Partitioning of a 2-bit hash function across 66 communicating cells.

Powerful distributed computing can be achieved by communicating cells that individually perform simple operations. Here, we report design software to divide a large genetic circuit across cells as well as the genetic parts to implement the subcircuits in their genomes. These tools were demonstrated using a 2-bit version of the MD5 hashing algorithm, which is an early predecessor to the cryptographic functions underlying cryptocurrency.

Pattern Formation and Bistability in a Synthetic Intercellular Genetic Toggle.

Differentiation within multicellular organisms is a complex process that helps to establish spatial patterning and tissue formation within the body. Often, the differentiation of cells is governed by morphogens and intercellular signaling molecules that guide the fate of each cell, frequently using toggle-like regulatory components. Synthetic biologists have long sought to recapitulate patterned differentiation with engineered cellular communities, and various methods for differentiating bacteria have been invented.

Recovering biomolecular network dynamics from single-cell omics data requires three time points.

Single-cell omics technologies can measure millions of cells for up to thousands of biomolecular features, enabling data-driven studies of complex biological networks. However, these high-throughput experimental techniques often cannot track individual cells over time, thus complicating the understanding of dynamics such as time trajectories of cell states. These "dynamical phenotypes" are key to understanding biological phenomena such as differentiation fates.

What cannot be seen correctly in 2D visualizations of single-cell 'omics data?

A common strategy for exploring single-cell 'omics data is visualizing 2D nonlinear projections that aim to preserve high-dimensional data properties such as neighborhoods. Alternatively, mathematical theory and other computational tools can directly describe data geometry, while also showing that neighborhoods and other properties cannot be well-preserved in any 2D projection.

Epigenetic factor competition reshapes the EMT landscape.

The emergence of and transitions between distinct phenotypes in isogenic cells can be attributed to the intricate interplay of epigenetic marks, external signals, and gene-regulatory elements. These elements include chromatin remodelers, histone modifiers, transcription factors, and regulatory RNAs. Mathematical models known as gene-regulatory networks (GRNs) are an increasingly important tool to unravel the workings of such complex networks.

A synthetic distributed genetic multi-bit counter.

A design for genetically encoded counters is proposed via repressor-based circuits. An -bit counter reads sequences of input pulses and displays the total number of pulses, modulo . The design is based on distributed computation with specialized cell types allocated to specific tasks.

Perfect adaptation of CD8 T cell responses to constant antigen input over a wide range of affinities is overcome by costimulation.

Reduced T cell responses by contrast antigen stimulation can be rescued by signals from costimulatory receptors.

Maximizing average throughput in oscillatory biochemical synthesis systems: an optimal control approach.

A dynamical system to a periodic input if its state converges globally to an attractor with the same period. In particular, for a constant input, the state converges to a unique equilibrium point for any initial condition. We consider the problem of maximizing a weighted average of the system's output along the periodic attractor.

Derivation of stationary distributions of biochemical reaction networks via structure transformation.

Long-term behaviors of biochemical reaction networks (BRNs) are described by steady states in deterministic models and stationary distributions in stochastic models. Unlike deterministic steady states, stationary distributions capturing inherent fluctuations of reactions are extremely difficult to derive analytically due to the curse of dimensionality. Here, we develop a method to derive analytic stationary distributions from deterministic steady states by transforming BRNs to have a special dynamic property, called complex balancing.

Universal features of epidemic models under social distancing guidelines.

Social distancing as a form of nonpharmaceutical intervention has been enacted in many countries as a form of mitigating the spread of COVID-19. There has been a large interest in mathematical modeling to aid in the prediction of both the total infected population and virus-related deaths, as well as to aid government agencies in decision making. As the virus continues to spread, there are both economic and sociological incentives to minimize time spent with strict distancing mandates enforced, and/or to adopt periodically relaxed distancing protocols, which allow for scheduled economic activity.

A novel COVID-19 epidemiological model with explicit susceptible and asymptomatic isolation compartments reveals unexpected consequences of timing social distancing.

Motivated by the current COVID-19 epidemic, this work introduces an epidemiological model in which separate compartments are used for susceptible and asymptomatic "socially distant" populations. Distancing directives are represented by rates of flow into these compartments, as well as by a reduction in contacts that lessens disease transmission. The dynamical behavior of this system is analyzed, under various different rate control strategies, and the sensitivity of the basic reproduction number to various parameters is studied.

Short-Term Circulating Tumor Cell Dynamics in Mouse Xenograft Models and Implications for Liquid Biopsy.

Motivation: Circulating tumor cells (CTCs) are widely studied using liquid biopsy methods that analyze fractionally-small peripheral blood (PB) samples. However, little is known about natural fluctuations in CTC numbers that may occur over short timescales , and how these may affect detection and enumeration of rare CTCs from small blood samples.

Methods: We recently developed an optical instrument called "diffuse flow cytometry" (DiFC) that uniquely allows continuous, non-invasive counting of rare, green fluorescent protein expressing CTCs in large blood vessels in mice.

Integrating transcriptomics and bulk time course data into a mathematical framework to describe and predict therapeutic resistance in cancer.

A significant challenge in the field of biomedicine is the development of methods to integrate the multitude of dispersed data sets into comprehensive frameworks to be used to generate optimal clinical decisions. Recent technological advances in single cell analysis allow for high-dimensional molecular characterization of cells and populations, but to date, few mathematical models have attempted to integrate measurements from the single cell scale with other types of longitudinal data. Here, we present a framework that actionizes static outputs from a machine learning model and leverages these as measurements of state variables in a dynamic model of treatment response.

A mathematical model exhibiting the effect of DNA methylation on the stability boundary in cell-fate networks.

Cell-fate networks are traditionally studied within the framework of gene regulatory networks. This paradigm considers only interactions of genes through expressed transcription factors and does not incorporate chromatin modification processes. This paper introduces a mathematical model that seamlessly combines gene regulatory networks and DNA methylation (DNAm), with the goal of quantitatively characterizing the contribution of epigenetic regulation to gene silencing.

Delicate Balances in Cancer Chemotherapy: Modeling Immune Recruitment and Emergence of Systemic Drug Resistance.

Metronomic chemotherapy can drastically enhance immunogenic tumor cell death. However, the mechanisms responsible 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.

Mathematical Details on a Cancer Resistance Model.

One of the most important factors limiting the success of chemotherapy in cancer treatment is the phenomenon of drug resistance. We have recently introduced a framework for quantifying the effects of induced and non-induced resistance to cancer chemotherapy (Greene et al., 2018a, 2019).

Distributed Implementation of Boolean Functions by Transcriptional Synthetic Circuits.

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.

Stochastic analysis of genetic feedback controllers to reprogram a pluripotency gene regulatory network.

Cellular reprogramming is traditionally accomplished through an open loop (OL) control approach, wherein key transcription factors (TFs) are injected in cells to steer the state of the pluripotency (PL) gene regulatory network (GRN), as encoded by TFs concentrations, to the pluripotent state. Due to the OL nature of this approach, the concentration of TFs cannot be accurately controlled. Recently, a closed loop (CL) feedback control strategy was proposed to overcome this problem with promising theoretical results.

A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks.

Complex molecular biological processes such as transcription and translation, signal transduction, post-translational modification cascades, and metabolic pathways can be described in principle by biochemical reactions that explicitly take into account the sophisticated network of chemical interactions regulating cell life. The ability to deduce the possible qualitative behaviors of such networks from a set of reactions is a central objective and an ongoing challenge in the field of systems biology. Unfortunately, the construction of complete mathematical models is often hindered by a pervasive problem: despite the wealth of qualitative graphical knowledge about network interactions, the form of the governing nonlinearities and/or the values of kinetic constants are hard to uncover experimentally.

Mathematical Models of Protease-Based Enzymatic Biosensors.

An important goal of synthetic biology is to build biosensors and circuits with well-defined input-output relationships that operate at speeds found in natural biological systems. However, for molecular computation, most commonly used genetic circuit elements typically involve several steps from input detection to output signal production: transcription, translation, and post-translational modifications. These multiple steps together require up to several hours to respond to a single stimulus, and this limits the overall speed and complexity of genetic circuits.