| Publications of Eduardo D. Sontag jointly with M. Sadeghi |
| Articles in journal or book chapters |
| Bispecific T Cell Engagers (BTC) constitute an exciting antibody design in immuno-oncology that acts to bypass antigen presentation and forms a direct link between cancer and immune cells in the tumor microenvironment (TME). By design, BTCs are efficacious only when the drug is bound to both immune and cancer cell targets, and therefore approaches to maximize drug-target trimer in the TME should maximize the drug's efficacy. In this study, we quantitatively investigate how the concentration of ternary complex and its distribution depend on both the targets' specific properties and the design characteristics of the BTC, and specifically on the binding kinetics of the drug to its targets. A simplified mathematical model of drug-target interactions is considered here, with insights from the "three-body" problem applied to the model. Parameter identifiability analysis performed on the model demonstrates that steady-state data, which is often available at the early pre-clinical stages, is sufficient to estimate the binding affinity of the BTC molecule to both targets. The model is used to analyze several existing antibodies that are either clinically approved or are under development, and to explore the common kinetic features. We conclude with a discussion of the limitations of the BTCs, such as the increased likelihood of cytokine release syndrome, and an assessment for a full quantitative pharmacology model that accounts for drug distribution into the peripheral compartment. |
| In order to control highly-contagious and prolonged outbreaks, public health authorities intervene to institute social distancing, lock-down policies, and other Non-Pharmaceutical Interventions (NPIs). Given the high social, educational, psychological, and economic costs of NPIs, authorities tune them, alternatively tightening up or relaxing rules, with the result that, in effect, a relatively flat infection rate results. For example, during the summer of 2020 in parts of the United States, daily COVID-19 infection numbers dropped to a plateau. This paper approaches NPI tuning as a control-theoretic problem, starting from a simple dynamic model for social distancing based on the classical SIR epidemics model. Using a singular-perturbation approach, the plateau becomes a Quasi-Steady-State (QSS) of a reduced two-dimensional SIR model regulated by adaptive dynamic feedback. It is shown that the QSS can be assigned and it is globally asymptotically stable. Interestingly, the dynamic model for social distancing can be interpreted as a nonlinear integral controller. Problems of data fitting and parameter identifiability are also studied for this model. This letter also discusses how this simple model allows for a meaningful study of the effect of population size, vaccinations, and the emergence of second waves. |
| Different epidemiological models, from the classical SIR system to more sophisticated ones involving population compartments for socially distanced, quarantined, infection aware, asymptomatic infected, and other individuals, share some remarkable dynamic characteristics when contact rates are subject to periodic or one-shot changes. In simple pulsed isolation policies, a linear relationship is found among optimal start time and duration for reduction of the infected peak. If a single interval social distancing starts too early or too late it will be ineffective with respect to decreasing the peak of infection. On the other hand, the nonlinearity of epidemic models leads to non-monotone behavior of the peak of infected population under periodic relaxation policies. This observation led us to hypothesize that an additional single interval social distancing at a proper time can significantly decrease the infected peak of periodic policies, and we verified this improvement. |
| We consider a nonlinear SISO system that is a cascade of a scalar "bottleneck entrance" with a stable positive linear system. In response to any periodic inflow, all solutions converge to a unique periodic solution with the same period. We study the problem of maximizing the averaged throughput via controlled switching. We compare two strategies: 1) switching between a high and low value, and 2 ~using a constant inflow equal to the prescribed mean value. We show that no possible switching policy can outperform a constant inflow rate, though it can approach it asymptotically. We describe several potential applications of this problem in traffic systems, ribosome flow models, and scheduling at security checks. |
| Internal reports |
| We consider a compartmental model for ribosome flow during RNA translation, the Ribosome Flow Model (RFM). This model includes a set of positive transition rates that control the flow from every site to the consecutive site. It has been shown that when these rates are time-varying and jointly T-periodic, the protein production rate converges to a unique T-periodic pattern. Here, we study a problem that can be roughly stated as: can periodic rates yield a higher average production rate than constant rates? We rigorously formulate this question and show via simulations, and rigorous analysis in one simple case, that the answer is no. |
This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders.
This document was translated from BibTEX by bibtex2html