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Publications of Eduardo D. Sontag jointly with A.P. Tran
Articles in journal or book chapters
  1. M. Ali Al-Radhawi, A.P. Tran, E. Ernst, T. Chen, C.A. Voigt, and E.D. Sontag. Distributed implementation of Boolean functions by transcriptional synthetic circuits. ACS Synthetic Biology, pp A-P, 2020. [PDF] [doi:10.1021/acssynbio.0c00228] Keyword(s): synthetic biology, transcriptional networks, gene networks, boolean circuits, boolean gates.
    Abstract:
    Starting in the early 2000s, sophisticated technologies have been developed for the rational construction of synthetic genetic networks that implement specified logical functionalities. Despite impressive progress, however, the scaling necessary in order to achieve greater computational power has been hampered by many constraints, including repressor toxicity and the lack of large sets of mutually-orthogonal repressors. As a consequence, a typical circuit contains no more than roughly seven repressor-based gates per cell. A possible way around this scalability problem is to distribute the computation among multiple cell types, which communicate among themselves using diffusible small molecules (DSMs) and each of which implements a small sub-circuit. Examples of DSMs are those employed by quorum sensing systems in bacteria. This paper focuses on systematic ways to implement this distributed approach, in the context of the evaluation of arbitrary Boolean functions. The unique characteristics of genetic circuits and the properties of DSMs require the development of new Boolean synthesis methods, distinct from those classically used in electronic circuit design. In this work, we propose a fast algorithm to synthesize distributed realizations for any Boolean function, under constraints on the number of gates per cell and the number of orthogonal DSMs. The method is based on an exact synthesis algorithm to find the minimal circuit per cell, which in turn allows us to build an extensive database of Boolean functions up to a given number of inputs. For concreteness, we will specifically focus on circuits of up to 4 inputs, which might represent, for example, two chemical inducers and two light inputs at different frequencies. Our method shows that, with a constraint of no more than seven gates per cell, the use of a single DSM increases the total number of realizable circuits by at least 7.58-fold compared to centralized computation. Moreover, when allowing two DSM's, one can realize 99.995\% of all possible 4-input Boolean functions, still with at most 7 gates per cell. The methodology introduced here can be readily adapted to complement recent genetic circuit design automation software.


  2. A.P. Tran, M. Ali Al-Radhawi, I. Kareva, J. Wu, D.J. Waxman, and E.D. Sontag. Delicate balances in cancer chemotherapy: Modeling immune recruitment and emergence of systemic drug resistance. Frontiers in Immunology, 11:1376-, 2020. [PDF] [doi:10.3389/fimmu.2020.01376] Keyword(s): metronomic chemotherapy, cyclophosphamide, mathematical modeling, immune recruitment, cancer, resistance, oncology, immunology.
    Abstract:
    Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the responsible mechanisms are still incompletely understood. Here, we develop a mathematical model to elucidate the underlying complex interactions between tumor growth, immune system activation, and therapy-mediated immunogenic cell death. Our model is conceptually simple, yet it provides a surprisingly excellent fit to empirical data obtained from a GL261 mouse glioma model treated with cyclophosphamide on a metronomic schedule. The model includes terms representing immune recruitment as well as the emergence of drug resistance during prolonged metronomic treatments. Strikingly, a fixed set of parameters, not adjusted for individuals nor for drug schedule, excellently recapitulates experimental data across various drug regimens, including treatments administered at intervals ranging from 6 to 12 days. Additionally, the model predicts peak immune activation times, rediscovering experimental data that had not been used in parameter fitting or in model construction. The validated model was then used to make predictions about expected tumor-immune dynamics for novel drug administration schedules. Notably, the validated model suggests that immunostimulatory and immunosuppressive intermediates are responsible for the observed phenomena of resistance and immune cell recruitment, and thus for variation of responses with respect to different schedules of drug administration.


  3. A.P. Tran, J.H. Meldon, and E.D. Sontag. Transient diffusion into a bi-layer membrane with mass transfer resistance: Exact solution and time lag analysis. 2020. Note: Submitted.Keyword(s): Bi-layer membrane, transient diffusion, heat conduction, mass transfer resistance.
    Abstract:
    Exact analytical and closed-form solutions to a problem involving transient diffusion in a bi-layer membrane with external transfer resistance are presented. In addition to the solutions of the transient response, the lead and lag times that are often of importance in the characterization of membranes and arise from the analysis of the asymptotic behavior of the mass permeated through the membrane are also provided. The solutions presented here are also compared to previously derived limiting cases of the diffusion in a bi-layer with an impermeable wall and constant concentrations at the upstream and downstream boundaries. Analysis of the time lag shows that this membrane property is independent of the direction of flow. Finally, an outline is provided of how these solutions, which characterize the response to a step function increase in concentration, can be also used to derive more complex input conditions. Adequately handling boundary layer effects has a wide array of potential applications such as the study of bi-layer undergoing phenomena of heat convection, gas film resistance, and absorption/desorption.


Internal reports
  1. A. P. Tran, M. A. Al-Radhawi, I. Kareva, J. Wu, D. J. Waxman, and E. D. Sontag. Delicate balances in cancer chemotherapy: modeling immune recruitment and emergence of systemic drug resistance. Technical report, Cold Spring Harbor Laboratory, 2019. Note: BioRxiv 2019.12.12.874891. Keyword(s): chemotherapy, immunology, immune system, oncology, cancer, metronomic.
    Abstract:
    Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the responsible mechanisms are still incompletely understood. Here, we develop a mathematical model to elucidate the underlying complex interactions between tumor growth, immune system activation, and therapy-mediated immunogenic cell death. Our model is conceptually simple, yet it provides a surprisingly excellent fit to empirical data obtained from a GL261 mouse glioma model treated with cyclophosphamide on a metronomic schedule. The model includes terms representing immune recruitment as well as the emergence of drug resistance during prolonged metronomic treatments. Strikingly, a fixed set of parameters, not adjusted for individuals nor for drug schedule, excellently recapitulates experimental data across various drug regimens, including treatments administered at intervals ranging from 6 to 12 days. Additionally, the model predicts peak immune activation times, rediscovering experimental data that had not been used in parameter fitting or in model construction. The validated model was then used to make predictions about expected tumor-immune dynamics for novel drug administration schedules. Notably, the validated model suggests that immunostimulatory and immunosuppressive intermediates are responsible for the observed phenomena of resistance and immune cell recruitment, and thus for variation of responses with respect to different schedules of drug administration.



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Last modified: Thu Sep 24 12:35:48 2020
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