Mechanistic and quantitative insight into cell surface targeted molecular imaging agent design

Molecular imaging agent design involves simultaneously optimizing multiple probe properties. While several desired characteristics are straightforward, including high affinity and low non-specific background signal, in practice there are quantitative trade-offs between these properties. These include plasma clearance, where fast clearance lowers background signal but can reduce target uptake, and binding, where high affinity compounds sometimes suffer from lower stability or increased non-specific interactions. Further complicating probe development, many of the optimal parameters vary depending on both target tissue and imaging agent properties, making empirical approaches or previous experience difficult to translate. Here, we focus on low molecular weight compounds targeting extracellular receptors, which have some of the highest contrast values for imaging agents. We use a mechanistic approach to provide a quantitative framework for weighing trade-offs between molecules. Our results show that specific target uptake is well-described by quantitative simulations for a variety of targeting agents, whereas non-specific background signal is more difficult to predict. Two in vitro experimental methods for estimating background signal in vivo are compared – non-specific cellular uptake and plasma protein binding. Together, these data provide a quantitative method to guide probe design and focus animal work for more cost-effective and time-efficient development of molecular imaging agents.


Literature Data on Plasma Protein Binding Cutoff
The 60% cutoff includes other examples from the literature of low plasma protein binding molecules in addition to the integrin binders presented here. Not many papers report the plasma signal at 24 h for low molecular weight compounds with low plasma protein binding, likely because the sensitivity of the technique has to be very high to detect several logs of clearance. It is also pertinent that extrapolation of a bi-exponential decay is not appropriate. While this provides a good description of clearance over several hours, over longer times other mechanisms besides redistribution and liver/kidney clearance become important. For example, the data in Fig 5A was not fit to a biexponential decay, since these fits could not account for the 24 h time point. Although it does not have a functional handle to label molecules, the NIR dye SIDAG has a reported low 57% bound fraction in the plasma. This uses two sugar molecules to provide hydrophilicity along with two sulfate groups, resulting in a hydrophilic dye with only -1 net charge. With SIDAG, the authors postulated that tubular reabsorption from the kidney as a mechanism that could play a role in the signal over 24 to 48 hrs. Since the clearance values are several orders of magnitude (3-5 logs of clearance), even a small amount of reabsorption could impact the plasma signal. Harris et al. 2003 reports a 24 h blood signal of 0.06 %ID/g 1 . Estimating the initial signal as ~31 %ID/g (100% of the dose in 3.2 mL of blood assuming the reported 27 g mouse 2 and 12 mL/100g 3  Another estimate of plasma clearance for a low molecular weight compound can be found in the pre-targeting literature. Kranenborg et al. reported a 24 h time point for tumor and the tumor-to-blood ratio with In-DTPA. Using the reported tumor signal at 24 h (1.3 %ID/g) and the tumor-to-blood ratio of 480, this results in a blood signal of 0.0027 %ID/g at 24 h. Using the same initial concentration in the blood as above (31 %ID/g), this results in approximately 4 logs of clearance. Since In-DTPA has less plasma protein binding than 99mTc-DTPA 4 , which has been measured at < 5% 5 , the protein binding is negligible for In-DTPA. One caveat of this estimate is that 4 days prior to the measurement, a bispecific antibody was injected, which could slow down clearance due to specific binding. However, the In-DTPA was given in 10-fold excess, and based on the reversible monovalent binding to the antibody, it is not known how much this impacts the 24 h clearance.
The two results above with much lower plasma protein binding levels than the current dyes indicate that 3-4 logs of clearance may be the maximum attainable. Since 3-4 logs of clearance were obtained with the AF680 and ZW800 conjugates that have 70-80% plasma protein binding, there is likely a limited benefit in obtaining a lower fraction bound. Based on the extrapolation in Fig. 5C, the limit of 60% bound was selected.

Reported plasma protein binding data and cell uptake
Rapid Equilibrium Dialysis (RED) was used to quantify plasma protein binding for various fluorescent dyes (carboxylate form) and fluorescent conjugates. RED plates are available with membrane molecular weight cutoffs of either 8 kDa or 12 kDa. Given that many of the fluorescent conjugates are >1 kDa, the 12 kDa plate were used to reduce the equilibration time between chambers (Table 1). The 12 kDa RED plate gave consistent results with small variation for all compounds tested except for ZW800 carboxylate, as seen in the higher standard deviations reported. It is possible the overall net positive charge on the molecule is responsible for interactions with the dialysis membrane. The 8 kDa RED plate resulted in lower plasma protein binding, which would be unexpected based simply on equilibration time. An ultrafiltration method (Centrifree Ultrafiltration Device, Millipore) resulted in lower but variable values of 41 +/-9% bound for ZW800 carboxylate.
With the exception of ICG and SIDAG, which do not have functional handles for conjugation, the other dyes contain a carboxylate group that will not be present once the dye is conjugated to the targeting ligand. The optical properties of ICG are highly dependent on the microenvironment of the dye, which is impacted by plasma protein binding and partitioning 6,7 . Additionally, ICG is often delivered at very high doses, which can potentially saturate some binding sites in plasma and increase the free fraction. The estimates here are based on a subsaturating concentration of ICG 8 .
For cellular uptake experiments, HEK-293 cells were used initially. However, the high blocking dose of integrin binder caused dissociation of these cells, so the cancer line MDA-MB-231 was used instead. Pinocytosis rates for macrophages and some tumor cell lines can approach 1.1x10 -5 /s from fluid phase uptake 9 . Therefore, the measured uptake rates are postulated to be higher due to non-specific association with the cell surface and internalization.

Tissue concentration:
Assumptions: -Equilibrium -Well mixed -"Tissue" compartment consists of bound and free imaging agent. In actuality, imaging agent leaves plasma and into the target tissue; once in the tissue, the free imaging agent binds to target receptors. We assume binding equilibrium is very fast compared to diffusion of the imaging agent out of the plasma. The model assumes the receptor in excess. For these two reasons: 1) fast equilibrium and 2) receptor in excess, target tissue and receptor-expressing cells are combined into one compartment.
Governing equations: Assuming biexponential decay in plasma: In the tissue, the peptide can be either bound or free The binding affinity, K d , can be used to relate bound, free, and receptor concentrations: Assuming P tissue is the total imaging agent concentration in the islet is the sum of P free and P bound . Assume receptor R is in excess, following equilibria equations are obtained.
The overall balance on extracellular islet concentration P islet can be written The initial condition is P(t=0) tissue =0. Substitute P plasma (t), and the equation can be written in the form dx dt Multiplying both sides by the integrating factor and reverse product rule the RHS to give d dt integration and application of the boundary condition gives (with appropriate coefficients) This will model the extracellular concentration of probe in the tissue. To find the intracellular concentration, we use the governing equation for the intracellular compartment Boundary condition is at t=0, P int =0. With appropriate substitutions, the resulting ODE can be written in the form dP int dt Multiplying both sides by the integrating factor e k deg t and reverse product rule the RHS to give d dt integration and application of the boundary condition gives (with appropriate coefficients)

Assumptions
Model assumptions 1. Subsaturating dose higher doses will lower TBR, so optimal assumption 2. No blood flow limitations Important for tumors, which have slower blood flow rates. An extremely rapid clearance may not allow the tumor vessels to fill with probe. 3. Non-specific uptake is linear with concentration There could be non-linear background uptake (e.g. target specific), but pinocytosis, nonspecific binding, etc. are often linear. Simplifying assumptions 4. High affinity Assumes all probe that enters tissue binds and does not dissociate, so optimal assumption. Internalization may help put a limit on the affinity, since once k e >> k off , all of the bound probe internalizes. 5. k deg << k α and k deg << kint This is an optimal estimate to maximize the signal.
6. The imaging time is greater than k α so the majority of probe is cleared from the blood This is a optimal estimate. The signal in blood (both target and non-target) will lower the specific TBR since it is non-specific signal. The combination of assumptions 4 and 5 above allows us to assume k deg ~ 0 so exp(-kdegt) ~ 1 and exp(-k α t) ~ 0

Target Tissue
For the target tissue, starting with the model solution above: At long times, all the blood and surface signal is gone, so only P int determines the signal.
If the imaging time is after clearance, and degradation is negligible Using assumption that k deg << k alpha/beta and k int and adding phi:

Non-target tissue
For non-target tissue, assuming first order internalization of probe non-specifically in the tissue. This in place of the high affinity assumption, but all other assumptions apply.
Looking at long times after the probe has cleared from the blood: If the uptake is non-specific and linear with concentration, this is the same as a very low affinity antibody where the bound portion is linear with concentration (Kd ! large): The first term incorporates washout from the tissue for the unbound probe, and the second term is linear in concentration. The form is first order, but the mechanism is completely different, so we will substitute a new constant, k int,ns , which stands for k internalization, non-specific (ns): We will also assume that the imaging time as after plasma clearance but before significant degradation (assumptions 5 and 6) Using assumption 5 (specifically that k deg << k int,ns and clearance, in this case Maximizing TBR: The initial plasma concentration (dose) and plasma clearance cancel from the analysis.
The PS/V terms do not cancel, since these are the permeability surface area products for the target and non-target tissues, which can be different.
The permeability surface area product on the right is for the non-target tissue: If the washout rate is higher than non-specific internalization (which is critical for imaging), the ratio is: Since the physiology of the target tissue is difficult to manipulate, the probe should be designed to have minimal non-specific uptake.
Other notes: a.
If there is no non-specific uptake in the background tissue, then the background always goes to zero at long times. This assumption is likely not true and ignores the background from autofluorescence or instrument noise (for radioactivity). b.
Faster clearance helps to keep assumption 5 and 6 true (imaging after everything cleared from the blood but little degradation), which is not the case for antibodies, for example.
c. The internalization rate, k int , can help if there is low expression of target in the tissue. The internalization and recycle will prevent the dose from reaching saturation (since super-saturating doses lower the TBR). In other words, it helps maintain assumption 1.

d.
Lower affinity would increase washout from the target tissue, lowering the TBR.
e. The MW of the probe affects clearance, but this appears to cancel out for TBR.
However, the permeability of the target and non-target organs are a function of MW. For certain tissues (such as tumors), maximizing the ratio of permeabilities between target and non-target tissue would maximize the TBR.  Table S2. Plasma flow rate, organ volume, and organ mass % were compiled from the literature. To convert plasma flow rates to mL/min/g, organ masses were used. Organ masses were either reported or calculated using organ mass % and total animal mass of 25 g for mouse data 27 . For tumor, a literature reported value of 0.1 mL/min/g was used as the blood flow rate and converted to plasma flow rate assuming a hematocrit of 0.45 29 .

Capillary permeability data
Endocrine and exocrine pancreas plasma flow rates were reported in literature 30 .  Table S5. Previously published data on tumor and endocrine pancreas uptake. For tumor, several affibody probes were considered in addition to various radiolabels. For islet targeting, three exendin-based compounds were considered. For predicted uptake values, dissociation constants were recalculated assuming constant activation energy to account for temperature differences between affinity measurements and the in vivo experiments.

Impact of vascular density on simulations
Figure S1. Contour plots for tumor uptake of a small peptide to demonstrate the effect of blood vessel surface area to volume (S/V). Top plot uses an S/V value of 60 cm -1 ; bottom plot uses an S/V value of 200 cm -1 . Two noticeable differences between the plots include 1) a higher maximum tumor uptake with a greater S/V (top) and 2) near-maximum uptake occurs at a higher binding potential (higher expression or lower affinity) for greater S/V.  54 and Kossodo et al. 55 and obtained from ChemPartner.   Figure S3. HPLC chromatogram (254 nm) for purified 800CW conjugate. Figure S4. HPLC chromatogram (254 nm) for purified AF680 conjugate. Figure S5. HPLC chromatogram (254 nm) for purified ZW800 conjugate.  Figure S6. HPLC chromatogram (254 nm) for purified B650 conjugate. The peak at 3.5 min is DMSO used to dissolve the extremely lipophilic conjugate. Figure S7. MALDI for the IRDye 800CW conjugate.

Charge versus Tumor to Muscle Ratio
A correlation between charge and TBR was also investigated using uptake values from the PSMA and integrin targeting compounds. Figure (above) shows a plot of TBR versus the overall charge of all compounds at pH 7.4. The plot suggests no evident trend between charge and uptake (R 2 =0.05, R 2 =0.01 for PSMA and integrin binders, respectively) likely due to the importance of chelation chemistry in determining overall molecular charge and highlighting one challenge in prediction from pure structure. 9. Exendin non-specific uptake HT1080 cells were grown in 24-well tissue culture plates. After adhering overnight, cells were incubated with 100 nM of different fluorescent exendin conjugates at 37°C. Fluorescent exendin conjugates are conjugated with either lipophilic or hydrophilic fluorophores to increase or decrease non-specific plasma protein and membrane interactions. After the each time point, cells were harvested and analyzed on an Attune Focusing cytometer to quantify the intracellular signal as a function of time. A blocking control was performed with excess non-fluorescent exendin to demonstrate the fluorescent signal is from non-specific uptake. The number of internalized molecules per cell as a function of time was used to calculate the non-specific uptake rate. Cy7 s-Exendin