Post on 11-Apr-2019
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