Poster: Session B #114: 1pm-2pm HopLand: Single-cell pseudotime recovery using continuous Hopfield network based modeling of Waddington’s epigenetic landscape Jing Guo1,2 and Jie Zheng1,3,4 1Biomedical Informatics Lab, School of Computer Science and Engineering, Nanyang Technological University 2Bioinformatics Institute, Agency for Science, Technology, and Research (A*STAR) 3Genome Institute of Singapore, A*STAR 4Complexity Institute, Nanyang Technological University ISMB/ECCB 2017

Pseudo-time recovery in single-cell data What Biological Time Physical Time Input: DN*S Tree=Mapping(D) Output: Tree multiple time points

Pseudo-time recovery in single-cell data Why Understand the transition of gene expression profiles Increases the temporal resolution

Current methods Wanderlust (Bendall et al., 2014) Wishbone (Setty et al., 2016) Monocle (Trapnell et al., 2014) Diffusion map (Haghverdi et al., 2015) Dimensionality reduction SCUBA (Marco et al., 2014) Modeling system dynamics Topslam (Zwiessele and Lawrence, 2016) Waddington’s epigenetic landscape Current methods… 1. Common… 2. specific one…. Summary: Dimensionality reduction Mapping cells to the latent space drawbacks….. 1. common… 2. specific one….

The overview of HopLand A landscape inferred from single cell sequencing data Individual cells are placed on the surface regions corresponding to their developmental stages The order of cells is determined by the geodesic distances in the landscape

Waddington’s epigenetic landscape Figure from (Mohammad and Baylin, 2010) Attractor system

Continuous Hopfield network (John Hopfield in 1984) 1) continuous variables and predicts continuous responses 2) Neurons == Genes describe the regulatory function of a gene What they do… W The discrete Hopfield network (John Hopfield in 1982) has been used to study biological systems with each neuron representing a gene (Taherian Fard et al., 2016, Maetschke and Ragan, 2014, Lang et al., 2014). discrete variables and predicts discrete responses

1. Data preprocessing Temporal single cell data Physical Time How…….. edgeR, DESeq Identify differentially expressed genes genes are detected in only a subset of cells and such dropout events are thought to be rooted in the stochasticity of single-cell library preparation [8] Dropout effect  Over-dispersion Data types: qPCR, scRNA-seq MAST,SCDE… (Scadden, 2014, Nature Methods)

2. Parameter estimation CHN Initial parameters Generate real trajectories Optimize objective function CHN W There are several parameters in the ODE model of kinetics in Eq. 4.1. To infer these parameters = fi; Ii;Ci;Wij ; i; j = 1; 2; :::;Ng from the sequencing data, an optimization method (Algorithm 4) which ts the simulated and observed single-cell data is proposed based on the premise that a realistic model should be able to generate simulated data consistent with the real data.

3. Landscape construction GP-LVM Dimensionality reduction Generate a grid Get high-dimensional vectors Calculate energies Plot the landscape Altitude Comp2 Comp1 Interpolation

4. Pseudotime recovery Calculate geodesic distances Build the minimum spanning tree

Evaluation Synthetic dataset: Applied to real single-cell gene expression data from different types of biological experiments and compared against other methods, HopLand outperformed most of the other methods in most cases. In addition, our method could also be used to identify key regulators and interactions which is helpful for the understanding of underlying mechanisms.

Dataset: mouse pre-implantation development The expression profiles of 438 cells with 48 genes per cell covering the developmental stage from the 1-cell to 64-cell stages (Guo et al., 2010).

(a) The Waddington’s epigenetic landscape recovered using HopLand (a) The Waddington’s epigenetic landscape recovered using HopLand. (b) The minimum spanning tree constructed from Waddington’s epigenetic landscape. The dots are colored according to the developmental stages of the cells in the dataset of GUO2010.

Mapping gene expression values to the landscape using (a) FGF4, (b) GATA4, (c) CDX2 and (d) SOX2. The value decreases from dark red to white.

The core network found by searching GeneGo MetaCore for interactions overlapping with HopLand’s top interactions and genes.

Summary Poster: Session B #114: 1pm-2pm Limitations & Future work: Continuous Hopfield network Provide a non-linear mapping between the Waddington's epigenetic landscape and the phenotype space. Waddington’s epigenetic landscape Construct the landscape based on biological interactions between genes that allows to simulate real biological processes. Geodesic distance Use the geodesic distances in the landscape to refine the estimation of distances between cells. Waddington's epigenetic landscape which merges the genotype-phenotype mapping with the last developments of genomics on transcriptional regulation, epigenetic modification and signalling pathways, is applied to analyze and visualize the system kinetic. Limitations & Future work: Supervised method ---- unsupervised cluster methods Computationally costly ---- Stochastic gradient descent (SGD), HPC Data noise ---- different types of sequencing technologies Poster: Session B #114: 1pm-2pm

Acknowledgement Jie Zheng The SCE-BII joint PhD program