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Summary Ordinary differential equation (ODE)-based modeling is a powerful tool in the design and characterization of synthetic gene circuits. Despite its popularity, identifying the model parameters based off experimental measurement is a nontrivial task. In this study, we leverage cell-free experimental measurement of two RNA-based regulators to investigate the impact and the incorporation of measurement variance in the pair-wise squared error objective function used for ODE-model parameterization. Our findings suggest that while unweighted objective function and weighting by the inverse variance can provide reasonably accurate parameter estimation, weighing the objective function with the inverse stabilized variance could further improve the parameterization, by also capturing the system variance with a mitigated prediction variance. 

Abstract Immune response is critical in septic wound healing. The aberrant and imbalanced signaling dynamics primarily cause a dysfunctional innate immune response, exacerbating pathogen invasion of injured tissue and further stalling the healing process. To design biological controllers that regulate the critical divergence of the immune response during septicemia, we need to understand the intricate differences in immune cell dynamics and coordinated molecular signals of healthy and sepsis injury. Here, we deployed an ordinary differential equation (ODE)-based model to capture the hyper and hypo-inflammatory phases of sepsis wound healing. Our results indicate that impaired macrophage polarization leads to a high abundance of monocytes, M1, and M2 macrophage phenotypes, resulting in immune paralysis. Using a model-based analysis framework, we designed a biological controller which successfully regulates macrophage dysregulation observed in septic wounds. Our model describes a systems biology approach to predict and explore critical parameters as potential therapeutic targets capable of transitioning septic wound inflammation toward a healthy, wound-healing state. 

Perfect adaptation, the ability to regulate and maintain gene expression to its desired value despite disturbances, is important in the development of organisms. Building biological controllers to endow engineered biological systems with such perfect adaptation capability is a key goal in synthetic biology. Model-guided exploration of such synthetic circuits has been effective in designing such systems. However, theoretical analysis to guarantee controller properties with nonlinear models, such as Hill functions, remains challenging, while use of linear models fails to capture the inherent nonlinear dynamics of gene expression systems. Here, we propose a reverse engineering approach to infer the kinetic parameters for nonlinear Hill function-type models from analysis of linear models and apply our method to design controllers, which achieve perfect adaptation. Focusing on three biological network motif-based controllers, we demonstrate via simulation the efficacy of the proposed approach in combining linear system theories with nonlinear modelling, to design multiple gene circuits that could deliver perfect adaptation. Given the ubiquitous use of Hill functions in describing the dynamics of biological regulatory networks, we anticipate the proposed reverse engineering approach to benefit a wide range of systems and synthetic biology applications. 

Integral controller is widely used in industry for its capability of endowing perfect adaptation to disturbances. To harness such capability for precise gene expression regulation, synthetic biologists have endeavoured in building biomolecular (quasi-)integral controllers, such as the antithetic integral controller. Despite demonstrated successes, challenges remain with designing the controller for improved transient dynamics and adaptation. Here, we explore and investigate the design principles of alternative RNA-based biological controllers, by modifying an antithetic integral controller with prevalently found natural feed-forward loops (FFL), to improve its transient dynamics and adaptation performance. With model-based analysis, we demonstrate that while the base antithetic controller shows excellent responsiveness and adaptation to system disturbances, incorporating the type-1 incoherent FFL into the base antithetic controller could attenuate the transient dynamics caused by changes in the stimuli, especially in mitigating the undesired overshoot in the output gene expression. Further analysis on the kinetic parameters reveals similar findings to previous studies that the degradation and transcription rates of the circuit RNA species would dominate in shaping the performance of the controllers.