Kinetics

The broad goals of kinetics this year is to (i) inform wetlab and protein modeling’s approach, (ii) evaluate feasibility of our project given data from wetlab and (iii) work with human practices to refine our implementation.

PKPD

Introduction

Given our project and focus on designing a novel therapeutic we immediately thought of pharmacokinetic-pharmacodynamic modeling (PKPD). PKPD is the combination of pharmacokinetics which describes where a drug goes in the body and pharmacodynamics which describes what happens when the drug gets there. Our focus on antivirulence meant that we would likely need to give our drug adjunctively with antibiotics and so the pharmacokinetics of antibiotics commonly used against pseudomonas were found from literature in addition to other common antibiotics. Specifically the elimination rate constants and volumes of distribution were found, for some antibiotics a two compartment model fit experimental data better and so k12 and k21 values were found as well.

Results

Graphs for erythromycin [top left] Azithromycin [top right] cefepime [bottom left] and cefotaxime [bottom right] are shown above along with associated MICs. Appropriate PD indices are bolded above and match literature on effective antibiotics. For example cefotaxime is known to be ineffective against pseudomonas and has T>MIC <80% while cefepime which is known to be effective has >90% coverage.

Conclusion

The PKPD data here will allow us to make predictions about the impacts of our drug on antibiotic dosing and serve as a foundation as we model adjunctive therapy.

PBPK

Introduction

While the pharmacokinetics of antibiotics have been well characterized in literature our inhibitor, being a novel therapeutic, has no data available. This presents a challenge as determining the feasibility of the inhibitor in affecting patient outcomes as any decrease in toxicity will be reliant on our binder’s concentration at site. Physiologically based pharmacokinetics (PBPK) allows us to predict a drug’s behavior in the body given known physiological parameters and its physical properties. This allows us a great insight into the behavior of our therapeutic while avoiding the need for testing in humans. PBPK also allows for the designing of our own cohort of virtual patients allowing us to predict how different weights, ages, renal functions or pregnancy status might influence our therapeutic’s pharmacokinetics and thus effects on patients. This helps us design a dosing strategy which maximizes efficacy and safety for most patients and allows us to consider people who may need a different dosing schedule, for example those with renal failure.

Results

PBPK Drug Plasma Concentrations Shown Above. In vivo data shown for cefepime and chloramphenicol displayed as dotted lines. Given high disagreement between in vivo data and predicted curves, a parameter identification on the dosage to allow for a comparison of predicted and observed clearance. In the graph, we can see that the clearance of chloramphenicol and cefepime is not as quick as expected. In the case of cefepime, some metabolism to N-methyl pyrrolidine is known to occur, which was not included in our model [5]. To better recreate cefepime’s ADME, one important step may be to include optimizing the model to clinical data from patients with renal failure. Additionally, while we had learned that piperacillin and tazobactam are both substrates of OAT1 and OAT3 [4], we could not sufficiently model transporter behavior on the antibiotics due to a lack of experimental data.

To simulate the pharmacokinetics of exotoxin A, physical and chemical properties were input into PKsim’s model for large molecules. Given that in vivo plasma concentrations for exotoxin A were not found and a dependence on infection severity, upper and lower-bound models were developed by fitting the rate such that the steady-state concentrations of our exotoxin A models to concentrations at high (95% death, 50uM) and low ends (5% death 0.2uM) of exotoxin A’s dose-response curve. The resulting rates of exotoxin A production were used in the upper-bound model and for the lower-bound model. Using rate constant estimations from the molecular dynamics simulation, a kon of 0.0001 ns^-1 * N_A * V_box = 3.41*10¹² M_-1s_-1 was used and a k_off of 2.4*107s^-1 was used. Simulations were done with intravenous administration of inhibitor every 12 hours at doses of 50mg, 100mg, and 300mg.

For the upper-bound case of exotoxin A production in the plasma and interstitial space of the lungs, only the 800mg dosage of inhibitor significantly reduces the concentration of free exotoxin in the plasma, going from the 50μM steady state to 38.37μM, while exotoxin A with 300mg doses remains at 45.67μM. Results for lung interstitial fluid exotoxin A concentrations are comparable to those of the plasma concentrations, with 800mg doses reducing exotoxin A concentration to 28.64μM. Meanwhile, we see that 800mg doses of inhibitor reduce the amount of free exotoxin A in the interstitial space of the muscles to 2.48μM from 19.26μM, and 300mg doses reduce exotoxin A concentration to 6.85μM, which can mostly be attributed to the inhibitor’s better diffusion and convection through tissues due to its smaller size relative to exotoxin A. These data would suggest that a high dosage above 800mg inhibitor every 12 hours would be required to substantially reduce the endocytosis of exotoxin A in the pessimistic case of high exotoxin A production during infection.

For the lower-bound case of exotoxin A production, higher doses were still needed to substantially reduce exotoxin A’s steady-state concentration. For example, 50ng doses of inhibitor only reduced exotoxin A’s concentration from 0.20μM to 0.19μM. 300ng doses of inhibitor reduced exotoxin A’s concentration from 0.20μM to 0.16μM in the plasma. Meanwhile, 300ng doses reduced exotoxin A’s concentration to 0.11μM and 9μM in the lung interstitial space and muscular interstitial space respectively.

The inclusion of FcRn binding of our inhibitor increases the plasma concentration of our inhibitor; at hour 120, the inhibitor’s concentration (with 800mg doses) is 21.34μM compared to 15.21μM without FcRn interaction, which we would expect given that FcRn binding typically increases therapeutic protein half-life. Meanwhile, exotoxin A final concentrations drop from 38.37μM to 35.05μM when including an interaction between FcRn. This result demonstrates the importance of binding affinity to FcRn to protein half-life. Further exploration of how we can take advantage of binding to FcRn may include simulations of the inhibition and exotoxin under different protonation states to best describe how our inhibitor might bind FcRn. In the likely case that our inhibitor does not strongly bind to FcRn, we may consider the effects of creating a fusion protein between our inhibitor and an Fc domain which can bind to FcRn. In this case, we would also anticipate reductions in renal excretion of our therapeutic and significant changes to distribution given an increase an size.

Conclusion

Predictions of the binding affinity between our designed inhibitors and exotoxin A were favorable and showed potential for our designs to be effective in reducing pseudomonas virulence. A more in depth investigation of binding between inhibitor 5 and exotoxin A showed that binding between the molecules could be simulated. Kinetic and thermodynamic descriptions of the binding could be described, but a limitation in simulation time resulted in high uncertainty in any of our predicted figures. The same problem applied to our exploration of binding to FcRn. An interesting prospect would be to employ enhanced sampling techniques such as umbrella sampling, which can provide insights without requiring unlikely events to be sampled through brute force. Through developing PBPK models, we learned about important aspects like specific interactions with enzymes and transporters that affect ADME. Meanwhile, protein therapeutics are a relatively new and exciting area of study within pharmacology, involving very different mechanisms for distribution and elimination in comparison to studies of small molecules. Our exploration of our inhibitor’s interaction with exotoxin A modeling ADME largely based on protein size showed that the population of free exotoxin A that can be endocytosed can be reduced with administration of our inhibitor, given our kinetic figures from our brief molecular dynamics simulation. We also observed that the small size of our protein inhibitor resulted in adequate penetration into peripheral tissues. Meanwhile, implementing the interaction between inhibitor and FcRn suggests that our inhibitor might possibly benefit from FcRn binding in the body, given an increase in inhibitor concentration for the same dose.

PD - Dose Response

Introduction

With the pharmacokinetics of our therapeutic known the question becomes what will happen when our therapeutic reaches its target and how this will affect the patient. To evaluate this we used the Hill Equation to predict our therapeutic's binding to ExoA then followed up with a LD50 curve to predict death rates of cells at site. Data for LD50 was sourced from liturature[3]. PBPK’s ability to predict concentrations at the level of organ systems meant we were able to tailor dosing strategies to different infections which have different localizations of pseudomonas.

Results

A simulation of C38 lung cell exposure to 100ng/mL ExoA was performed at varying drug concentrations as well as with varied kd for our inhibitor and ExoA. We found that even at ng/mL concentrations for our drug we would be able to effectively inhibit cytotoxicity given a reasonably strong hit for binding.

Conclusion

Using cytotoxicity data from literature our model proves that our drug can effectively inhibit cytotoxicity at reasonable concentrations for a therapeutic. This work provide a benchmark for protein modeling and wetlab as they design and test protein binders and gives a strong basis for the pharmacodynamics of our drug and future modeling for dosing.

Modeling of Inhibitor-Exotoxin A Binding Affinity

To model our inhibitor’s performance as a potential therapeutic against exotoxin, it is critical to be able to describe binding between the molecules. Five of our designed inhibitors with an AlphaFold ipTM > 0.9 bound to exotoxin A were selected for additional modeling. To model the competitive inhibition of exotoxin A in the body, Kd values were predicted by inputting AlphaFold structures onto Prodigy webserver. Low predicted dissociation constants for all five complexes suggest that the five selected inhibitors would strongly bind exotoxin A and viably inhibit the endocytosis of exotoxin A.

Complex Five Simulation RMSD

*RMSD of frames compared to initial structure shown. Top five most abundant clusters labeled.

Given that complex five was predicted to have the lowest dissociation constant, we were most interested in complex five’s ability to inhibit exotoxin A. Frames classified as cluster 30 appear to belong to a stable structure for complex given the steady RMSD. Residue pair energies between exotoxin A and inhibitor were calculated using Pyrosetta. Stabilizing pairwise interactions from the original AlphaFold structure were conserved to a good degree within all five structures representing the major clusters found in the simulation for complex five. Furthermore, the proteins maintained a distance similar to that of the AlphaFold structure in all five major clusters. These observations support the prediction of a low dissociation constant for inhibitor 5, given that a clearly unbound structure was not observed during the simulation.

Exotoxin and Inhibitor Five Interactions Visualized

*Pairwise residue energies below zero shown for residues with paired interactions < -0.5kJ/mol in the original AlphaFold structure.

*Pairs of residues with interaction energies < 0.5kJ/mol recorded in the original structure. The proportions of these interactions maintained during the simulation are shown.

Without observation of inhibitor unbinding during the 50ns simulation, we could not meaningfully describe the kinetics of inhibitor binding to exotoxin A. A major limitation of the simulation seems to be a limited exploration of structures due to short simulation time; there is a high uncertainty. Treating cluster 30 as the stable bound state between inhibitor 5 and exotoxin A, rate constants to bound and unbound states can be estimated as the frequency of transition from the other of the two states.

K_on = n_{binding events} / t_unbound
K_off = n_{unbinding events} / t_bound

In this case, k_on is estimated to be 0.0001/ns and k_off is 2.42E-5ns, with a binding event at 8.82ns, although k_off is likely overestimated given that an unbinding event was not identified within the simulation. Calculating K_d as k_off/k_on, we would estimate a dissociation constant of 0.214. Modeling binding and unbinding as Markov processes, a 95% confidence interval can be obtained according to [K_d / qF_{2nbinding, 2nunbinding} (p=0.975), K_d / qF_{2nbinding, 2nunbinding} (p=0.025)] [2], where qF(P) is the pth quantile of the F-distribution. In this case, the 95% confidence interval for K_d would be [0.0549, 8.23]; this amount of variation about K_d = 1 is high, and it is within uncertainty that the interaction between inhibitor and exotoxin A is unfavorable.

Inhibitor Five and Exotoxin A Simulation Trajectory

Visualizing the trajectory, we can further support that the molecules remained bound throughout the simulation, as reflected in the consistent conservation of stabilizing interactions seen throughout the simulation. This inference would suggest that the dissociation constant is likely much lower than estimated, and would better affirm the Kd predicted using Haddock. With this information, the appearance of cluster 30 as a stable bound configuration of the two proteins is likely an artifact of the proteins’ individual conformational states and possibly equilibration with the solvent in the earlier phases of the simulation. We continued to use the rough values for our PBPK models, but our findings here show that accurate prediction of binding behavior would either require simulations at much longer length (recommended lengths can exceed 500ns) or adoption of enhanced sampling techniques to estimate free energy change and transition state energies.
A check of potential binding between inhibitor 5 and the neonatal fragment crystallizable receptor (FcRn) was done to see if there would be any rescue of the inhibitor from endosomal degradation, given that FcRn is a typical target for extension of therapeutic antibody half lives. Docking was performed between FcRn’s IgG binding domain and inhibitor 5’s available residues on Haddock web server [8,9], and the Kd value for the best-docked structure was 1.3E-6M, which is unexpected given the specificity of protein therapeutics [11, 12].

In a conversation with Dr. Yvonne Lin, UW School of Pharmacy, we learned that specific enzymatic and transporter activity on protein therapeutics would be unlikely to happen as opposed to the case for small molecule drugs, limiting the number of specific interactions needed to model protein ADME. However, a variety of drug-drug interactions between proteins and small molecules should be considered for protein therapeutics, such as an alteration of protein clearance or alterations on inflammatory or immune responses [10]. Given that our therapeutic would likely be administered with other antibiotics to treat Pseudomonas infections, potential interactions between our inhibitor and expected antibiotics would be important to study. An advantage of PBPK modeling is that many mechanisms of drug-drug interactions can be simulated, whether through alterations of host physiology or modeling of reactions. To evaluate the efficacy of PBPK models for our case, piperacillin, tazobactam, ceftazidime, and chloramphenicol were selected for additional modeling.

Rosetta Interace Analysis

In addition to molecular dynamics simulations on high-ipTM candidate binders, the interfaces of 95 binder sequences with an ipTM > 0.8 were analyzed using Rosetta and compared to each sequence’s ipTM value. Based on our discussions with Professor Frank DiMaio of the University of Washington’s Institute for Protein Design, who helped create Rosetta, we first relaxed the structures in Rosetta to reach an energy minimum and then selected three metrics from the InterfaceAnalyzer tool to study in-depth: dG_cross, delta_unsatHbonds, and dSASA_int [2]. dG_cross measures the change in Gibbs free energy across the interface when two proteins bind, which in our case are ExoA and our designed inhibitor. Delta_unsatHbonds shows the number of unsatisfied hydrogen bonds at the protein-protein interface. Finally, dSASA_int is the surface area of the interface, which is measured as the area previously accessible to solvent which is now buried. Based on this information, we considered higher values to be better for dSASA_int and lower values to be better for both dG_Cross and delta_unsatHbonds.

Though none of the values shown above are significant (low R2 values), we do see the expected positive correlation between ipTM and dSASA_int and the expected negative correlation between ipTM and dG_cross. Since increased interface surface area and a larger decrease in energy after binding are both favorable for protein binding, it is logical that structures with a higher AlphaFold confidence value (ipTM) would have these trends. In future work, we hope to use additional AlphaFold confidence metrics such as ipAE and compare how our Rosetta scores correlate to those metrics. Unexpectedly, we saw that sequences with higher ipTMs had slightly larger numbers of unsatisfied hydrogen bonds. Though additional unsatisfied hydrogen bonds are likely less favorable for an interface, we explained this phenomenon by first noting the very small R2 value, which shows low correlation, and by noting that many high-ipTM structures also have larger interface surface areas, so there are more hydrogen bonds which have the potential to remain unsatisfied. To further understand why this trend may be occurring, we hope to calculate per-square Angstrom delta_unsatHbond values (delta_unsatHbond / dSASA_int), which will show us whether high-ipTM, high-delta_unsatHbond sequences also had a high interface surface area and thus more opportunities for unsatisfied hydrogen bonds to be present.

Bioinformatics

Introduction

While the toxic effects of ExoA can be quantified as above the effects may differ between cell types. The above data was generated from C38 lung cells, a model from cystic fibrosis tissue. This makes sense when studying pneumonia in cystic fibrosis patients but for other types of pseudomonas infections for example septicemia, UTIs or cellulitis the toxicity to the respective cell type can vary depending on the cell's LRP1 receptor and eF2 expression. To solve this we found data of differential expression between cell types for the LRP1 and EEF2 genes and compared tissues of interest [1].

Reults

LRP1

RNA-seq data was sourced from GTEx, a large dataset with over 800 donors. Through this we found that fat, ovary and placental tissue had the highest expression of LRP1. Increased expression of LRP1 implies greater sensitivity to ExoA in that tissue type and means our drug may need to be given at a higher dose to be effective. Increased expression in ovary and placental tissues in particular mean that greater care for pregnant patients should be taken especially those with septicemia or UTI. Fat cells also had a markedly higher expression of LRP1 implying a need for greater doses in septicemia patients. Skin had relatively low LRP1 and is thus not as sensitive to ExoA, however ExoA does play a role in breaking down the skin barrier, letting pseudomonas enter its host. A topical administration of our drug could help prevent this and buy time in a clinical setting.

ef2

Ef2 expression stays relatively constant in the body though ovary, thyroid and fat have greater expression and the liver has lower ef2 expression. All else being equal, greater ef2 expression decreases sensitivity to ExoA as more ef2 needs to be ribosylated. However, while fat, thyroid and ovary tissue have higher ef2 expression, dosing levels should be maintained to match concentrations with lung treatment as these tissues require that extra ef2 to function. The liver’s lower expression implies a need for greater doses in treatment for septicemia. As one of the most profused organs circulation of bacterial toxins in the liver is higher than in other tissues this means that blood infections can be particularly damaging. Combined with lower ef2 expression it is likely that septicemia patients will require greater dosing compared to pneumonia patients.

Conclusion

We explored differential expression data to predict how our therapeutic’s dosing may need to change in different pseudomonas infection types. We found that septicemia was likely to need greater dosing as well as pregnant patients with either septicemia or UTI. This work builds up our understanding of our drugs pharmacodynamics and presents a case for its clinical impact.

Epidemiology

Introduction

To get an understanding of the broader issue our intervention is addressing, we considered current public health conditions to better visualize the scope of our method. In particular, by focusing on ventilator associated pneumonia (VAP), the predominant form of pseudomonas-associated infection contributing to higher mortality cases in the ICU. These graphs visualize the broad impacts of pseudomonas aeruginosa infection and the relevance of treating this particular bacterial infection.

SEIR

[Fig. 1: SEIR Model of VAP infection in the U.S. at n = 800] [Fig. 2: SEIR Model of Pseudomonas aeruginosa VAP infection in the U.S. at n = 800]

[Fig. 1] This model accounts for both common means of pneumonia transmission via cross-contamination from lower airways and contact with contaminated equipment via endotracheal tube placement. Taking into account differences in hygiene standards between hospitals across the nation and variance in resistance level of bacterial populations, the infectious period is set to 2 days as different bacteria have a typical period of 1-7 days, varying due to hospital and strain-specific conditions. The broad rate of infection per a global surveillance study (Kollef, et. al.) sets the U.S.’s typical ventilator-associated pneumonia (VAP) prevalence at about 13.5%, which is used in this model. This data set includes broad infection standards, including infections specifically attributed to pseudomonas aeruginosa, as well as other bacterial origins.

[Fig. 2] The second model accounts for VAP cases directly caused by pseudomonas aeruginosa infection, including multidrug resistant and other higher intensity bacterial strains. Due to a lack of available data for pseudomonas specific transmission values, the second model uses the base prevalence in combination with case-specific ICU data to estimate a percentage as 26% of all bacterial infections (n=20 out of 75 positive cases). This shifted the prevalence to 3.64% for this 800 person population (from the original 13.5% prevalence). However, due to likelihood of resistance in pseudomonas aeruginosa, the infection period was consequently extended to account for changes in survivability and likelihood of implemented hygiene measures not working as intended to a period of 7 days that can be seen in resistant (non-multidrug) strains of the bacterium.

[Fig. 3: SEIR Model of VAP infection including differential equation for mortality (deceased) comparing and contrasting broad infection (bullet) vs. pseudomonas specific infections (linear)]

[Fig.3] One of the factors that separates severity of pseudomonas-related infection from others is the heightened mortality when compared to other bacterial populations. To account for this visually, a fifth differential equation was added to the model to select and estimate mortality after infection, moving data points from infected to the deceased category, not just recovered. VAP infection’s mortality is high, especially in undeveloped regions, reaching about 20% (and higher) throughout the nation and outside of it. But, pseudomonas aeruginosa, due to its multidimensional resistance evolution, has been reported to result in up to 68% mortality and lies between 35 and 40% mortality in the U.S. itself. While the mortality rate of the graph is slightly scaled down (presuming ideal healthcare conditions) to about 35% over a 30 day period post-infection, the staggering difference between PA-specific mortality and general VAP mortality is visualized. Time was raised to 44 days for visualization purposes as infection peaks at day 15 of PA VAP infection, to better visualize the mortality curve the x-axis was consequentially increased.

Antibacterial Resistance Evolution

[Fig. 4] The mutant selection window of a bacteria is the range where antibiotic treatment conditions help select for resistant bacteria. This window extends from the MIC needed to block wild-type bacteria until the MIC needed to block a resistant strain. Here, the antibiotic MIC is too low to suppress the growth of resistant bacterial strains, potentially fostering their growth. Using PA strain PAO7H data with a high MIC of 8-fold MIC toward ciprofloxacin and a higher susceptibility MIC of ciprofloxacin at 0.5-fold MIC for wild-type bacteria. These set the bounds of the “blue window” or MSW in the graph. Concentrations chosen were according to known administration targeting these respective MICs at 0.125 ug/ml up to 2.0 ug/ml. Although this resistant variant can go up to 16-fold MIC, the lower values were chosen for probability and to eliminate the need to account for multi-drug resistance while modeling. Interestingly, at this point the net growth rate of highly ciprofloxacin-resistant PA will not typically have a major net growth rate decrease post-exposure or infection.

Conclusion

The SEIR modeling of ventilator-associated pneumonia (VAP) highlights the differences in infection behaviors and overall outcomes between broad bacterial infections compared to Pseudomonas aeruginosa (PA) specific infections. A general VAP model, accounting for all bacterial infections, (Fig. 1) showed how a typical infection varied under standard hygiene protocols and, despite its relatively short infection period, was manageable from a public health standpoint. But, the PA model (Fig. 2) displayed a more severe infection behavior, especially considering its overall lower prevalence, showcasing how the heightened resistance of PA poses a threat to standardized public health measures. By incorporating mortality and a deceased group into the SEIR model (Fig. 3), this difference in severity becomes obvious because while broad-spectrum VAP mortality is substantial, PA related infection displayed a much higher mortality rate. The MSW window (Fig.4) displays how traditional interventions contribute to the heightened strength of infection and eventual development of damaging bacterial strains, indicating a need for alternate treatment. This demonstrates a clear need for improved infection control and measures to control infection severity such as regulating the ExoA system.

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