Poster Y20 - Pharmacokinetic Model of a Calpain Activity-Based Nanosensor for Traumatic Brain Injury

Introduction: Traumatic brain injury (TBI) affects over 2.8 million Americans per year and leads to 300,000 hospitalizations per year. While existing tools like the Glasgow Coma Scale and medical imaging are critical to diagnosing TBI, predicting long-term and classifying mild and moderate TBI outcomes remains a challenge. Long term outcomes in TBI are the result of neurodegeneration, inflammation, and excitotoxicity during secondary injury cascade. The calpain family of proteases is one of the primary mediators of the second injury cascade with greater calpain activity leading to greater negative downstream effects. Thus, measurement of calpain activity has the potential to classify severity of disease and predict long-term outcomes. Our lab has developed a novel nanosensor that measures ectopic proteolytic activity of calpain in TBI. This tool, called an activity based nanosensor (ABN), is composed of a calpain substrate on a nanomaterial delivery scaffold which can be cleaved and lead to the accumulation of a calpain-generated analyte in the urine. In this research, we measured key pharmacokinetic parameters and built a compartmental model of how the ABN distributes throughout the body and generates a TBI-specific signal in the urine. Using our model, we explain two previously observed physical phenomena and use those explanations to improve the ABN design and application. This model is a critical framework for the design of a nanosensor tool that is sufficiently sensitive and specific to classify mild and moderate TBI.

Materials and

Methods: Materials & Methods (250 words):
ABN was synthesized by taking a calpain substrate flanked by a fluorophore/quencher pair (CPC Scientific Inc.) and attaching it to a 40 kDa polyethylene glycol scaffold with tripentaerythritol core (Jenkem Technology) using maleimide-thiol chemistry. ABN enzyme kinetics rates (KmCal,kCatCal) were measured in vitro using recombinant calpain fit to Michaelis-Menten curves. Transport rates of ABN from the blood into the brain (kBBrABN, Figure 2.A), transport rate of the cleaved substrate out of the brain (kBrBRep, Figure 2.B), and transport rate of cleaved substrate from the blood to the urine (kBURep) were measured in vivo using a controlled cortical impact model of TBI in mice and were fitted to exponential decay and logistic growth functions. Enzyme concentrations and transport rates were determined from fitting experimental blood half-life data (Figure 1, blue values). The compartmental model (Figure 1) was coded in Python using the SciPy package to solve a system of differential equations that describes ABN pharmacokinetics with an initial concentration of 588 pM, time steps of 0.25 seconds, and a tolerance of 2e-14. Fitted values were computed in MATLAB or Python. Graphs were generated by NumPy. Signal to noise ratios were calculated by comparing TBI condition to uninjured condition in the model. Uninjured condition was modeled by setting brain transport to zero due to lack of blood brain barrier disruption, mirroring our experimental observation. Effect of targeting on sensor activity and transport was estimated using a quadratic function.

Results, Conclusions, and Discussions: Using the compartmental model (Figure 1), we were able to explain two experimental observations.
First, we previously observed higher nanosensor detection in the urine of female over male mice, despite having similar nanosensor activation measured from brain tissue. To explain this observation, we measured the transport rate of substrate from the blood to the urine in male and female mice (Figure 2.C) and found that adding this to the model meant the signal for each sex the model matched the ratio of male to female signal in vivo. We also modeled signal-to-noise ratio for blood and urine in both sexes and found that urine had a more consistent and larger magnitude signal-to-noise ratio.
Second, we previously observed that our nanosensor had the highest sensitivity at a moderate level of hyaluronic acid targeting ligands. Low levels of ligand modification lead to lower total output signal and high levels of ligand modification have a high background in the uninjured condition. The model recapitulated the loss of signal-to-noise ratio at high levels of targeting ligands due to high accumulation in other organs. By interpolating enzyme kinetics and transport kinetics data from various levels of targeting ligands, we found that a moderate amount of targeting showed the greatest signal-to-noise ratio.
The knowledge from this mathematical model can inform the design of future iterations of nanosensor technology to improve their ability to classify and predict outcomes in TBI. In the future, we plan to measure parameters for additional injury paradigms such as a close head injury model or a blast model to determine whether our current ABN has sufficient resolution to classify a more mild injury. Additionally, we plan to measure the diagnostic power of our nanosensor to predict various phenotypic and functional outcomes post-TBI, including neuronal apoptosis and animal behavior.

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