Loads in biological circuits: How to engineer modular systems?
Domitilla Del VecchioMechanical Engineering
MIT
Workshop on Dynamics, Randomness, and Control in Molecular and Cellular Networks, Harvard, Nov 2019
Engineering de novo gene circuits in living cells foruseful functionalities
BiofuelsControl of cell fate Tracking, recognizing, killing cancer cells
Courtesy of Tal Danino
2
s
Synthetic Biology
2000
To systems and LSI
201X
Genetic Engineering
Jacob and MonodArberMullis…
Motifs era
Understanding biologyBio-inspired principles
Programming cells for useful functionalities
From understanding biology to programming biological systems for useful functionalities
In synthetic biology, we miss a way to describe/analyze composition in a way that leads to practical design/verification tools- we have large library of
partsà technology advancing fast
- BUT: when modules are put together, they do not retain their behavior in isolationàcontext-dependentàneed to re-design modules after composition
3
Describing a sophisticated system as the composition of simpler subsystems helps overcoming the complexity of analysis, verification and design:- can “forget” the details
within a subsystem to design the final system
- feedback can maintain I/O properties providing simplified abstractions for layered design
Design abstractions in synthetic biology
Increased scale is becoming possible in synthetic biology by composing simpler gates
[Moon et al. Nature 2012][Hanahan & Weinberg (2000)]
In natural systemscore processes areconserved during evolution and recur in different systems
A promising approach
But for a circuit with 11genes it takes one PhD
thesis of 5-6 years
Some sources of context-dependence
These issues can be viewed as a problem of lack of robustness to perturbations
à This is a problem for the field of “Control Systems”
4
Cellular ‘circuitry’, growth,… Modules often have “off-target” interactionsare subject to noise and growth rate changes
Cellular resourcesLoads applied by downstream modules is onesource of context dependence
Modules apply a load to the cellular resources: creates subtle couplings
Some sources of context-dependence
Cellular resourcesLoads applied by downstream modules is onesource of context dependence
Modules apply a load to the cellular resources: createssubtle couplings
5
Example:
u
B Expected behavior
RNAP, Ribosomes
Actual behavior!
0
20000
40000
60000
80000
100000
120000
-2 0 2 4Fluo
resc
ence
(A.U
.)
u (AHL)
Bu
Activation cascade
A
Sharing a limited amount of resources creates subtle couplings
6
Outline
Predicting and modulating emergent interaction networks
Decentralized (quasi-integral) control for mitigating effects of hidden interactions
re-scaling of existing regulatory links(they are weakened)
“hidden” interactions
Gi(u)
resource demand coefficientsJk / dkkk
xT
k
new interactions emerge(not due to regulatory links)
Network-level effects of limited resources
piHill function
ui
ui
Hi ui activator
ui repressor↵i /x
i
y
ki
uj pj
pi = ↵iFi(ui)� �ipi
Hi(ui)
New model
pi = ↵iFi(ui)
1 + JiFi(ui) +P
j JjFj(uj)� �ipi
effective interaction graph@Gi(u)
@u=
↵i@Fi/@u
(1 +P
j JjFj)2�
↵iFiP
j Jj@Fj/@u
(1 +P
j JjFj)2
standard models assume x (RNAP) and y (Ribo) are constant parameters
xT = x+X
xi, yT = y +X
yibut they are not: resources occupied by node i
x y
7
Qian, Huang et al. ACS Syn Bio, 2017
Effective interaction graphspipj
If pj is an activator, it is an effective repressor for any node not regulatedby it (“lateral repression”)
pj pi
If pj is a repressor, it is an effective activator for any node not regulatedby it (“lateral activation”)
=
pj pi
The overall effect of pj on a node pi regulated by it is undetermined if pi is not the only node regulated by pj
Qian, Huang et al. ACS Syn Bio, 2017
=
The overall effect of pj on a node piregulated by it is not changed if pi
is the only node regulated by pj(but it is weaker)
pj pi
=
8
9
MBP 1.0
MBP-dRFP
MBP-gapA
Gyorgy et al. Biophysical J. 2015
pipj
Experiments confirm “lateral repression”
When only RFP mRNA is produced there is no effect on GFPà The coupling is due to loading translation resources
Competition for gene expressionresources leads to up to 70% inhibition of non-target genes formedium copy number plasmids
BACTERIA!!!
10
price increases as RBS strength decreases
Experimental data
Any pair of protein products is constrained on isocost lines
price of p1 price of p2
allowed ribosome
budget
↵p1 + �p2 = yT
x ⌧ i, y ⌧ ki linear binding assumptionp2p1
Gyorgy et al. Biophysical J. 2015
Realizable region is the intersection of simplexes
11
p1
p2
Theorem: The set of realizable protein concentrations is the intersection of the simplexesS =
\
i
Si
realizableregion
S
Gyorgy and Del Vecchio, Proc. IEEE CDC, 2014
p1 p2
pmax2
p11pmax1
p12ideal realizable regionwithout considering
resource sharing
Qian, Huang et al. ACS Syn Bio, 2017
12
with hidden interactions
p1 p2
10 20 30 40 50 60 70 80-1
0
101
Larger J 2
10
10
RB
S st
reng
th
J decre
asesJ / DNA copy #
RBS strengthof target
can use J to tunestrength of hidden interactions
The effective interaction graph of an activation cascade is an IFFL
u
p2Expected behavior
p2u p1
DNA copy #
13
Outline
Predicting and modulating emergent interaction networks
Decentralized (quasi-integral) control for mitigating effects of hidden interactions
System withouthidden interactions
Decentralized feedback control problem
14
System withhidden interactions
wi di
resource demand at node i
di / Ji
wi
di
yigenetic
module i
vi
vi
yi
i
wi =X
j 6=i
di
rest of net
Problem: Design a local feedback controllersuch that yi depends only on vi and it isindependent of wi
Decentralized feedback control problem
15
i vi
yi
biomolecularcontroller
wi
yigenetic
module i
vi
di
resource demand at node i
di / Ji
wi =X
j 6=i
di
System withhidden interactions
wi
di
System withouthidden interactions
rest of net
Disturbance rejection via quasi-integral controlbiomolecular
controller
genetic module
Problem: Determine a biomolecular controller such that the steady state input/output response v to y is independent of w
v
y
w x
z
Challenge: molecular decay is unavoidable in vivo due to cell growth à integrator leakiness
z = k(v � y)� �z
y = g(x)x = f(x, z, w),
Qian and Del Vecchio. J. Royal Society Interface, 2018
Approach: For v and w constants, use integral control, e.g.
y = g(x)
z = k(v � y)
x = f(x, v, z, w),
under stability, y is independent of w at steady state
y = g(x)cannot send growth to zeroà increase speed of
all controller’s reactions
x = f(x, z, w),
z =1
✏(v � y)� �z
z
quasi-integral controlstructure
16
Examples:
y = x<latexit sha1_base64="5IcvhTxSge5jXDRRGh40dr4bw5k=">AAAB63icbVBNS8NAEJ34WetX1aOXxSJ4KkkV9CIUvXisYD+gDWWz3bRLdzdhdyOG0L/gxYMiXv1D3vw3btoctPXBwOO9GWbmBTFn2rjut7Oyura+sVnaKm/v7O7tVw4O2zpKFKEtEvFIdQOsKWeStgwznHZjRbEIOO0Ek9vc7zxSpVkkH0waU1/gkWQhI9jkUnr9VB5Uqm7NnQEtE68gVSjQHFS++sOIJIJKQzjWuue5sfEzrAwjnE7L/UTTGJMJHtGepRILqv1sdusUnVpliMJI2ZIGzdTfExkWWqcisJ0Cm7Fe9HLxP6+XmPDKz5iME0MlmS8KE45MhPLH0ZApSgxPLcFEMXsrImOsMDE2njwEb/HlZdKu17zzWv3+otq4KeIowTGcwBl4cAkNuIMmtIDAGJ7hFd4c4bw4787HvHXFKWaO4A+czx97tI3e</latexit>
y
w<latexit sha1_base64="QTJW+ZXlGFskIVTQXzavcle4NeE=">AAAB+3icbVC7TsMwFHXKq4RXKCOLRYXEVCUFCcYKFsYi0YfURJXjOK1Vx4lsB6ii/AoLAwix8iNs/A1OmgFajnSlo3Pu9fU9fsKoVLb9bdTW1jc2t+rb5s7u3v6BddjoyzgVmPRwzGIx9JEkjHLSU1QxMkwEQZHPyMCf3RT+4IEISWN+r+YJ8SI04TSkGCktja2GmbnlK5kgQf6Yu645tpp2yy4BV4lTkSao0B1bX24Q4zQiXGGGpBw5dqK8DAlFMSO56aaSJAjP0ISMNOUoItLLyq05PNVKAMNY6OIKlurviQxFUs4jX3dGSE3lsleI/3mjVIVXXkZ5kirC8WJRmDKoYlgEAQMqCFZsrgnCguq/QjxFAmGl4ypCcJZPXiX9dss5b7XvLpqd6yqOOjgGJ+AMOOASdMAt6IIewOAJPINX8GbkxovxbnwsWmtGNXME/sD4/AHSvpRM</latexit> no leakiness
2D controller: sequestration-basedx = z1 � x+ w
z1 =1
✏(v � z1z2)� z1
z2 =1
✏(x� z1z2)� z2
<latexit sha1_base64="3aht390dOgKgdG+T7wUW+DwYarI=">AAACf3ichVFbS8MwFE7rbc7b1EdfwoY3dKOtgvowEH3xUcGpsI6RZqcaTNOSpLpZ+jf8Yb75X3ww3SY4FTwQ+PguOScnQcKZ0o7zbtlT0zOzc6X58sLi0vJKZXXtRsWppNCiMY/lXUAUcCagpZnmcJdIIFHA4TZ4PC/02yeQisXiWg8S6ETkXrCQUaIN1a28bvm9WON+86Xr1vt7mT+8MpPQy/Fz7vvlkW7UJvZDSWjm5l+mgKeQ+5AoxmOR7zzVjcs4vd164f+W9f7N9ieyXrlbqTkNZ1j4N3DHoIbGddmtvJleNI1AaMqJUm3XSXQnI1IzyiEv+6mChNBHcg9tAwWJQHWy4Sw53jRMD4exNEdoPGS/JzISKTWIAuOMiH5QP7WC/Etrpzo87mRMJKkGQUeNwpRjHePiM3CPSaCaDwwgVDIzK6YPxGxKmy8rluD+fPJvcOM13IOGd3VYOz0br6OENlAV7SAXHaFTdIEuUQtR9GFVrT1r37bsbbthOyOrbY0z62ii7JNPbC6/jg==</latexit>
z = z1 � z2
z =1
✏(v � x)� z
<latexit sha1_base64="l9FHn5v4rMosv3WEQH/M7IPKZSc=">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</latexit>
note the memory variable:
w. leakinessw. leakiness/fast controller
biomolecularcontroller
genetic module
Problem: Determine a biomolecular controller such that the steady state input/output response v to y is independent of w
v
y
w x
z
Challenge: molecular decay is unavoidable in vivo due to cell growth à integrator leakiness
z = k(v � y)� �z
y = g(x)x = f(x, z, w),
Qian and Del Vecchio. J. Royal Society Interface, 2018
Approach: For v and w constants, use integral control, e.g.
y = g(x)
z = k(v � y)
x = f(x, v, z, w),
under stability, y is independent of w at steady state
y = g(x)cannot send growth to zeroà increase speed of
all controller’s reactions
x = f(x, z, w),
z =1
✏(v � y)� �z
z
quasi-integral controlstructure
Theorem: x = f(x, z, w)
z1 =1
✏h(v, z, x)� �z1
z2 =k
✏(v � y)� �z2
y = g(x)<latexit sha1_base64="MVekuLLkJa4SJItdkR3oZtY9VrI=">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</latexit>
If this closed loop system with is LES,� = 0<latexit sha1_base64="ReEE4Spm8VtgQNe2J67PQh1D1rw=">AAAB8XicbVBNS8NAEJ34WeNX1aOXxSJ4KkkV9CIUvXisYD+wDWWz3bRLdzdhdyOU0H/hxYMiXv033vw3btoctPXBwOO9GWbmhQln2njet7Oyura+sVnacrd3dvf2yweHLR2nitAmiXmsOiHWlDNJm4YZTjuJoliEnLbD8W3ut5+o0iyWD2aS0EDgoWQRI9hY6dHtDbEQ+Npz++WKV/VmQMvEL0gFCjT65a/eICapoNIQjrXu+l5iggwrwwinU7eXappgMsZD2rVUYkF1kM0unqJTqwxQFCtb0qCZ+nsiw0LriQhtp8BmpBe9XPzP66YmugoyJpPUUEnmi6KUIxOj/H00YIoSwyeWYKKYvRWREVaYGBtSHoK/+PIyadWq/nm1dn9Rqd8UcZTgGE7gDHy4hDrcQQOaQEDCM7zCm6OdF+fd+Zi3rjjFzBH8gfP5A+exj8I=</latexit>
y(✏) ! v as ✏ ! 0 independent of wThen: all fast controller reactions compute the difference and integrate
Biomolecular implementation:
17
Disturbance rejection via quasi-integral control
Tracking performance of quasi-integral controlProblem: Analytically determine tracking performance of the quasi-integral controller for time-varying inputs as timescale separation between controller reactions and molecular decay increases (i.e., smaller )✏
<latexit sha1_base64="IADNbfSLzf03DbPLELFcTrsJATM=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexKQI8BLx4jmAckS5id9CZDZmfWmVkhhPyEFw+KePV3vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMirTDJtMCaU7ETUouMSm5VZgJ9VIk0hgOxrfzv32E2rDlXywkxTDhA4ljzmj1kmdHqaGCyX75Ypf9Rcg6yTISQVyNPrlr95AsSxBaZmgxnQDP7XhlGrLmcBZqZcZTCkb0yF2HZU0QRNOF/fOyIVTBiRW2pW0ZKH+npjSxJhJErnOhNqRWfXm4n9eN7PxTTjlMs0sSrZcFGeCWEXmz5MB18ismDhCmebuVsJGVFNmXUQlF0Kw+vI6aV1VA78a3Ncq9VoeRxHO4BwuIYBrqMMdNKAJDAQ8wyu8eY/ei/fufSxbC14+cwp/4H3+AEibkBI=</latexit><latexit sha1_base64="IADNbfSLzf03DbPLELFcTrsJATM=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexKQI8BLx4jmAckS5id9CZDZmfWmVkhhPyEFw+KePV3vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMirTDJtMCaU7ETUouMSm5VZgJ9VIk0hgOxrfzv32E2rDlXywkxTDhA4ljzmj1kmdHqaGCyX75Ypf9Rcg6yTISQVyNPrlr95AsSxBaZmgxnQDP7XhlGrLmcBZqZcZTCkb0yF2HZU0QRNOF/fOyIVTBiRW2pW0ZKH+npjSxJhJErnOhNqRWfXm4n9eN7PxTTjlMs0sSrZcFGeCWEXmz5MB18ismDhCmebuVsJGVFNmXUQlF0Kw+vI6aV1VA78a3Ncq9VoeRxHO4BwuIYBrqMMdNKAJDAQ8wyu8eY/ei/fufSxbC14+cwp/4H3+AEibkBI=</latexit><latexit sha1_base64="IADNbfSLzf03DbPLELFcTrsJATM=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexKQI8BLx4jmAckS5id9CZDZmfWmVkhhPyEFw+KePV3vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMirTDJtMCaU7ETUouMSm5VZgJ9VIk0hgOxrfzv32E2rDlXywkxTDhA4ljzmj1kmdHqaGCyX75Ypf9Rcg6yTISQVyNPrlr95AsSxBaZmgxnQDP7XhlGrLmcBZqZcZTCkb0yF2HZU0QRNOF/fOyIVTBiRW2pW0ZKH+npjSxJhJErnOhNqRWfXm4n9eN7PxTTjlMs0sSrZcFGeCWEXmz5MB18ismDhCmebuVsJGVFNmXUQlF0Kw+vI6aV1VA78a3Ncq9VoeRxHO4BwuIYBrqMMdNKAJDAQ8wyu8eY/ei/fufSxbC14+cwp/4H3+AEibkBI=</latexit><latexit sha1_base64="IADNbfSLzf03DbPLELFcTrsJATM=">AAAB73icbVDLSgNBEOyNrxhfUY9eBoPgKexKQI8BLx4jmAckS5id9CZDZmfWmVkhhPyEFw+KePV3vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMirTDJtMCaU7ETUouMSm5VZgJ9VIk0hgOxrfzv32E2rDlXywkxTDhA4ljzmj1kmdHqaGCyX75Ypf9Rcg6yTISQVyNPrlr95AsSxBaZmgxnQDP7XhlGrLmcBZqZcZTCkb0yF2HZU0QRNOF/fOyIVTBiRW2pW0ZKH+npjSxJhJErnOhNqRWfXm4n9eN7PxTTjlMs0sSrZcFGeCWEXmz5MB18ismDhCmebuVsJGVFNmXUQlF0Kw+vI6aV1VA78a3Ncq9VoeRxHO4BwuIYBrqMMdNKAJDAQ8wyu8eY/ei/fufSxbC14+cwp/4H3+AEibkBI=</latexit>
Qian and Del Vecchio, IEEE Control Systems Letters, 2018
Real-10 4 -10 2 -10 0 -10 -2
Imag
-50
-40
-30
-20
-10
0
10
20
30
40
50 Poles of the full system
Real-10 4 -10 2 -10 0 -10 -2
Imag
-50
-40
-30
-20
-10
0
10
20
30
40
50 Poles of the reduced systemLinearized model pole map
Challenge: the quasi-integral control structure is a singular singularly perturbed (SSP) system:
Boundary layer dynamics: • Does not have an equilibrium unless
• Tikhonov theorem inapplicable
18
✏m = u(t)� ✓ms� ✏�m
✏s = y � ✓ms� ✏�s
y = R(w)m� �y<latexit sha1_base64="8fDSM365ZFxqxsRzwPBDElDZ2pc=">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</latexit>
m0 = u� ✓ms
s0 = y � ✓ms<latexit sha1_base64="W0KdoQzAnnkn0CQri6BVoUxql0U=">AAACDXicbZDLSgMxFIYz9VbHW9Wlm2C9bSwzWrwshIIblxXsBTqlZNJMG5rMDMkZoZS+gBtfxY0LRdy6d+fbmGmLVOsPgZ/vnMPJ+f1YcA2O82Vl5uYXFpeyy/bK6tr6Rm5zq6qjRFFWoZGIVN0nmgkesgpwEKweK0akL1jN712n9do9U5pH4R30Y9aUpBPygFMCBrVye/Lw4Co59qDLgGCJtefZ2iDcn2KtXN4pOCPhWeNOTB5NVG7lPr12RBPJQqCCaN1wnRiaA6KAU8GGtpdoFhPaIx3WMDYkkunmYHTNEO8b0sZBpMwLAY/o9MSASK370jedkkBX/62l8L9aI4HgojngYZwAC+l4UZAIDBFOo8FtrhgF0TeGUMXNXzHtEkUomADtUQiXqc5+Tp411ZOCe1oo3hbzpeIkjizaQbvoCLnoHJXQDSqjCqLoAT2hF/RqPVrP1pv1Pm7NWJOZbfRL1sc3o52Zfw==</latexit>
u = y<latexit sha1_base64="oGHP3bffzbuopYYSBo9QT163NOk=">AAAB6nicbVDLSsNAFL2pr1pfVZduBovgqiRafCyEghuXFe0D2lAm00k7dDIJMxMhhH6CGxeKuPWL3Pk3TtIgaj1w4XDOvdx7jxdxprRtf1qlpeWV1bXyemVjc2t7p7q711FhLAltk5CHsudhRTkTtK2Z5rQXSYoDj9OuN73O/O4DlYqF4l4nEXUDPBbMZwRrI93FV8mwWrPrdg60SJyC1KBAa1j9GIxCEgdUaMKxUn3HjrSbYqkZ4XRWGcSKRphM8Zj2DRU4oMpN81Nn6MgoI+SH0pTQKFd/TqQ4UCoJPNMZYD1Rf71M/M/rx9q/cFMmolhTQeaL/JgjHaLsbzRikhLNE0MwkczcisgES0y0SaeSh3CZ4ez75UXSOak7p/XGbaPWbBRxlOEADuEYHDiHJtxAC9pAYAyP8AwvFreerFfrbd5asoqZffgF6/0LVXiN7Q==</latexit>
A1. There exists a coordinate transformation to isolate the true fast variables
A2. The reduced system, obtained by setting the true fast variablesto QSS, is a high gain (1/𝛜) feedback interconnection of SPR systems
then:
Tikhonov-like theorem for general linear SSP systems:
lim supt!1
|y(t)� u(t)| = O(p✏)
<latexit sha1_base64="70iQP5a8rfKWJe3SMi9IIjWwCDY=">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</latexit>
Quasi-integral control implementation via sRNA silencing
19
Qian and Del Vecchio. IEEE CDC, 2016
high RNA transcription rates
fast RNAinteractions
biomolecularcontroller
genetic module
v
y
wx
z
regulatedgene sRNA
Ø
y<latexit sha1_base64="HeFEcJAPBKhU6LoK/9kzEMM2HZA=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lFUG8FLx5bMLbQhrLZTtq1m03Y3Qgh9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZekAiujet+O6W19Y3NrfJ2ZWd3b/+genj0oONUMfRYLGLVDahGwSV6hhuB3UQhjQKBnWByO/M7T6g0j+W9yRL0IzqSPOSMGiu1s0G15tbdOcgqaRSkBgVag+pXfxizNEJpmKBa9xpuYvycKsOZwGmln2pMKJvQEfYslTRC7efzQ6fkzCpDEsbKljRkrv6eyGmkdRYFtjOiZqyXvZn4n9dLTXjt51wmqUHJFovCVBATk9nXZMgVMiMySyhT3N5K2JgqyozNpmJDaCy/vEq8i/pN3W1f1pqXRRplOIFTOIcGXEET7qAFHjBAeIZXeHMenRfn3flYtJacYuYY/sD5/AFRmozC</latexit><latexit sha1_base64="HeFEcJAPBKhU6LoK/9kzEMM2HZA=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lFUG8FLx5bMLbQhrLZTtq1m03Y3Qgh9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZekAiujet+O6W19Y3NrfJ2ZWd3b/+genj0oONUMfRYLGLVDahGwSV6hhuB3UQhjQKBnWByO/M7T6g0j+W9yRL0IzqSPOSMGiu1s0G15tbdOcgqaRSkBgVag+pXfxizNEJpmKBa9xpuYvycKsOZwGmln2pMKJvQEfYslTRC7efzQ6fkzCpDEsbKljRkrv6eyGmkdRYFtjOiZqyXvZn4n9dLTXjt51wmqUHJFovCVBATk9nXZMgVMiMySyhT3N5K2JgqyozNpmJDaCy/vEq8i/pN3W1f1pqXRRplOIFTOIcGXEET7qAFHjBAeIZXeHMenRfn3flYtJacYuYY/sD5/AFRmozC</latexit><latexit sha1_base64="HeFEcJAPBKhU6LoK/9kzEMM2HZA=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lFUG8FLx5bMLbQhrLZTtq1m03Y3Qgh9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZekAiujet+O6W19Y3NrfJ2ZWd3b/+genj0oONUMfRYLGLVDahGwSV6hhuB3UQhjQKBnWByO/M7T6g0j+W9yRL0IzqSPOSMGiu1s0G15tbdOcgqaRSkBgVag+pXfxizNEJpmKBa9xpuYvycKsOZwGmln2pMKJvQEfYslTRC7efzQ6fkzCpDEsbKljRkrv6eyGmkdRYFtjOiZqyXvZn4n9dLTXjt51wmqUHJFovCVBATk9nXZMgVMiMySyhT3N5K2JgqyozNpmJDaCy/vEq8i/pN3W1f1pqXRRplOIFTOIcGXEET7qAFHjBAeIZXeHMenRfn3flYtJacYuYY/sD5/AFRmozC</latexit>
m<latexit sha1_base64="Dwj5TRChP0z4GP299Yoc+Cu/nW0=">AAAB53icbVBNS8NAEJ3Ur1q/qh69BIvgqSQiqLeCF48tGFtoQ9lsJ+3a3U3Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZelHKmjed9O6W19Y3NrfJ2ZWd3b/+genj0oJNMUQxowhPViYhGziQGhhmOnVQhERHHdjS+nfntJ1SaJfLeTFIMBRlKFjNKjJVaol+teXVvDneV+AWpQYFmv/rVGyQ0EygN5UTrru+lJsyJMoxynFZ6mcaU0DEZYtdSSQTqMJ8fOnXPrDJw40TZksadq78nciK0nojIdgpiRnrZm4n/ed3MxNdhzmSaGZR0sSjOuGsSd/a1O2AKqeETSwhVzN7q0hFRhBqbTcWG4C+/vEqCi/pN3Wtd1hqXRRplOIFTOAcfrqABd9CEACggPMMrvDmPzovz7nwsWktOMXMMf+B8/gA/doy2</latexit><latexit sha1_base64="Dwj5TRChP0z4GP299Yoc+Cu/nW0=">AAAB53icbVBNS8NAEJ3Ur1q/qh69BIvgqSQiqLeCF48tGFtoQ9lsJ+3a3U3Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZelHKmjed9O6W19Y3NrfJ2ZWd3b/+genj0oJNMUQxowhPViYhGziQGhhmOnVQhERHHdjS+nfntJ1SaJfLeTFIMBRlKFjNKjJVaol+teXVvDneV+AWpQYFmv/rVGyQ0EygN5UTrru+lJsyJMoxynFZ6mcaU0DEZYtdSSQTqMJ8fOnXPrDJw40TZksadq78nciK0nojIdgpiRnrZm4n/ed3MxNdhzmSaGZR0sSjOuGsSd/a1O2AKqeETSwhVzN7q0hFRhBqbTcWG4C+/vEqCi/pN3Wtd1hqXRRplOIFTOAcfrqABd9CEACggPMMrvDmPzovz7nwsWktOMXMMf+B8/gA/doy2</latexit><latexit sha1_base64="Dwj5TRChP0z4GP299Yoc+Cu/nW0=">AAAB53icbVBNS8NAEJ3Ur1q/qh69BIvgqSQiqLeCF48tGFtoQ9lsJ+3a3U3Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZelHKmjed9O6W19Y3NrfJ2ZWd3b/+genj0oJNMUQxowhPViYhGziQGhhmOnVQhERHHdjS+nfntJ1SaJfLeTFIMBRlKFjNKjJVaol+teXVvDneV+AWpQYFmv/rVGyQ0EygN5UTrru+lJsyJMoxynFZ6mcaU0DEZYtdSSQTqMJ8fOnXPrDJw40TZksadq78nciK0nojIdgpiRnrZm4n/ed3MxNdhzmSaGZR0sSjOuGsSd/a1O2AKqeETSwhVzN7q0hFRhBqbTcWG4C+/vEqCi/pN3Wtd1hqXRRplOIFTOAcfrqABd9CEACggPMMrvDmPzovz7nwsWktOMXMMf+B8/gA/doy2</latexit> s
<latexit sha1_base64="ihRlHvRgIdYpFlt1tOcejpvu4pU=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lEUG8FLx5bMLbQhrLZTtq1m03Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZemAqujet+O6W19Y3NrfJ2ZWd3b/+genj0oJNMMfRZIhLVCalGwSX6hhuBnVQhjUOB7XB8O/PbT6g0T+S9maQYxHQoecQZNVZq6X615tbdOcgq8QpSgwLNfvWrN0hYFqM0TFCtu56bmiCnynAmcFrpZRpTysZ0iF1LJY1RB/n80Ck5s8qARImyJQ2Zq78nchprPYlD2xlTM9LL3kz8z+tmJroOci7TzKBki0VRJohJyOxrMuAKmRETSyhT3N5K2IgqyozNpmJD8JZfXiX+Rf2m7rYua43LIo0ynMApnIMHV9CAO2iCDwwQnuEV3pxH58V5dz4WrSWnmDmGP3A+fwBIiIy8</latexit><latexit sha1_base64="ihRlHvRgIdYpFlt1tOcejpvu4pU=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lEUG8FLx5bMLbQhrLZTtq1m03Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZemAqujet+O6W19Y3NrfJ2ZWd3b/+genj0oJNMMfRZIhLVCalGwSX6hhuBnVQhjUOB7XB8O/PbT6g0T+S9maQYxHQoecQZNVZq6X615tbdOcgq8QpSgwLNfvWrN0hYFqM0TFCtu56bmiCnynAmcFrpZRpTysZ0iF1LJY1RB/n80Ck5s8qARImyJQ2Zq78nchprPYlD2xlTM9LL3kz8z+tmJroOci7TzKBki0VRJohJyOxrMuAKmRETSyhT3N5K2IgqyozNpmJD8JZfXiX+Rf2m7rYua43LIo0ynMApnIMHV9CAO2iCDwwQnuEV3pxH58V5dz4WrSWnmDmGP3A+fwBIiIy8</latexit><latexit sha1_base64="ihRlHvRgIdYpFlt1tOcejpvu4pU=">AAAB53icbVBNS8NAEJ3Ur1q/qh69LBbBU0lEUG8FLx5bMLbQhrLZTtq1m03Y3Qgl9Bd48aDi1b/kzX/jts1BWx8MPN6bYWZemAqujet+O6W19Y3NrfJ2ZWd3b/+genj0oJNMMfRZIhLVCalGwSX6hhuBnVQhjUOB7XB8O/PbT6g0T+S9maQYxHQoecQZNVZq6X615tbdOcgq8QpSgwLNfvWrN0hYFqM0TFCtu56bmiCnynAmcFrpZRpTysZ0iF1LJY1RB/n80Ck5s8qARImyJQ2Zq78nchprPYlD2xlTM9LL3kz8z+tmJroOci7TzKBki0VRJohJyOxrMuAKmRETSyhT3N5K2IgqyozNpmJD8JZfXiX+Rf2m7rYua43LIo0ynMApnIMHV9CAO2iCDwwQnuEV3pxH58V5dz4WrSWnmDmGP3A+fwBIiIy8</latexit>
ribosomeavailability change
w
v
y = R(w)m� �y
m =v
✏� ✓
✏ms� �m
s =y
✏� ✓
✏ms� �s
z = m� smemory variable
LES of closed loop system when Is satisfied
then
independent of disturbance (ribosome availability)
✏z = (v � y)� ✏�z
y(✏) ! v as ✏ ! 0
� = 0<latexit sha1_base64="ReEE4Spm8VtgQNe2J67PQh1D1rw=">AAAB8XicbVBNS8NAEJ34WeNX1aOXxSJ4KkkV9CIUvXisYD+wDWWz3bRLdzdhdyOU0H/hxYMiXv033vw3btoctPXBwOO9GWbmhQln2njet7Oyura+sVnacrd3dvf2yweHLR2nitAmiXmsOiHWlDNJm4YZTjuJoliEnLbD8W3ut5+o0iyWD2aS0EDgoWQRI9hY6dHtDbEQ+Npz++WKV/VmQMvEL0gFCjT65a/eICapoNIQjrXu+l5iggwrwwinU7eXappgMsZD2rVUYkF1kM0unqJTqwxQFCtb0qCZ+nsiw0LriQhtp8BmpBe9XPzP66YmugoyJpPUUEnmi6KUIxOj/H00YIoSwyeWYKKYvRWREVaYGBtSHoK/+PIyadWq/nm1dn9Rqd8UcZTgGE7gDHy4hDrcQQOaQEDCM7zCm6OdF+fd+Zi3rjjFzBH8gfP5A+exj8I=</latexit>
note: need both fast RNA interactions and high RNA transcription rate
(for “free”)
(we can tune)
20
unregulated device regulated deviceAHL = 0 AHL = 1000 nM
normalized fluorescence histograms from single-cell measurements by cytometery
GFP fluorescence GFP fluorescence
biological replicate #1
biologicalreplicate #2
biological replicate #3
OL CL
0
2
4
6× 104
0.4
1
0
2
4
6× 104
unregulated device regulated device
Nor
mal
ized
GF
P/O
DR
FP
/OD
(A
.U.)
time (hr)time (hr)
ln (
OD
600)
ln (
OD
600)
-0.5 1.5 3.5 5.5 7.5-2.5 -0.5 1.5 3.5 5.5 7.5-2.5
AHL induction AHL induction
population-level measurements by mircoplate photometerN
orm
aliz
edG
FP
/OD
RF
P/O
D (
A.U
.)
0 0
-4
-3
-4
-3
AHL = 0AHL = 1000 nM
0.4
1
0 7.5 0 7.5time (hr)time (hr)
(OL) (CL)
output interfaceunaltered by controller
input interfaceunaltered by controller
Huang, Qian, and Del Vecchio. Nat. Comm., December 2018
QIC control for resource decoupling via sRNA silencing
Summary
Cellular resourcesModules apply a load to the “cellular system”: creates subtle couplings
= =
We have uncovered andmodeled hidden interactionsà resource-aware circuit design
Resource decoupling for adaptation of
genetic modules to resource variability
through quasi-integral control (QIC) Implementing QIC withsRNA interference allows forhighly scalable and tunabledesign of post-TX controllersthat leave input and outputInterfaces of genetic modulesunchanged
21
Ross Jones Hussein Abdallah
Bose Research Award
Thanks to
Yili QianHsin-Ho Huang
Ross Jones
Former Students/Post-docs:
Andras Gyorgy(NYU, Abu Dhabi)
Hattie Chang(Harvard)
Jose Jimenez(U. of Surrey)
John Yazbek
22