Model-Free Network Control

Killian RyanLars SeemannAlexander Mo, UT AustinJason Shulman, Stockton College

Gregg Roman, Ole Miss

Model-Free Network Control

Network

[Ghezzi et al., PLOS Genetics 9, e1003986 (2013)]

Model-Free Network Control

Control

Model-Free Network Control

Model-Free

Formulation: Cells

• Difficult to reverse mutations or chromosomal rearrangement

• “Stationary” states• Assume that the state of the system can be

represented by the gene-expression profile; i.e., cells with identical gene expression profiles will behave the same way

• Differences differential expression of some genes; obtained from microarrays, RNA-Seq, RT-PCR, …

• Control problem is reduced to changing – state target state

• Can the target be reached by controlling the expression levels of a small set of genes?

Example: (with G. Roman, Ole Miss)

• homeostatic network prevents trauma

• Quantifiable behavioral changes: – Shorter sleep latency– Longer sleep– Increased arousal threshold– Lower associative learning

• Genetics: – Up/Down regulation of 159 genes– Nodes belonging to network

• Goal– Genetically move the head transcriptome to a

sleep-deprived-like state

• A small # of controls

Sleep Deprivation in Drosophila[Zimmermann et.al., Physiol Genomics 27, 337 (2006)]

Outline

• System responses to perturbations are easily found• Proposal: use response surfaces for control

• Network: nodes, interactions• Specify the “state” with “node values”

• Response surfaces are smooth low order approximations small # of experiments

Control Algorithm: Step 1

• Select a node; measure system response as its level is altered; can use a low-order approxn

• If the target Z is close done

• If not, need a second control node

• How does one determine the next “best” node?

Control Algorithm: Step 2

• Extreme case: if node “n” caused the deviation, redefining δ with wn=0 will let the system close in on Z

• Compute δn by setting one wn=0 at a time; find the minimum; that corresponds to the “best” next control node

• Now, we can try to reach Z by altering the levels of 2 genes externally

Control Algorithm: Ctd.

• Observation: it is possible to reach “close” to Z through external control of the levels of a few genes

• Control nodes and their order of appearance depend on the first choice and the target state

Outline

• Use response surfaces for control• Systematically increase the number of control

nodes; only a small number needed to get “close” to target

• Lack of convergence: non-linearily

• Network represents nodes, interactions• “State” can be specified using the “node values”

• Example

Nonlinear Electrical Circuit

• State: node potentials (gene expression levels)– ground a node ≅ gene KO

• Electrical elements: coupling• Node potentials are

controlled/measured [MiniLab-1008 cards]

• Control algorithms works;– # control nodes = # “mutations”

Electrical Circuit: Prediction Errors

• Errors are due to differences between the response surface and approximation

• on P0P1P3 mean magnitude = 5.19 Volts• What about more refined approximation?• Errors in data limit the advantages of higher-order

fitting

Planar Approximation

Quadratic Approximation

Noise = 0% 152 mV 24 mV

Noise = 5% 255 mV 207 mV

Noise = 10% 450 mV 430 mV

Note on “Epistasis”

Outline

• Use response surfaces for control• Systematically increase the number of control

nodes; only a small number needed to get “close” to target

• Validated in synthetic models, and in nonlinear electrical circuits

• Genetic applications require sequencing mutants• Lack of convergence: approximation

- Limited utility in refinements due to noise

• Network represents nodes, interactions• “State” can be specified using the “node values”

• Other testable predictions?

Predicting Double/Triple Knockouts

• Proximity of approximation to response surface?

• Approximation can be used to predict the values of double/triple knockout mutants

• Especially useful test for gene regulatory networks

Application: O2-Deprivation Network of E.coli(Covert, Knight, Reed, Hergaard, Palsson, 2004)

• Gene Ontology O2-deprivation network: 284 genes• WT + 5 SKOs 5D planar approximation • Expression levels of the DKO and all organisms in anaerobic conditions can be

predicted• ~70% predictions are within 95% confidence level

O2-Deprivation Network of E.coli

Feed forward loop bistability

~70%

~30%

Proposal: Sleep Homeostasis in Drosophila(Gregg Roman, Ole Miss)

• Sleep-like state:- consolidated periods of immobility- species-specific posture- increased arousal threshold

• As in mammals, sleep in Drosophila is regulated by the circadian network and a homeostatic network.

• Behavioral changes due to sleep deprivation:- arousal threshold- longer duration of sleep

- lower associative learning

Sleep Homeostasis: Genetics (Zimmermann et.al., 2006)

• Genetics: sleep deprivation: - regulates 114 genes -regulates 55 genes

• DroID➪ Known Interactions

Fasciclin 2: transmembrane receptorbrahma: chromatin-remodeling protein; facilitates global transcriptionSaf-B: mRNA bindingCrc: calcium signaling & protein folding cg6724: WD40-repeat, potential scaffold protein Syndecan: transmembrane receptor Creb4: transcription factor

To be done!

Double Knockout Predictions

• Predict the genetic profile of ΔSdcΔSafB using the profiles of the wildtype, ΔSdc, and ΔSafB

• 45/45 predictions were within 5% confidence intervals

• However, error bars are large

Circadian/Seasonally Driven Processes

• Consider a model of the form

• Can be written

• Surfaces are in a complex space

Circadian Model: Double KO Predictions(Jason Shulman)

Summary

• Model-free control - only requires response surfaces- low-order approximations work well (evolution?)

• Generalizes to circadian/periodically-driven networks

• Proposed applications in Drosophila to- sleep deprivation- addiction- anxiety

• Model vs. Model-Free

Possible Issues

• There is genetic variability even between cells of the sametissue

• Can the tissue (or its action) be modified by changing the meanlevels of genes?

[Newell et al., Cell 36, 142 (2012)]

[Sandberg, Nature Methods 11, 22 (2014)]

Publications

• G.H. Gunaratne, P.H. Gunaratne, L. Seemann, and A. Torok, “Using Effective Networks to Predict Selected Properties of Gene Networks,“ PLoS One, 5, e13080 (2010).

• J. Shulman, L. Seemann, and G.H. Gunaratne, “Effective Models of Periodically Driven Networks,“ Biophysical Journal 101, 2563 (2011).

• J. Shulman, L. Seemann, G.W. Roman, and G.H. Gunaratne, “Effective Models for Gene Networks and their Applications, “ Biophysical Reviews and Letters 7, 41 (2012).

• J. Shulman, F. Malatino, A. Mo, K. Ryan, and G.H. Gunaratne, “Response Surfaces of Networks: Experimental Results,” Scientific Reports, 4, 7574 (2014).

• J. Shulman, F. Malatino, W. Widjaja, and G.H. Gunaratne, “Experimental Determination of Circuit Equations,” American Journal of Physics, 83, 64 (2015).

Response Surface Methodology

• Designed to control complex/unknown processes (Box and Hunter, 1957)

• Goal: phenomenological relationship between the response of interest and control variables

• Model find optimum control parameters

• For networks• Control variables are part of the response• The “response space” is high dimensional• # of control variables?

which nodes? their levels?

Outline

• Use response surfaces for control• Systematically increase the number of control

nodes; only a small number needed to get “close” to target

• Validated in synthetic models, and in nonlinear electrical circuits

• Genetic applications require sequencing mutants

• Network represents nodes, interactions• “State” can be specified using the “node values”

• Convergence or lack thereof?

A Model Food Web• A model food web 7 species was

invaded by an eight. The interactions were of the Lotka-Volterra type

• Need to find how to manipulate two nodes to mitigate the effects of the invader

• Can nearly eliminate changes in the 7 original species and reduce the population of the invading species to 7% of post-invasion value.

• Next: Chesapeake Bay model and Coachella Valley food webs.

Putting Flies to Sleep: Genetics

• Move from Normal Sleep Deprived state

• increase: pan-neural elav-Gene switch• decrease: UAS-RNAi transgenes

Sleep Homeostatis: Behavior• Move from Normal Sleep Deprived state• Compare behavioral features

- longer sleep- sleep latency- arousal threshold- associative learning