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1 Introduction 2 A Differential Bioreactor Model 2.1 Goals 2.2 Mathematical Formulation 2.3 Equations 2.4 Numerical Solution 2.5 Sensitivity Analysis 2.6 Hypothetical Applications 3 A Mechanistic Buoyancy Model: Maximum Carrying Capacity Determination 3.1 Goal 3.2 Mathematical Formulation 3.3 Analytic Solution 3.4 Determining Buoyant Force: Temporal Tracking Algorithm 3.5 Discussion On Maximum Carrying Capacity 4 Growth Dynamics 4.1 Objective 4.2 Approach 4.3 Results 5 Discussion and Future Directions 6 Appendix 7 References

1 Introduction

Our goal in the dry lab this year was to create four different models that allows our wet lab team tocharacterize their results, and allow future researchers to benchmark their results, creating standardmeasures in the field of cellular flotation. First we created a generic differential bioreactor model thatallowed our team to predict the effectiveness of our E. coli cells to clean waste waters if coupled withany surface binding method. We performed a complete sensitivity analysis on this model to allowfuture researchers to reuse this model with completely different parameters, strain of cells and objectof waste. Then we created an algorithm that can track cellular flotation from frame to frame, andcharacterize exactly how the cells float; previously, we could only tell whether they floated or not.This coupled with our ODE buoyancy model allows us to define a maximum carrying capacity foreach strain. Both of these models allowed our team to benchmark their results, and will allow futureresearchers to quantify the performance of flotation as well.Note: In the very end of this paper, we included a nomenclature defining all the variables used.

2 A Differential Bioreactor Model

2.1 Goals
• Explore a possible application for our genetically engineered E. coli biomass that utilizes flota-tion.
• Develop a generic bioreactor that can be reused in many different conditions and for a varietyof purposes.