Complex dynamical systems are the kind of systems with many interacting components that usually have nonlinear dynamics. Those systems exist in a wide range of disciplines, such as physical, biological, and social fields. Those systems, due to a large amount of interacting components, tend to possess very high dimensionality. Additionally, due to the intrinsic nonlinear dynamics, they have tremendous rich system behavior, such as bifurcation, synchronization, chaos, solitons. To develop methods to predict and control those systems has always been a challenge and an active research area.

My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.

Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.

Alzheimer’s disease (AD) affects over 5 million individuals each year in the United States. Furthermore, most cases of AD are sporadic, making it extremely difficult to model and study in vitro. CRISPR/Cas9 and base editing technologies have been of recent interest because of their ability to create single nucleotide edits at nearly any genomic sequence using a Cas9 protein and a guide RNA (sgRNA). Currently, there is no available phenotype to differentiate edited cells from unedited cells. Past research has employed fluorescent proteins bound to Cas9 proteins to attempt to enrich for edited cells, however, these methods are only reporters of transfection (RoT) and are no indicative of actual base-editing occurring. Thus, this study proposes a transient reporter for editing enrichment (TREE) and Cas9-mediated adenosine TREE (CasMasTREE) which use plasmids to co-transfect with CRISPR/Cas9 technologies to serve as an indicator of base-editing. Specifically, TREE features a blue fluorescent protein (BFP) mutant that, upon a C-T conversion, changes the emission spectrum to a green fluorescent protein (GFP). CasMasTREE features a mCherry and GFP protein separated by a stop codon which can be negated using an A-G conversion. By employing a sgRNA that targets one of the TREE plasmids and at least one genomic site, cells can be sorted for GFP(+) cells. Using these methods, base-edited isogenic hiPSC line generation using TREE (BIG-TREE) was created to generate isogenic hiPSC lines with AD-relevant edits. For example, BIG-TREE demonstrates the capability of converting Apolipoprotein E (APOE), a gene associated with AD-risk development, wildtype (3/3) into another isoform, APOE2/2, to create isogenic hiPSC lines. The capabilities of TREE are vast and can be applied to generate various models of diseases with specific genomic edits.

The Hippo signaling pathway is responsible for regulating organ size through cell proliferation, stemness, and apoptosis. Through targeting proteins Yes-associated kinase 1(YAP) and transcriptional co-activator with a PDZ-binding domain(TAZ), YAP/TAZ are unable to enter the nucleus and bind with coactivators to express target genes. To understand YAP/TAZ dynamics and its role in tumorigenesis, tissue regeneration, and tissue degeneration, a regulatory network was modeled by ordinary differential equations. Using MATLAB, the deterministic behavior of the network was observed to determine YAP/TAZ activity in different states. Performing the bifurcation analysis of the system through Oscill8, three states were identified: tumorigenic/regenerative, degenerative, and homeostatic states. Further analysis through parameter modification allowed a better understanding of which proteins can be targeted for cancer and degenerative disease.

Fusion proteins that specifically interact with biochemical marks on chromosomes represent a new class of synthetic transcriptional regulators that decode cell state information rather than deoxyribose nucleic acid (DNA) sequences. In multicellular organisms, information relevant to cell state, tissue identity, and oncogenesis is often encoded as biochemical modifications of histones, which are bound to DNA in eukaryotic nuclei and regulate gene expression states. In 2011, Haynes et al. showed that a synthetic regulator called the Polycomb chromatin Transcription Factor (PcTF), a fusion protein that binds methylated histones, reactivated an artificially-silenced luciferase reporter gene. These synthetic transcription activators are derived from the polycomb repressive complex (PRC) and associate with the epigenetic silencing mark H3K27me3 to reactivate the expression of silenced genes. It is demonstrated here that the duration of epigenetic silencing does not perturb reactivation via PcTF fusion proteins. After 96 hours PcTF shows the strongest reactivation activity. A variant called Pc2TF, which has roughly double the affinity for H3K27me3 in vitro, reactivated the silenced luciferase gene by at least 2-fold in living cells.

The WNT signaling pathway plays numerous roles in development and maintenance of adult homeostasis. In concordance with it’s numerous roles, dysfunction of WNT signaling leads to a variety of human diseases ranging from developmental disorders to cancer. WNT signaling is composed of a family of 19 WNT soluble secreted glycoproteins, which are evolutionarily conserved across all phyla of the animal kingdom. WNT ligands interact most commonly with a family of receptors known as frizzled (FZ) receptors, composed of 10 independent genes. Specific interactions between WNT proteins and FZ receptors are not well characterized and are known to be promiscuous, Traditionally canonical WNT signaling is described as a binary system in which WNT signaling is either off or on. In the ‘off’ state, in the absence of a WNT ligand, cytoplasmic β-catenin is continuously degraded by the action of the APC/Axin/GSK-3β destruction complex. In the ‘on’ state, when WNT binds to its Frizzled (Fz) receptor and LRP coreceptor, this protein destruction complex is disrupted, allowing β-catenin to translocate into the nucleus where it interacts with the DNA-bound T cell factor/lymphoid factor (TCF/LEF) family of proteins to regulate target gene expression. However in a variety of systems in development and disease canonical WNT signaling acts in a gradient fashion, suggesting more complex regulation of β-catenin transcriptional activity. As such, the traditional ‘binary’ view of WNT signaling does not clearly explain how this graded signal is transmitted intracellularly to control concentration-dependent changes in gene expression and cell identity. I have developed an in vitro human pluripotent stem cell (hPSC)-based model that recapitulates the same in vivo developmental effects of the WNT signaling gradient on the anterior-posterior (A/P) patterning of the neural tube observed during early development. Using RNA-seq and ChIP-seq I have characterized β-catenin binding at different levels of WNT signaling and identified different classes of β-catenin peaks that bind cis-regulatory elements to influence neural cell fate. This work expands the traditional binary view of canonical WNT signaling and illuminates WNT/β-catenin activity in other developmental and diseased contexts.

YAP/TAZ is the key effector in the Hippo pathway, but it is also involved in many other regulatory pathways to control tissue and organ size. To better understand its regulation and effects in tumorigenesis and degeneration, a preliminary feedback network was created with the species YAP/TAZ, phosphorylated YAP/TAZ, LATS, miR-130a, VGLL4, and β-catenin. From this network a set of ordinary differential equations were written and analyzed for parameter effects. A model showing the healthy, tumorigenic, and degenerative states was created and preliminary parameter analysis identified the effects of parameter modifications on the overall levels of YAP/TAZ. Further analysis is required and connections with the underlying biology should continue to be pursued to better understand how parameter modifications could improve disease treatments.

Cell fate is a complex and dynamic process with many genetic components. It has often been likened to “multistable” mathematical systems because of the numerous possible “stable” states, or cell types, that cells may end up in. Due to its complexity, understanding the process of cell fate and differentiation has proven challenging. A better understanding of cell differentiation has applications in regenerative stem cell therapies, disease pathologies, and gene regulatory networks.
A variety of different genes have been associated with cell fate. For example, the Nanog/Oct-4/Sox2 network forms the core interaction of a gene network that maintains stem cell pluripotency, and Oct-4 and Sox2 also play a role in the tissue types that stem cells eventually differentiate into. Using the CRISPR/cas9 based homology independent targeted integration (HITI) method developed by Suzuki et al., we can integrate fluorescent tags behind genes with reasonable efficiency via the non-homologous end joining (NHEJ) DNA repair pathway. With human embryonic kidney (HEK) 293T cells, which can be transfected with high efficiencies, we aim to create a three-parameter reporter cell line with fluorescent tags for three different genes related to cell fate. This cell line would provide several advantages for the study of cell fate, including the ability to quantitatively measure cell state, observe expression heterogeneity among a population of genetically identical cells, and easily monitor fluctuations in expression patterns.
The project is partially complete at this time. This report discusses progress thus far, as well as the challenges faced and the future steps for completing the reporter line.

Synthetic biology is an emerging field which melds genetics, molecular biology, network theory, and mathematical systems to understand, build, and predict gene network behavior. As an engineering discipline, developing a mathematical understanding of the genetic circuits being studied is of fundamental importance. In this dissertation, mathematical concepts for understanding, predicting, and controlling gene transcriptional networks are presented and applied to two synthetic gene network contexts. First, this engineering approach is used to improve the function of the guide ribonucleic acid (gRNA)-targeted, dCas9-regulated transcriptional cascades through analysis and targeted modification of the RNA transcript. In so doing, a fluorescent guide RNA (fgRNA) is developed to more clearly observe gRNA dynamics and aid design. It is shown that through careful optimization, RNA Polymerase II (Pol II) driven gRNA transcripts can be strong enough to exhibit measurable cascading behavior, previously only shown in RNA Polymerase III (Pol III) circuits. Second, inherent gene expression noise is used to achieve precise fractional differentiation of a population. Mathematical methods are employed to predict and understand the observed behavior, and metrics for analyzing and quantifying similar differentiation kinetics are presented. Through careful mathematical analysis and simulation, coupled with experimental data, two methods for achieving ratio control are presented, with the optimal schema for any application being dependent on the noisiness of the system under study. Together, these studies push the boundaries of gene network control, with potential applications in stem cell differentiation, therapeutics, and bio-production.

Neurodegenerative diseases such as Alzheimer’s disease, Parkinson’s disease, or amyotrophic lateral sclerosis are defined by the loss of several types of neurons and glial cells within the central nervous system (CNS). Combatting these diseases requires a robust population of relevant cell types that can be employed in cell therapies, drug screening, or patient specific disease modeling. Human induced pluripotent stem cells (hiPSC)-derived neural progenitor cells (hNPCs) have the ability to self-renew indefinitely and differentiate into the various neuronal and glial cell types of the CNS. In order to realize the potential of hNPCs, it is necessary to develop a xeno-free scalable platform for effective expansion and differentiation. Previous work in the Brafman lab led to the engineering of a chemically defined substrate—vitronectin derived peptide (VDP), which allows for the long-term expansion and differentiation of hNPCs. In this work, we use this substrate as the basis for a microcarrier (MC)-based suspension culture system. Several independently derived hNPC lines were cultured on MCs for multiple passages as well as efficiently differentiated to neurons. Finally, this MC-based system was used in conjunction with a low shear rotating wall vessel (RWV) bioreactor for the integrated, large-scale expansion and neuronal differentiation of hNPCs. Finally, VDP was shown to support the differentiation of hNPCs into functional astrocytes. Overall, this fully defined and scalable biomanufacturing system will facilitate the generation of hNPCs and their derivatives in quantities necessary for basic and translational applications.

Recombinases are powerful tools for genome engineering and synthetic biology, however recombinases are limited by a lack of user-programmability and often require complex directed-evolution experiments to retarget specificity. Conversely, CRISPR systems have extreme versatility yet can induce off-target mutations and karyotypic destabilization. To address these constraints we developed an RNA-guided recombinase protein by fusing a hyperactive mutant resolvase from transposon TN3 to catalytically inactive Cas9. We validated recombinase-Cas9 (rCas9) function in model eukaryote Saccharomyces cerevisiae using a chromosomally integrated fluorescent reporter. Moreover, we demonstrated cooperative targeting by CRISPR RNAs at spacings of 22 or 40bps is necessary for directing recombination. Using PCR and Sanger sequencing, we confirmed rCas9 targets DNA recombination. With further development we envision rCas9 becoming useful in the development of RNA-programmed genetic circuitry as well as high-specificity genome engineering.