Stop Optimizing for the Affinity Alone Why conditional binding is the missing dimension in AI drug discovery—and how to predict it
A methods note on quantifying how binding changes between two pH environments — worked through Fc–FcRn.
Two Fc variants. Both bind FcRn tightly at acidic pH. One is engineered to extend serum half-life for months; the other to block the receptor and clear a patient’s own pathogenic antibodies.
Measured by affinity, they are indistinguishable.
Designing for the pH Switch: Adding a Fifth Axis to Apotek Landscape
When engineering biologics, tighter binding isn't always better. Consider Fc-FcRn recycling: an antibody must bind tightly in the acidic endosome but release efficiently in the neutral bloodstream to achieve a long serum half-life. If you optimize solely for target affinity, your candidate may fail in the clinic.
Today, we are introducing a fifth axis to the Apotek Landscape: Conditional Binding. By quantifying how interface binding shifts between two pH environments, this module allows teams to predict recycling efficiency and conditional release directly from structure—on day zero, with no cold-start penalty.
Key Takeaways
A quantity the existing axes cannot express. Stability, solubility, aggregation propensity and binding affinity each describe a molecule under one set of conditions. Conditional binding is a difference between two conditions, so no single-condition prediction can represent it regardless of accuracy.
Affinity tells you how tightly. This tells you under which condition. The output is a single energy in kcal/mol, convertible to an affinity ratio between the two pH values (at 37 °C, 2 kcal/mol corresponds to a KD ratio of about 26), together with the interface residues responsible for it.
No model is trained on binding data. The conversion from pKa shift to binding free energy follows from an exact thermodynamic linkage relation, evaluated here under an independent-site approximation; it is not a fitted correlation. pKa itself is estimated by an established empirical method calibrated against experimental pKa measurements — not against binding affinities — so there is no cold start, and a novel molecule can be scored on the day it is designed.
Residue-level attribution, not just a score. The output decomposes to named positions, which turns a ranking into a starting point for design discussion.
Why Landscape Needed a Fifth Axis
A blind spot shared by every single-condition prediction
The four axes Landscape already reports share an assumption so basic it is easy to miss: each describes a molecule under one set of conditions. Stability at a temperature. Solubility in a formulation. Affinity in a buffer.
That assumption breaks for any mechanism that depends on a molecule behaving differently in two places — and FcRn-mediated recycling is exactly such a mechanism. IgG survives in circulation for weeks because FcRn captures it in the acidified endosome and releases it at the neutral cell surface [6, 7]. Capture and release are both required. A variant that improves one at the expense of the other has not been improved.
A counterintuitive consequence: tighter is not better. An antibody that fails to let go at neutral pH is not efficiently recycled, and published work in human FcRn transgenic mice found a neutral-pH affinity threshold: a variant with a pH 7.4 KD of 860 nM still cleared more slowly than the parent antibody, one at 383 nM showed no pharmacokinetic gain, and a variant with ultra-high affinity at both pH values cleared about six times faster [7]. The threshold shifts with the antibody backbone and the assay, so no single value should be assumed. Optimising affinity alone can move a candidate in precisely the wrong direction.
No single-condition prediction can express this, because the quantity of interest is a difference between two conditions. It is not a question of accuracy. It is a question of dimensionality.
What the fifth axis changes operationally
Two Fc variants with near-identical affinity scores separate cleanly once the second axis is present:
Strong binding, strong selectivity — the recycling profile, the direction for half-life extension.
Strong binding, selectivity near zero — the blockade profile, where pH dependence has been deliberately engineered away.
Weak binding — excluded regardless of selectivity.
Screening runs along the affinity axis first; selectivity ranks the candidates that survive. For the comparison to hold, both numbers must come from the same structure and the same interface residue list.
On Provenance
The thermodynamic relation underlying this method has been examined for decades and applied to protein–protein association by multiple groups, including in combination with structure-based pKa prediction [3]. Proteome-scale surveys now pair fast pKa predictors with predicted structures to screen for pH dependence [9].
This is not a new theory of conditional binding. What is specific here is the system, the window, and the intent to report the result alongside the other developability axes — not the physics.
The same expression carries both directions of the switch through the sign of the pKa shift, so designs intended to release under acidic conditions require no change to the formulation.
What the Quantity Cannot Tell You
These are properties of the quantity itself, not gaps to be closed by more computation.
It reports a difference, by design. The pH-independent term cancels in the derivation — which is exactly why the calculation is affordable. The same cancellation means no absolute KD is produced, so published neutral-pH affinity thresholds [7] cannot be checked against this output alone. That is what the affinity axis is for.
No half-life prediction. Recycling efficiency depends on dissociation kinetics as well as equilibrium position. This module covers thermodynamics only.
Ranking, not de novo design. The accuracy of pKa prediction is a known limitation, particularly for buried or strongly shifted groups [11], and prior art has argued explicitly that pKa shifts cannot be predicted accurately enough to guide the placement of new ionisable residues [8]. Evaluating a defined variant asks only whether the calculation ranks it correctly; designing one asks the pKa prediction to be accurate enough to place a new ionisable residue, which is a materially harder requirement.
Sites are assumed to titrate independently. The closed form requires it. Where two titratable residues sit close enough to influence one another the assumption is approximate, and coupling is documented in the very system used here as the worked example: computational work on Fc–FcRn has treated the interface histidines with explicitly coupled titration [5]. The closed form does not implement coupled titration; close pairs can be identified from the structure, and results should be read with that in mind.
Structure is assumed not to change between the two pH values. Protonation is treated as a perturbation on fixed coordinates; side-chain rearrangement, salt-bridge breakage or domain motion between the two states is not captured. For Fc this is not a remote concern: computational work on Fc–FcRn found that the free-state domain arrangement differs from the bound one and affects predictions for variants near the CH2–CH3 interface [5].
Accuracy follows structure quality, and comparisons stay within one frame. Variant structures are modelled rather than solved, so any error in the model passes into the pKa estimate; benchmark studies of high-throughput pKa predictors give the reference scale for how large such errors can be [10, 11]. Error cancellation between bound and free states also depends on shared coordinates, so comparisons across different structural sources are not valid.
Validating the Fifth Axis Together
We are actively benchmarking this thermodynamic model against proprietary, multi-pH variant datasets. If your team is engineering Fc domains, lysosomal release mechanisms, or tumor-microenvironment therapeutics and has experimental pH-dependent affinity data, let’s collaborate. — 👉 Contact us
The method
The Physical Basis
Binding and protonation are two readings of the same event. When FcRn approaches, its acidic residues stabilise the positive charge on an interface histidine. Viewed from the proton, that histidine becomes more willing to hold a proton — its pKa rises. Viewed from the binding event, the protonated histidine holds the receptor more tightly. The two descriptions report the same energy.
The binding polynomial formalism introduced by Wyman and the linkage relation developed by Tanford make this exact rather than analogical; the same formalism has since been applied to protein–protein association in computational work [3, 4]. Writing a two-state partition function for each titratable site and assuming the sites titrate independently, the pH dependence of binding has a closed form:
where Z(pH) = 1 + 10(pKa − pH) for each titratable site
Sign convention. ΔΔGpH = ΔGbind(pH 6.0) − ΔGbind(pH 7.4). A negative value means binding is tighter at the acidic pH, which is the recycling direction for FcRn; a positive value means it is looser.
In plain terms: how much more willing the interface is to hold a proton when the partner is present than when it is absent, and how much of that difference falls inside the physiological pH window.
Every term that does not depend on pH — van der Waals contacts, the hydrophobic effect, configurational entropy — cancels when the two pH values are subtracted. Those are precisely the terms that make absolute binding free energy expensive and unreliable to compute. What remains is a function of pKa alone, and pKa can be estimated from a static structure in seconds.
The calculation is cheap because it is not computing binding energy twice. It is computing a difference that happens to depend only on protonation.
The trade is explicit. By removing the terms that dominate absolute binding free energy, the accuracy of the result rests entirely on how well the pKa values are estimated. That is a narrower and better-characterised problem than absolute affinity — but it is where the remaining uncertainty is concentrated.
Which residues matter is set by the window, not by the method
Proteins contain nine kinds of titratable group: the side chains of aspartate, glutamate, histidine, cysteine, tyrosine, lysine and arginine, plus the two chain termini. Their unperturbed transition points span roughly pH 3 to 12.
A group only responds to pH near its own transition. Outside that range both of its states are saturated, and it contributes nothing to a difference between two pH values — however large its pKa shift on binding. A glutamate at an interface can shift by several pKa units and still contribute almost nothing, because its transition sits near pH 4 and both states are already saturated at 6.0 and at 7.4.
The selection is therefore done by the window, not by us. For FcRn recycling the window is 6.0 to 7.4, and histidine, with an unperturbed pKa near 6.5 [1], is the only common side chain whose transition sits inside it. That is why the problem collapses to a handful of interface histidines — not because the method looks only at histidine.
Move the window and the answer changes:
Lysosomal or conditional release, around pH 5.5 — histidine still dominates, but acidic side chains begin to contribute.
Tumour microenvironment, 6.5 against 7.4 — still histidine, but a narrower window: less of each shift is realised, so the signal is smaller and the tolerance for pKa error is tighter.
Formulation, 5.5 to 6.5 — aspartate and glutamate carry a meaningful share.
For this reason no group is excluded in advance. The environment can move a pKa a long way — buried acidic residues shifted into the neutral range are documented — so every titratable group at the interface is computed, and the arithmetic sends the irrelevant ones to zero on its own.
How the Calculation Runs
Four steps, two of which are existing Landscape capability.
Structure preparation. The binary Fc–FcRn system is extracted from a reference complex and missing side chains are completed. Variants are built on that common scaffold so that every comparison shares coordinates, and interface residues are identified by the same heavy-atom distance criterion the binding module already uses. Albumin and Fc occupy distinct sites on FcRn in the co-crystal structure used as the scaffold [6], so the Fc–FcRn interface can be taken from it by removing albumin.
Protonation and pKa. Hydrogens are placed and the hydrogen-bond network optimised, then pKa is estimated for every titratable interface residue from three empirical environment corrections — desolvation, hydrogen bonding and charge–charge interaction [1, 2]. The free state is produced by deleting the partner chain from the same coordinates, so the pKa difference reflects the partner’s electrostatics and nothing else.
Selectivity conversion. The two pKa sets enter the closed-form expression above. This is the only component written in-house.
Scoring and attribution. Ranking across variants, plus a per-residue decomposition identifying which positions drive the result.
Because pKa is a property of the structure rather than a function of pH, only two pKa calculations are required per molecule. The two pH values appear solely as substitutions in the final expression. The stack is fully open-source; the pKa and conversion steps run in seconds, with structure preparation dominating end-to-end runtime.
Why There Is No Model Trained on Binding Data
Most computational offerings in this space share a dependency: they need labelled data. For conditional binding, that data barely exists. Published Fc–FcRn variant panels run to the order of tens to low hundreds of measurements, not thousands, and they are scattered across instruments, immobilisation chemistries and receptor sources.
A supervised model built on that foundation would be difficult to validate, and would carry the usual risk of degrading quietly outside its training distribution. The module avoids that particular problem: the relation between pKa shift and binding free energy carries no fitted weights and is not learned from the affinity data it is used to rank.
There is an empirical component, and it is worth being precise about where it sits. pKa estimation uses empirical rules whose coefficients were calibrated against experimental pKa measurements [1, 2]. That calibration target is directly measurable and comparatively well sampled, which is a materially different position from fitting a model to a few dozen scattered affinity measurements.
The practical consequence for a partner: a novel molecule can be scored the day it is designed. No data package required, no cold-start penalty, and an output that decomposes to named residues rather than a score with no provenance.
What this does not mean
It does not mean the method is parameter-free. pKa estimation is empirical, and its coefficients were fitted to data.
It does not mean accuracy is guaranteed. No training set also means no learned correction for systematic error. Whatever bias the pKa estimation carries is passed through.
It does not mean trained models are the wrong choice everywhere. Where a large and internally consistent dataset exists, a supervised model may well do better. The argument here is about the regime where such a dataset does not exist — which is the regime conditional binding is in.
What the Equation Already Tells Us
Before any calculation is run, the closed form already constrains what a pH switch can look like. These are properties of the equation, not empirical findings, and each can be checked by hand.
A single residue has a ceiling
A titratable site can hold at most one proton, so the difference in proton occupancy between the bound and free states can never exceed one. Across a window 1.4 pH units wide, that places a hard upper bound on what any single residue can contribute:
RT · ln10 × 1.4 ≈ 2.0 kcal/mol at 37 °C
No pKa shift, however large, can push a single site past that limit. A molecule showing a switch of several kcal/mol therefore requires several residues acting together — which is consistent with experimental work on engineered pH-dependent binders, where appreciable pH sensitivity has been obtained from multiple histidines each undergoing a modest shift, rather than from one residue undergoing a large one [8].
This also provides a free diagnostic: any per-residue contribution exceeding the ceiling is an implementation error, not a result.
Only part of a shift is realised
A pKa shift of Δ units corresponds to 1.42 × Δ kcal/mol at 37 °C (1.36 at 25 °C) if the proton is driven fully on and fully off. Physiology does not do that — it moves across 1.4 pH units and no further, so only part of that amplitude is realised.
How much is realised depends on two things, not one. Even with the transition optimally placed, the best achievable fraction falls as the shift grows: about 66 percent at half a pKa unit, 63 percent at one unit, 53 percent at two and 43 percent at three. Place the transition outside the window and the realised fraction approaches zero however large the shift. The optimum position itself moves — a large shift is best served by sitting toward the acidic edge, so that the two states fall at opposite ends of the window.
Two practical readings follow. Beyond roughly one pKa unit, additional shift buys progressively less. And moving a transition into the window matters more than enlarging one that sits outside it.
Where the sensitivity to error sits
The same curvature determines where prediction error hurts, and what matters is where each state’s transition sits relative to the window, not the size of the shift. Take a site whose free-state transition sits near pKa 6.5, and express error as a central difference over one pKa unit. While the bound-state transition remains inside the window, such an error moves the result by roughly 0.6 to 0.9 kcal/mol. Once the shift pushes the bound state above the window, so that it is saturated across it, the same error moves the result by about 0.1 kcal/mol at a two-unit shift and by less than 0.02 at three. Place the free state lower, however, and even a two-unit shift stays sensitive, at about 0.5 kcal/mol. Errors of one to two pKa units have been reported even for buried ionisable groups [11], so this sensitivity is not hypothetical. Sites whose transitions lie inside the window are therefore the fragile ones, and should be flagged rather than reported at equal confidence.
About Apotek
Apotek Biotechnologies is an AI-native drug redevelopment company focused on unlocking new therapeutic potential from drug assets. By integrating causal AI, generative AI, and physics-based modeling, our platform uncovers hidden biological relationships and connects them with molecular design, developability assessment, and experimental validation. Through proprietary drug programs and collaborative partnerships, Apotek bridges computational insights with experimental validation to identify, optimize, and advance promising therapeutic opportunities.
References
Li H., Robertson A.D., Jensen J.H. Very fast empirical prediction and rationalization of protein pKa values. Proteins (2005) 61:704–721, doi:10.1002/prot.20660.
Bas D.C., Rogers D.M., Jensen J.H. Very fast prediction and rationalization of pKa values for protein–ligand complexes. Proteins (2008) 73:765–783.
Harris R.C., Shen J. et al. Protocols utilizing constant pH molecular dynamics to compute pH-dependent binding free energies. J. Phys. Chem. B (2014). Reviews use of Wyman’s binding polynomial formalism for protein–protein complexes, including in combination with structure-based pKa predictors.
Approach to study pH-dependent protein association using constant-pH molecular dynamics: application to the dimerization of β-lactoglobulin. J. Chem. Theory Comput. (2021).
A functional investigation of antibody Fc–FcRn variant binding guided by in silico free energy perturbation methods. J. Mol. Biol. (2026) 438(21):169982. Prior computational work on Fc–FcRn variants that treats the interface histidines, including His310 and His435, with explicitly coupled titration.
Oganesyan V., Damschroder M.M., Cook K.E., Li Q., Gao C., Wu H., Dall’Acqua W.F. Structural insights into neonatal Fc receptor-based recycling mechanisms. J. Biol. Chem. (2014) 289:7812–7824. Co-crystal structure of human FcRn with serum albumin and Fc (carrying the YTE mutations), PDB ID 4N0U, used as the reference scaffold.
Borrok M.J., Wu Y., Beyaz N., Yu X.Q., Oganesyan V., Dall’Acqua W.F., Tsui P. pH-dependent binding engineering reveals an FcRn affinity threshold that governs IgG recycling. J. Biol. Chem. (2015). In human FcRn transgenic mice, neutral-pH affinity above a threshold offset the benefit of tighter pH 6.0 binding, and ultra-high affinity at both pH values led to rapid clearance.
US Patent 10,927,368. Library-based methods and compositions for introducing molecular switch functionality into protein affinity reagents. Reports that appreciable pH-dependent binding requires several ionisable residues each undergoing a modest pKa shift, rather than one undergoing a large shift; also argues that pKa shifts cannot be predicted accurately enough to guide the design of such switches, and adopts combinatorial selection instead.
Sallah S., Warwicker J. Computation suggests that the cell adhesion sub-proteome is enriched for sites of pH-dependence and charge burial. PLOS ONE (2025) 20(12):e0338186. Proteome-scale pH-dependence screening combining fast pKa predictors with predicted structures.
https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0338186
Wei W., Hogues H., Sulea T. Comparative performance of high-throughput methods for protein pKa predictions. (2023). Benchmarks high-throughput, structure-based pKa prediction methods against experimental values, motivated by the structure-based engineering of pH selectivity in protein therapeutics.
Olsson M.H.M. et al. Protein electrostatics and pKa blind predictions; contribution from empirical predictions of internal ionizable residues. Proteins (2011) 79(12):3333–3345. Blind and post-prediction tests on ionisable groups introduced into a hydrophobic protein interior, with root-mean-square errors of roughly 1 to 2 pKa units.
