Mechanistic computational modeling of monospecific and bispecific antibodies targeting interleukin-6/8 receptors

The spread of cancer from organ to organ (metastasis) is responsible for the vast majority of cancer deaths; however, most current anti-cancer drugs are designed to arrest or reverse tumor growth without directly addressing disease spread. It was recently discovered that tumor cell-secreted interleukin-6 (IL-6) and interleukin-8 (IL-8) synergize to enhance cancer metastasis in a cell-density dependent manner, and blockade of the IL-6 and IL-8 receptors (IL-6R and IL-8R) with a novel bispecific antibody, BS1, significantly reduced metastatic burden in multiple preclinical mouse models of cancer. Bispecific antibodies (BsAbs), which combine two different antigen-binding sites into one molecule, are a promising modality for drug development due to their enhanced avidity and dual targeting effects. However, while BsAbs have tremendous therapeutic potential, elucidating the mechanisms underlying their binding and inhibition will be critical for maximizing the efficacy of new BsAb treatments. Here, we describe a quantitative, computational model of the BS1 BsAb, exhibiting how modeling multivalent binding provides key insights into antibody affinity and avidity effects and can guide therapeutic design. We present detailed simulations of the monovalent and bivalent binding interactions between different antibody constructs and the IL-6 and IL-8 receptors to establish how antibody properties and system conditions impact the formation of binary (antibody-receptor) and ternary (receptor-antibody-receptor) complexes. Model results demonstrate how the balance of these complex types drives receptor inhibition, providing important and generalizable predictions for effective therapeutic design.

in the experiment or simulation, V is the volume containing the cells and the antibodies, and NA is Avogadro's number, 6.022 × 10 23 molecules per mole.For the conditions used in the flow cytometry binding assays and in the model simulations, ncell = 10 5 cells and V = 200 μL, making α = 8.3 × 10 -7 nM/(# / cell).

Normalization-Schemes
Optimization of the binding model rate constants with the different normalization schemes (detailed in Table 3) yields similar optimized parameter sets, with slightly different parameter value distributions for each scheme [Figure S4].For the optimizations normalized to the BS1 data at binding saturation in particular, the optimizations converged to a single parameter set at a very high frequency [Figure S4A].
While the optimizations with normalization against the individual antibodies do still contain a most frequent optimal point, they also yield a wider variety of possible parameter values In total, these results demonstrate that ideal normalization scheme for the model output is normalization to the amount of bound BS1 at binding saturation (i.e., "BS1, Data").This scheme showed a strong convergence to a single optimal parameter set, and simulations with this optimal parameter set replicate the experimental data well.For these reasons, this normalization scheme was selected as the primary normalization method for the model analysis as described in the Results.
Table S1.Original model parameters and their relationship to the simplified parameters after applying the model assumptions.Parameter sets where the optimization did not converge were omitted.

[
Figure S4B].Each of the distributions shows two or more commonly reoccurring values, and the lowest cost parameter value is not always the same as the most frequent value.Some of the parameter values are similar to the values from the normalization against BS1, but the kon,6R* and the koff,8R values differ by almost two orders of magnitude.Further, optimizations performed with normalization against the BS1 data, both normalized to the bound concentrations at binding saturation and normalized to the maximum bound concentration, demonstrate a greater proportion of low-cost optimal sets than the optimizations normalized to each antibody separately, as illustrated by the cumulative distribution of the cost of each set of optimal values [Figure S5].The greater variance in optimal values for the normalization to individual antibodies separately is likely due to a reduction in data meaningfulness when comparisons between antibodies are lost.Many of the parameter sets from the different normalization schemes match well to the experimental data, but a few sets show more substantial variation [Figure S7].

Figure S1 .
Figure S1.Monoclonal antibody binding model kinetics.Schematic of the IL-6Rα/IL-8RB antibody-binding model for the two monoclonal antibodies, tocilizumab (anti-IL-6Rα) (A) and 10H2 (anti-IL-8RB) (B).As in the BS1 binding model [Figure 1B], kon,6R and kon,8R describe the association rates for the formation of binary antibody-receptor complexes, and kon,6R* and kon,8R* describe the association rates for the formation ternary receptor-antibody-receptor complexes.The same koff,6R and koff,8R rate constants are used for the dissociation of both the binary and the ternary complexes.Notably, in this study we simplify the parameter optimization by assuming that the binding rate constants for the bispecific antibody [Figure 1B] are the same as the equivalent reactions for the monospecific antibodies.This figure was created with BioRender.com.

Figure S2 .
Figure S2.Relationship between initial guesses and optimized values for each binding reaction rate constant, separated by normalization options used.BS1 describes simulations that were normalized against the concentration of bound BS1 at the end time point, and Ab indicates simulations that werenormalized against the concentration of that specific antibody at the end time point.Data depicts simulations that were normalized using the bound concentrations at the binding saturation, as was done for the experimental data, and Max describes simulations that were normalized using the bound concentration at the maximum initial antibody concentration.

Figure S3 .
Figure S3.Frequency and cost of optimized binding model parameter sets, showing a limited range of values around the lowest-cost parameter set.To better visualize the distribution of the parameter sets, the plotted values are limited to one order of magnitude above and below the values from the lowest cost parameter set [Table 2].A, Distribution of optimized parameter values across all optimizations performed, with marked points indicating the values of the lowest cost parameter set.B, Relationship between optimized parameter values and the cost of the optimized parameter sets compared to experimental data, separated by parameter.Optimized points with the same value are grouped into a single point, with the point size indicating how many optimized parameter values are in the group.

Figure S4 .
Figure S4.Distribution of optimized parameter values and cost compared to experimental data, separated by parameter and normalization type.Normalization types are separated in the same way as for the initial guesses [Figure S2].A, Distribution of optimized parameter values across all optimizations performed, separated by normalization options.Marked points and corresponding labels indicate the values of the lowest cost parameter set for those specific normalization options.B, Relationship between optimized

Figure S5 .
Figure S5.Cumulative distribution of the cost of the optimized parameter sets, separated by normalization options used.The curves depict the fraction of optimal parameter sets that were below a given cost value.

Figure S6 .
Figure S6.Comparison of normalized binding curves between the different antibodies.Bound concentrations are divided among binary complexes, ternary complexes, and total bound antibody.Simulations were performed under the same conditions as the binding experiments: 10 5 cells/well, receptor expression levels from the transduced cell lines [Table1], and with a 2-hour initial association period followed by a 15-minute free antibody washout.Model output is normalized to the bound concentration of BS1 at the same initial antibody concentrations used to normalize the experimental data.

Figure S7 .
Figure S7.Model simulation results using each of the optimized parameter sets compared to the experimental data used to fit the model parameters.Simulations were performed under the same conditions as the experiment, with a 2-hour initial binding period followed by a 15-minute antibody washout

Figure S8 .
Figure S8.Simulations quantify bivalent antibody binding to IL-6R and IL-8R over time.Cell number = 1 × 10 5 for all simulations.Free antibody concentration was set to 0 nM at 2 hours to simulate antibody washout from the system.The expressions of IL-6R and IL-8R from the transduced experimental cell lines were used in the simulations [Table 1].A, Simulations with an initial BS1 concentration of 10 nM, compared to the simulations with 100 nM of BS1 shown in the main text [Figure 4].B, Simulations of tocilizumab at an initial concentration of 100 nM in the IL-6R + cell lines.C, Simulations of 10H2 at an initial concentration of 100 nM in the IL-8R + cell lines.

Figure S9 .
Figure S9.Simulated Binary (Ab-R), Ternary (R-Ab-R), and Total Bound (Binary + Ternary) concentrations of Antibody-Receptor complexes using the combination of tocilizumab and 10H2.IL-6R and IL-8R are present in a 1:1 ratio, as are tocilizumab and 10H2.Simulations were performed for 24 hours after antibody dosing.The color indicates the fraction of the total receptor (IL-6R + IL-8R) that is bound in each antibody-receptor complex type.

Figure S10 .
Figure S10.Simulations of monovalent BS1 binding.Fraction of total BS1 and receptor concentrations free and bound over varying initial BS1 concentration.The first panel shows the fraction of total BS1concentration that is unbound, and the other panels show the fraction of total receptor concentration (IL-6R + IL-8R) that is unbound and bound.The association rate constants for the formation of ternary complexes (kon,6R* and kon,8R*) were set to 0 to restrict BS1 to monovalent binding only.IL-6R and IL-8R are present in a 1:1 ratio, and simulations were performed for 24 hours after antibody dosing.

Figure S11 .
Figure S11.Simulations of the combination of tocilizumab and 10H2 restricted to monovalent binding only.Simulations were performed for over varying initial antibody and receptor concentrations.The association rate constants for the formation of ternary complexes (kon,6R* and kon,8R*) were set to 0 to restrict both antibodies to monovalent binding only.IL-6R and IL-8R are present in a 1:1 ratio, as were tocilizumab and 10H2, and simulations were performed for 24 hours after antibody dosing.The simulation conditions are the same as those shown for BS1 in the main text [Figure 6].A, Fraction of total antibody concentration (tocilizumab + 10H2) that is free (unbound) for different levels of receptor expression and initial antibody concentration.B, Fraction of total receptor concentration (IL-6R + IL-8R) that is unbound (free) or bound (in binary antibody-receptor complexes) for different levels of receptor expression and initial total antibody (tocilizumab + 10H2) concentration.C, Heat map of bound receptor fraction over varying antibody and receptor concentrations.The color indicates the fraction of the total receptor (IL-6R + IL-8R) that is bound to antibody.D, Comparison of monovalent and bivalent binding.The lines indicate the fraction of total receptor (IL-6R + IL-8R) that is bound in different complex types in the original simulations and the simulations restricted to monovalent binding only.The panels are divided by the total receptor concentration (in # receptors/cell).

Figure S12 .
Figure S12.Fraction of receptors bound in Binary and Ternary complexes and Total Bound receptor (Binary + Ternary) across different IL-6R and IL-8R expression levels and initial antibody concentrations.The color indicates the fraction of total receptor (IL-6R + IL-8R) that is bound in each antibody-receptor complex type.The antibody concentration is the total initial concentration of antibody in the system; "mAbs" refers to tocilizumab and 10H2 together in a 1:1 concentration ratio.Simulations were performed for 24 hours after antibody dosing.The panels for [Ab] = 10 nM were presented in the main text [Figure7A] and are repeated here for comparison to the other concentrations.

Figure S13 .
Figure S13.The fractional occupancy of each receptor individually when one receptor (IL-6R) is in excess.IL-8R was fixed at 10 3 receptors/cell for these simulations, while IL-6R ranged from 10 2 to 10 7 receptors/cell.The fractional occupancy indicates the fraction of the specific receptor concentration (either IL-6R or IL-8R) that is bound to antibody (either BS1 or the combination of tocilizumab and 10H2).The fractional occupancy when IL-6R was fixed and IL-8R was in excess was shown in the main text [Figure 7]

Table S2 .
binding affinities for the monospecific and bispecific antibodies calculated directly from in vitro HEK 293T cell surface binding assays.Values are given as dissociation constants (KD) in nM and were originally reported by Yang et al[28].