Mathematical modeling is a promising tool for studying complex systems. In systems biology, mathematical models are often constructed by including all known interactions among individual components (genes/proteins) in the system, leading to highly complex models with many unknown parameters. On the other hand, the amount of available experimental data is typically limited, not enough to constrain the model parameters. As a result, parameter estimation in this context can be a difficult and ill-posed problem. To fit complex models and limited data, we explored two simple intuitive ideas (1) perform additional experiments to get more data, (2) perform model reduction to derive simpler models. The challenges are how to design optimal experiments that are maximally informative, and how to write down reduced models in a systematic and automated way. Although these two problems are quite different, they can be tackled by one common mathematical framework. We consider a complex model as a high-dimensional manifold that lives in a higher-dimensional space defined by the experimental measurements, and examine the Jacobian, Fisher Information Matrix and geodesics around on the manifold locally at the observed data. Experiment design is to identify new experiments that remove the singularity, whereas model reduction is to identify the nearest extreme singularity which suggests appropriate form of reduced models.

Small molecule drugs are the foundation of modern medical practice, yet their use is limited by the onset of unexpected and severe adverse events (AEs). Regulatory agencies rely on postmarketing surveillance to monitor safety once drugs are approved for clinical use. Despite advances in pharmacovigilance methods that address issues of confounding bias, clinical data of AEs are inherently noisy. Systems pharmacology—the integration of systems biology and chemical genomics—can illuminate drug mechanisms of action. We hypothesize that these data can improve drug safety surveillance by highlighting drugs with a mechanistic connection to the target phenotype (enriching true positives) and filtering those that do not (depleting false positives). I will go through examples of how observational data can be used to discover new adverse drug events and interactions and how systems pharmacology methods can be used to substantiate those findings.

Characterizing the functional impact of human genetic variation is essential for understanding the molecular underpinnings of disease risk.  While human genome sequencing has enabled rapid and efficient cataloging of tens of millions of genomic variants, for the majority of these, we know little about their functional impact.  This is particularly true for variants and mutations in non-coding regions. Unlocking new disease biology, therefore, requires the development of novel computational methods and experimental validation that can systematically identify causal non-coding variants. I will discuss our efforts to interpret rare non-coding variants and their effects in individuals, families and populations.

• Aberrant DNA methylation is an important mechanism that contributes to oncogenesis. Yet, few algorithms exist that exploit this vast dataset to identify hypo- and hyper-methylated genes in cancer. We developed a novel computational algorithm called MethylMix to identify differentially methylated genes that are also predictive of transcription. We apply MethylMix to twelve individual cancer sites, and additionally combine all cancer sites in a pancancer analysis. We discover pancancer hypo- and hyper-methylated genes and identify novel methylation-driven subgroups with clinical implications. MethylMix analysis on combined cancer sites reveals ten pancancer clusters reflecting new similarities across malignantly transformed tissues.

• It remains an open question when and how the first cell fate decision is  made in mammals. Using deep single-cell RNA-seq of matched sister  blastomeres, we report highly reproducible inter-blastomere differences  among 10 2-cell and five 4-cell mouse embryos. Inter-blastomere gene  expression differences dominated between-embryo differences and noise,  and were sufficient to cluster sister blastomeres into distinct groups.  Dozens of protein-coding genes exhibited reproducible bimodal expression  in sister blastomeres, which cannot be explained by random  fluctuations. The highly correlated gene pairs at the 4-cell stage  overlapped with those showing the same directions of differential  expression between inner cell mass (ICM) and trophectoderm (TE). These  data substantiate the hypothesis of inter-blastomere differences in 2-  and 4-cell mouse embryos, and associate these differences with ICM/TE  differences. In addition, we initiated a class of statistical methods  that simultaneously infer spatial and temporal groupings. Such methods  explicitly model the time dependencies of clustering indices over time.  Our method inferred three genes to be associated with the earliest cell  fate decision, which was corroborated by experimental validations.