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Desired

configuration

Initial configuration

Given an initial condition, target configuration, and the dynamics, are there input(s) that steer the system towards the desired configuration?

Controllability: An engineering perspective

Discrete model

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Controllability: A genome perspective

TF Binding data from TRANSFAC and JASPAR to define a B matrix for each TF

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The Team

Ronquist S, Patterson G, Muir LA, Lindsly S, Chen H, Brown M, Wicha MS, Bloch A, Brockett R, Rajapakse I. "Algorithm for cellular reprogramming." Proceedings of the National Academy of Sciences. 2017 Nov 7;114(45):11832-7. Data-guided Control (DGC) Supporting Information
Chen H, Chen J, Muir LA, Ronquist S, Meixner W, Ljungman M, Ried T, Smale S, Rajapakse I. "Functional Organization of the Human 4D Nucleome. " Proceedings of the National Academy of Sciences 112.26 (2015): 8002-8007. Supporting Information

Cellular Reprogramming and Controllability of Complex Systems

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Adjacency Matrix from Data

Adjacency Matrix

Intra-chromosomal contacts

Inter-chromosomal

contacts

Hi-C

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(1880 x 1880)

Active

Inactive

Mixed

LOC100

TTC29

ZNF827

SLC10A7

PROM1

FGFBP2

FGFBP1

CD38

LSM6

POU4F2

CLOCK

SRD5A3

TMEM165

8

16

24

32

40

48

56

0

-1

-0.5

0.5

1

1.5

2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

Time (h)

Function (RPKM)

PNAS 2015

Chromatin organization

(static information is shown)

Gene expression over time

human fibroblasts

TADs

4DN Data

Fig. 1. Topologically associating domain (TAD) and corresponding gene expression dynamics of Chr 4. (A) Mean RNA-seq counts (RPKM) of binned genes. (B) Fiedler vector computed from the normalized Hi-C matrix. Red bins are the genes associated with the positive Fiedler vector entries, and green bins are the genes associated with negative Fiedler vector entries. (C) Hi-C matrix of Chr 4 with activity of identified TADs annotated by colored boxes on the diagonal. Active (green), inactive (blue), or mixed (black) TADs contain genes that are all actively transcribed, repressed, or a mix of both, respectively. (D1) Left, fragment read contact map of an inactive TAD with genes annotated by color; Right, no detectable transcripts from any genes in this TAD over time, with individual genes colored corresponding to the left maps. (D2) Left, fragment read contact map of an active TAD; Right, active transcription of all genes in this TAD over time. (D3) Left, fragment read contact map of a mixed TAD; Right, expression patterns of its genes are both active and inactive over time. Dashed green lines on the maps indicate Hind-III cutting sites.

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Our methods and data for the algorithm

TADs

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G1

M

S

G2

Cell Cycle

Time-dependent state-transition matrix

A Matrix

Closest transition matrix to Identity subject to constraints from the data

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Natural dimension reduction

G1

M

S

G2

Cell Cycle

Data + Biology = Dimension-Reduced Data

Gene-Level

RNA-seq

TADs

Topological Associated Domains

TAD-Level

RNA-seq

+

=

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Gene A

Transcription factor = Protein that binds to DNA and changes local gene expression

Gene A

Gene Expression

Gene A

Controllability – Control Input

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Gene A

Cannot bind to protein inhibited regions

Gene A

Gene Expression

Gene A

Controllability – Control Input

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Gene A

expression

Gene A

expression

Activator

Repressor

Transcription factors can be activators or repressors

Controllability – Control Input

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Closed or open

Activator or Repressor

From Hi-C

Controllability – Control Input

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Controllability – TF Scoring

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Controllability – TF Scoring

[1] Lawson, C. L. and R. J. Hanson. Solving Least-Squares Problems. Upper Saddle River, NJ: Prentice Hall. 1974. Chapter 23, p. 161.

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An overview of “Algorithm for cellular reprogramming”

2000 functional units inferred

Mathematics + Bioinformatics

(TRANSFAC and FIMO databases)

Dimension reduction using intrinsic delineations in the genome (TADs)

Our algorithm predicted transcription factors

(TF) with known reprogramming capability²

Prediction: any cell to any cell!

TAD: Topologically associating domain, an inherent unit of chromatin organization

TAD₁ = g₁+g₂+g₃

TAD₂ = g₄+g₅

TAD₃ = g₆

+ Gene expression

Initial partioning using Fiedler vector¹

Genome-wide contact map (Hi-C)

Rank	TF
1	MyoD
2	PitX2
3	PKNOX2+
4	Six2

Skin to Muscle

Weintraub, 1989

Rank	TF
1	NANOG+OCT4+SOX2
2-11	NANOG+OCT4+other
12	SOX2+OCT4+MYCN

Skin to Stem Cell

Yamanaka, 2007