E_0\), and maximum response \(E_{\max}\), the response is:
Here \(C\) is the concentration used in the model. At \(C=EC_{50}\), the response is halfway between \(E_0\) and \(E_{\max}\). This equation is a useful way to define and compare potency in a simple setting; it is not a claim that every assay follows this form. In particular, \(EC_{50}\) is defined relative to the response range in that assay. A change in maximum response does not, by itself, tell us whether potency changed.
Functional potency can differ between species even when binding affinity is similar. Possible explanations include differences in receptor abundance, signal amplification, coupling efficiency, or downstream pathways. Conversely, a binding-affinity difference may not yield the same-sized potency difference in a functional system. A functional response incorporates more than the binding event.
Worked Example: Similar Potency Despite Different Maximum Responses
In hypothetical functional assays using the same response definition, a compound has \(EC_{50}=30\) nM and \(E_{\max}=100\) response units in species A, and \(EC_{50}=10\) nM and \(E_{\max}=60\) response units in species B. Let baseline be zero and use the Hill-1 equation above. Calculate the responses at \(C=30\) nM and compare potency with maximum response.
For species A:
For species B:
Species B has the lower \(EC_{50}\), so it is more potent in this assay by the \(EC_{50}\) measure, but its maximum response is lower. At 30 nM, the responses are 50 and 45 units, respectively; the species with greater potency does not have the larger response at this particular concentration. The example demonstrates why potency and maximum response must be reported and interpreted separately.
Quantifying Species Differences and Judging Translation
For a positive parameter measured on the same scale in two species, a fold difference can be written as a ratio. State the direction explicitly. For potency, one useful convention is \(EC_{50,\mathrm{animal}}/EC_{50,\mathrm{human}}\); a ratio above 1 means the human \(EC_{50}\) is lower and the compound is more potent in the human assay. For affinity, \(K_{d,\mathrm{animal}}/K_{d,\mathrm{human}}>1\) means the human \(K_d\) is lower and affinity is higher for the human target. The same ratio convention must not obscure which parameter is being compared.
Worked Example: Opposing Affinity and Potency Differences
In hypothetical matched binding and functional experiments, a compound has \(K_d=5.0\) nM for a dog target and \(K_d=20\) nM for a human target. In the functional assays, \(EC_{50}=40\) nM in dog cells and \(EC_{50}=10\) nM in human cells. Assume the values are based on comparable free concentration measures and the assays use the same response definition. Calculate the fold differences and interpret their direction.
For affinity, the ratio of dog to human \(K_d\) is:
Equivalently, the human \(K_d\) is fourfold larger, so the dog target has fourfold higher binding affinity in these experiments. For functional potency:
The human functional \(EC_{50}\) is fourfold lower, indicating greater potency in the human assay. The directions oppose one another: dog binding affinity is higher, but the human functional potency is higher. Therefore, the binding result alone cannot justify directly carrying the dog concentration-effect parameter into a human projection. The discordance calls for scrutiny of the functional systems and the relationship between binding and response; it does not, by itself, identify the biological cause.
Diagnostics, Alternatives, and Limitations
A species comparison is most informative when binding and functional data are examined side by side, with species identity and concentration basis verified. Before interpreting an apparent shift, check that the target construct or ortholog is correct, that the binding experiment supports its equilibrium and competition assumptions, and that the response assays measure comparable endpoints. Inspect the full concentration-response data rather than relying only on a reported midpoint: sparse observations near the transition, an unstable baseline, or failure to define a response range can make an estimated \(EC_{50}\) unreliable.
Binding affinity can be summarized with \(K_d\) or model-based \(K_i\); functional potency can be summarized with \(EC_{50}\). Neither is universally preferable because they answer different questions. A binding measurement isolates interaction with the target more directly, while a functional assay captures the target interaction within a biological response system. Comparing both is more informative than treating either as a substitute for the other. When results are discordant, repeating a binding assay alone does not resolve differences in functional coupling; functional follow-up in appropriately characterized systems may be needed.
Direct translation of a concentration-effect parameter is most defensible when species-specific target pharmacology is sufficiently similar for the intended use, the measured concentrations are comparable, and the functional endpoints and experimental systems support the comparison. If affinity or potency differs materially, a single pooled parameter can conceal that difference. Species-specific parameters, or a mechanistic explanation for the shift, may be more appropriate than assuming identity. Even then, in vitro differences alone do not determine the in vivo response: exposure at the target and other biological processes also matter.
This comparison has limits. \(K_d\), \(K_i\), and \(EC_{50}\) are estimates with uncertainty, and small apparent differences may not be meaningful relative to that uncertainty. Assay-specific conditions can also affect the estimates. A clean cross-species comparison therefore supports a judgment about target pharmacology under those conditions, not a guarantee of equal clinical response or a complete explanation of species differences.
Check Your Understanding
Answer each question, then compare your reasoning with the solutions.
- A compound has \(K_d=8\) nM for species X and \(K_d=2\) nM for species Y. Which target has higher affinity, and by what fold difference?
- A competitive assay reports \(IC_{50}=30\) nM with tracer concentration \([L]=4\) nM and tracer \(K_{d,L}=2\) nM. Under the stated conversion assumptions, what is \(K_i\)?
- Two species have the same functional \(EC_{50}\), but species A has a larger \(E_{\max}\). Are they equally potent under the \(EC_{50}\) definition? Do they have the same maximum response?
- Why is it not sufficient to infer equal human and animal functional potency from similar binding affinity?
Solutions. (1) Species Y has higher affinity because its \(K_d\) is smaller. The ratio \(8/2=4\), so affinity is fourfold higher for Y by this \(K_d\) comparison. (2) The tracer factor is \(1+4/2=3\), so \(K_i=30/3=10\) nM. (3) They have equal potency by the \(EC_{50}\) measure, but not the same maximum response; species A has the larger \(E_{\max}\). (4) Similar binding affinity does not establish equal receptor abundance, coupling, signal amplification, or downstream response. Functional potency must be compared using functional data from appropriately comparable assays.