Swimming in complex environments: from biofilms to bacteria powered micro-devices - ROBERTO DI LEONARDO
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Swimming in complex environments: from biofilms to bacteria powered micro-devices ROBERTO DI LEONARDO Dip. Fisica, Sapienza Università di Roma, Italy CNR-NANOTEC Soft and Living Matter Laboratory School for Advanced Studies Sapienza
Outline
TODAY
A SELF-PROPELLED MICRO-MACHINE Statistical Mechanics
d) BACTERIA POWERED MICRODEVICES
TUESDAY
Microhydrodynamics
a) SELF PROPELLING BACTERIA
c) STOCHASTIC DYNAMICS IN ACTIVE BATHS
b) CONFINED SWIMMING
+
STOCHASTIC DYNAMICS IN ACTIVE BATHS I targeted delivery of colloidal cargos
Brownian motion: thermal motion at equilibrium
1827
“Extremely minute particles of solid
matter, when suspended in pure
water ... exhibit motions for which I
am unable to account.”
ROBERT BROWN
1867
“Brownian motion [...] provides us with one of
the most beautiful and direct experimental
demonstrations of the fundamental principles
of the mechanical theory of heat, making
manifest the assiduous vibrational state that
Theory of Brownian motion must exist both in liquids and solids”
GIOVANNI CANTONI
1905
W. Sutherland (1858-1911) A. Einstein (1879-1955) M. Smoluchowski
A. EINSTEIN W. SUTHERLAND (1872-1917)
MEAN-SQUARE
DISPLACEMENT
2
h r (t)i = 6Dt
DIFFUSION
COEFFICIENT STOKES DRAG
D = kB T / = 6⇡µa
Source: www.theage.com.au Source: wikipedia.org Source: wikipedia.org
Langevin equation
FRICTION RANDOM FORCE
1908 PAUL LANGEVIN: LANGEVIN EQUATION
IT IS EASY TO GIVE A mẍ ⇠ 0 = f (x) ẋ(t) + ⌘(t)
DEMONSTRATION THAT IS
EXTERNAL INTERACTION WITH SOLVENT
INFINITELY MORE SIMPLE
BY MEANS OF A METHOD
THAT IS ENTIRELY UNBIASED h⌘(t)i = 0
DIFFERENT
0 0
WHITE NOISE h⌘(t)⌘(t )i = kB T 2 (t t)
FLUCTUATION
Z t DISSIPATION
FRICTION ẋ(t) = 2 (t t0 ) ẋ(t0 )dt0
0
+
"Z #
B
⇢B f (x)
= exp dx
⇢A A kB T
=
UB UA
BOLTZMANN DISTRIBUTION exp
kB T
Colloidal delivery at equilibrium
PEAKED CONCENTRATION (DELIVERY TO B)
FLAT CONCENTRATION (MAXIMUM ENTROPY)
EXTERNAL WORK ! ENTROPY DECREASE
U (x)
DENSITY
EXTERNAL FIELD
ENERGY
A
A B x B
"Z #
B
⇢B f (x)
= exp dx
⇢A A kB T
=
A
ASYMMETRIC BARRIER
NO NET WORK B
UB UA
BOLTZMANN DISTRIBUTION exp
kB T
Transport with external fields
ELECTRIC FIELDS
HEATING)
TEMPERATURE FIELDS (LASER
SULLIVAN et al. PRL (2006)
MAGNETIC, FLOW ...
DUHR & BRAUN, APL (2005)
Optical micromanipulation: Holographic Tweezers
GRIER, NATURE (2003)
SPATIAL LIGHT MODULATOR MICROSCOPE OBJECTIVE PADGETT & DI LEONARDO, Lab Chip (2011)
NA 1.4
100x
LIQUID CRYSTALS SLM
8 bit, 0-2π phase modulation
1 Megapixel resolution
SLM
GRAPHICS PROCESSING UNIT (GPU)
R. DI LEONARDO
ED BY
SPONSOR
ERSHIP
IC PARTN
ACADEM
DIGITAL PARALLEL HOLOGRAPHY
Highly optimized holograms in real time
DI LEONARDO et al., Opt. Express (2006)
BIANCHI & DI LEONARDO Comp. Phys. Comm. (2010)
5 µm
2 µm SILICA BEADS IN WATER
Using active particles as micro-oxen
SYNTHETIC SWIMMERS SWIMMING CELLS
CATALYTIC Pt-Au NANOMOTOR C. reinhardtii
unicatSioUNDncAosRAmRAm unicat ns
JAN et al. SMAio AS (2005)
LL (2010) L. PN
WEIBEL ET A
In another meth In another meth
od of carg od o
bifunctional, pho bifunctioonadl,ropph-o ff, a f cargo drop-off, a
tocleavable o-nit otocl
based linker (P based linkero benzyl-eavable o-nitrobenzyl-
CL) was used r (PCL) was used to
to attach
the motor to th the
e cargo. mTohto r to athtteacchargo.
of o-nitrobenzy of o-niterop hotolysis The photolysis
l-group-based li b e n zy l-g up-based li
widely employed widely emplo nkers ro is nkers is
In another meth in combinatoria yed in combinatorial
osydnoth f ecasirg synth s forl th organic organic
bifunctional, pho s ofodr ro thpe-ore , aase ofesi
ffle e re le a se o f moieties from
toclso eali vadbsu le po p -n
o rt
it s.
ro [14] solid sum p
oietie[1
p o rt s.
s 4]from
based linker (P b e nW zyhl-itesides et al. W hitesides et al. d
CL)stra wates duse th ed re st ra te d th e d e m o n - emon-
the motor to th toleatt seacohf cargo fromrelease o f c a rg o from photo-
e cta argctioc. Tbhaecteprihaotou tactic bacteriaphuosi to-
of o-nitrobenzy ly
si ngs such linkers [15,16n]g such linkers [15,16]
si
l-groFuigpu-brease2dA lish Fig 2A sho.ws a sc .
widely employed no kwers s aisschuere m atic image of h e m a tic image of
in P coCm Lb-ainssais PCL ss
synthesis for the toteridalco argo andicrop-o-a isted cargo drop
ff. Pt"Au"PPy -off. Pt"Au"PP
releroad
EXTERNAL FIELDS
Figure 1. A) Sche se s ow f e re
m o sy
ie tineth ro d s w e re sy nthesized incorp y
ematic image of matic image of m so li d su p p orts. [1 4] s e fr
sioz e
m d in c o rp orating car-
Au
tached to p"oPsiPtiyve
m moototorrdaettsiagn
ched for silver-assis otor design for si
lver-assis te
Whbit oexsiylidcesaceid t a
g l.
ro d boxylic acoid rating car-
g ro u
to po si ti te d ca rg o d st rate d ca rg o d rop-off. Pt"Au"A ue pm s in
o n th
- e polymer segm p s in th e polymer segme
a
he Ag sectrrioonwopfoints to th
ly charged 0.8-m vely
m-diameterchPaSrg ed 0ro .8p -m-om .dPiat"
ff-d th Aeeute"
re APle
g" a–se o T fh is
c a w g" T h is w e n t. nt.
e Ag sectio n
e rod that dissolv of the rod thatmdid – a ta
in
m r S a m rg ao
idine cargo. The phs a
fr coc o
m m li sh
o toe a s a c c o m p li sh e d
releasingthth e
c ti
cac rg o
b .a Th
c d
- b y e le c b y e le c tr
es in the presence solves in thte pyrrtr
go. B) TEM image e cargo. B) TEM im is e
e prirelu
b ase e usiniz b lue[1 izing opolymer- opolymer-
nce ogfin
MICROSWIMMERS
depictingssiolvf ePr-t" a ge s o f P o f U V li U gV lipcgh
su yhrrt oli le
n k ae nrsd . 4 5,16]
-( o le a n d 4 -(
A u "lu Agti"Au–Ppy rods. t" A u " F ig
Ag Auure gh
–Pp2yAt (3 6 5shnm (3 6 5 nm), 3 -p yrrolyl) 3
butyric yrrolyl)-p
ssolution-assiste
and the imdaca
disso on-assisted cargCo) Screen" -c ap
rod s. oCw ),
) Sscraeaecnsc id
-cha ep mtu a to
ti c im acid to butyric
rg o d ro p -o ff . d ro
age n the left is b -a p-o P C
ff . L
Th tu re im a ge s re im a ge a
y
s giee ld o f y ie ld a
PPyaPPyCcOoO
the right is post U ge on the right is peoim Th e imssis
erefore UV ete copolymer,
aged oncth arg polymer,
clarity, theVre exposure where th st UV eoxp o su re w h e xp o su re
e leoftdP isro
Pbye
p P-o
fo P ff
rey C
.
U P
VO t"
e O
xp AH
o u
.
su FP
"
re igPuyre 2B shows H . Figure 2B show
ow points to the d arrow points toe cargo dissoci rodsthw e ca rergosydnisth
motor and th the motor andath tes from the e m
so ecisiazteim
e sd fr
a o
g
in m
e c th
o f
rpe m o im a g e o f a Pt"AuE"Ma T s a TEM
sign for silver-ass e black arrow to ebo bx layck a rr o o
w
lic acid grouepca
to
tor.thFo r ao P
ra to
t"tir.n
A Fo
g u rc
" a Pr-
P y P P P y P P
ged 0.8-mm-diam
isted cargo drop
-off. Pt"Au"Ag"
th e cargo. s inrgFoth . eure
ig p o ly3 m she o
r w
se FiguPre yCOOH motor.
3 sh o w s
yCOOH motor.
This was accomp s
g mtheent.structure of th e structure of P
hpaat rt where, n eisteth r PS–amidine ca
e rg o . Th li sh w
e dh ic
b y
h th
e le e cptrhoopto w h ic h th e p P C L
hotocleavable min CL in
dis
icsolelvsp
esein e d th
, eanp re particle speed, a blue e iz in g p o ly
c le
m a evr-
a b le m
u"Agm o se
b–ilPitpyy orof thde mbenim ce
is othf UeV elile
ghcttr(3o6p5h nd me is the eleyrrole and 4-(b 3-py ayn by an o iety is flanked oiety is flanked
bAim eta" A u
llic particle (aCfu d s. e ta n
o mre
llic tuarerticle (a fu acbid ),
ti c c tr o p h o re ti c rr oa m
ly in
l) e fu n
b uc ti
ty
biotin on the othorincality on one sid a m in e fu n c tio nality on one sid
drop-ocffo. Th n st a nction aopfp
) Screen-c
im a nctioniootifnthoto n the oyth ie e
ld r. T e r. T e a n d e and
PICKUP TRANSPORT DELIVERY
e imn t,
a so lu ti th e d ie ge s e d ie h ea
lectric end of cxoyploalycid c a rb o h e c a rb o x y
n viscosity, parton tho ge e n
le v
ft is
is c
b oe si
fo ty , p a le c tr ic P e
P n
y Pd P o
y m egr,
ro u
the rod were b on the polymer p s l a c id g ro u p s o
ure whzeeretathpeoca tergnotiic le dimension, U re
a
V exprtic leredimension, faCnO
osu thO eH ro. dFig wuere 2bB o u o u
n the polymer
J is th da l)
is ,
so J
ci a is
te s th n d p a rt ic le d p a rt ic le n
sh d o wto s th
a e
T E a n d to th e a m
nd þ the e current
cbhla
e ckic
m arr
a orew to dth þ fr
enesicaty dueemtocthuth
o errm t r.deFonrsityim
eonto d
baifguenocftiaonPat"
u e to l A PC u "L P v
P
bifunctional PC M
ia
y P L
mine terminus
v ia of the ine terminus of the
l a c ti o rg
n, and. s is e con ctro- Fig e e le th e e le ctro- dimethy li P 3y -(
C eO th Oy 3 -( e th y li
n, and s is the con l-pH mr.ethyleneaminominomethyleneamino
o dim mm inooto
However, Wdauncgtivity of theth d u c ti v it y o f
ureeth3yl-
th e b sh po row p
s a n
th -1e -a st
m ruin ro p a n -1-amine coupli )-N,N- )-N,N-
et al. recently sh et al. recenbtluylkshsolution. wh oicfh
ulk solution. o ceture c o u p
o fli n
P gC
f the PCL was C). The biotin L(E D
in n g (E D C
ions, the spoew e
ed that in the case owed that in
d o o f si th
thth
e
e ePpChLoto
c a se o f
wcale
si s auvse a d
b leto m li
o niek ty th is used to link the end ). The biotin end
fe th
is ethpe f the pa lver by lver s eflm anokto edr motor
oes nor any modulator with computer-generated holograms. Thus,
Colloids in active baths
5 µm LATEX BEADS IN E.coli
0.6
101 kB T ⇤
MSD/4t
+ 0.4 D⇤ =
0.2
MSD (µm2)
0.0 –2
100 10 10–1 100
D=
kB T
t
ξ
0 1 2 3
10–1
!
10–2
10–2 10–1 100
t (s)
ACTIVE NOISE
A schematic representation of the main geometric and dynamic features of transition
ning electron microscopy image of a square0 =structure
f (x) that ẋ(t) + ⌘(t)
gathers + ⇠(t)
particles to the c
r, 10 mm in length. (c) The mean squared displacements (MSD) of the beads in the
h⇠(t)i = 0
and in the bacterial bath (filled symbols). Solid and dashed
2
lines
t/⌧
are fits to the data
ve system. Inset depicts the same datah⇠(0)⇠(t)i = h⇠diffusivity
as an effective ie COLORED NOISE
(divided by 4t), clNon-equilibrium random walks
1D RUN AND TUMBLE
SCHNITZER, PRE (1993) ⇠(t)
TAILLEUR & CATES, PRL (2008)
ANGELANI, COSTANZO, RDL, EPL (2011) ⇠0
⇠0 ⌧ ⇠0 t
⇠0
COLORED DICOTOMOUS(1D) NOISE
h⇠(t)i = 0
h⇠(0)⇠(t)i = ⇠02 e t/⌧
RUN LENGTH
MOBILITY
FREE PARTICLE
RUN & TUMBLE IN EXTERNAL FIELD (J=0)
ẋ(t) = ⇠(t)/ Z
⇤ x
v 0 = ⇠0 / ⇢(x) T (0) f (x)
= ⇤ exp ⇤
dx
2v02 ⇢(0) T (x) 0 kB T (x)
2 t
h r(t) i = 2
( t 1+e )
t⌧⌧ T ⇤ (x) = T ⇤ f (x)2 ⌧ /
v02 t2 BALLISTIC
SPACE DEPENDENT TEMPERATURE
t ⌧
2D⇤ t DIFFUSIVE
⇤ v02 ⇤ WHITE NOISE LIMIT
U (x)
D = = KB T / ⌧ !0 ⇢(x) / exp
KB T ⇤
f0 v0 1 T (x) ! T ⇤ BOLTZMANN-LIKE STATISTICSHolographic
(a) microfabrication
OPTICAL UV GLUE
COVERGLASS
MICROSCOPE OBJECTIVE
100x N. J. JENNESS, ET AL. OPT. EXPRESS 16, 15942 (2008).
NA 1.4
A MICROPATTERNED SURFACE WITH A 3D TOPOGRAPHY
SPATIAL LIGHT MODULATOR
Fig. 6. SEM images of four simultaneo
ACTS AS A STATIC (GRAVITATIONAL) ENERGY LANDSCAPE
and (b) 45± from the surface.
SLM
A
GRAVITY
# B
Examining the results, the desired struct
sive. The average side length and height oCollecting and ejecting structures
KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013)
IN
50µm
2µm~20 kBT
OUTTargeted delivery of colloids
KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013)
IN OUT
t=0 t=20 minAverage particle densities
KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013)
THERMAL BATH ACTIVE BATHwith a finite
onto persistence allowing
a photopolymer of beads forinmicron-featured
the three internal poly-regions of all structures.
cting
ngthe
on sedimenting
merization
surface into
acomposed
di↵ractive
[20]. Fig.beads
aan
bymasklessenergy
series
translates
1b Averaged
shows a SEM
landscape.
of ing structures,
three
compartments
data, image
corresponding
In order
are reported
square boundaries
Fitting transition rates
of a device
intofig.
having
(fig.collecting
to the
get3.a As
2d).
quantitative
and eject-Ṅ(t)
a starting model estimate
ecoherent
bacteria laser
to light
drive fo-
colloidal we assume
beads with that the number
rates we of
have beads in
recorded with
each
KOUMAKIS,
the
LEPORE, ⇤time
region
MAGGI,the
RDL,is rate
gov-
evolutio
Nature ma
Comm. (2013)
the larger slope pointing towards the inner region. Struc-
jectivetures of this kind are designed to acollect
ochastic and shaped
forces with bya a
finite erned by a
persistence coupled of set
beads
particlesof linear therate
in the three equations.
internalCalling regions o
omputer-generated holo- N = (n , n , n ) the
2 Averaged array of particle numbers we have:0
innermost chamber. The final structures 0 1 approximately data, corresponding to the colle 01
rwere
spots can
built be projected
using a height
di↵ractiveof 2 maskless ing structures,
shaped byare reported in⇤fig. 3. As01a
have a vertical µm, with slopes =@
or micron-featured
ique, utilizingdistances
horizontal poly- oflaser
coherent a = light
0.5 µm fo-and we =assume
bṄ(t) 2=µm⇤(Fig. that the number of beads in0ea
SEM image of a device · N(t) + S (1)
microscope
1a). Theobjective and shaped
corresponding by a for
energy barrier erned by a coupled
thermally ac- set of linear rate equ
quare boundaries having
dulatortivated with computer-generated
particles is 20 kB Twith holo-
meaning
⇤ thethat rateNin =the(n0absence
matrix: , n1 , n2 ) theand array S =of(0,particle 0, s) a sou nu
h the ofinner region.particles
bacteria,
intensity Struc- are strictly confined by the walls.
laser spots can be projected per unit time that a b
o collect particles in the 0 slopes, we can
merBy simply for
allowing reversing the direction
micron-featured poly- of the outside.1Since in the st
tructures approximately
ig. build
1b devices
shows a that are
SEM image expected
of a to eject beads
device 01 outside. 10 to0 be
Ṅ(t) = within ⇤ · N(t) the+sam S
with slopes shaped by ⇤ = @ + A
ries ofInthree
fig. 2a we digitally
square boundaries trackhaving 01
colloidal beads, shown in 10 12 it is1 reasonable(2)
21 to as
µm andbb = 2 µm (Fig. 0with ⇤ the = 0.66 min
+12 rate21matrix:+ 23
ointinggreen, on a surface with collecting and ejecting struc- 21 1= 10 = in . Ho
barrier towards the inner
for thermally ac- region. Struc- =of0.36 min
are tures.
designed We
ning that in the absence
set
to time
collect t = 0 soon
particles inafter
the the introduction significantly lower tha
and S = (0, 0, s) a source term, where 0 s is the probability
er. bacteria,
The final while
y confined by the walls. the
structures distribution
approximately of beads is still homo-
per unit time that a bead enters the structures at a larger from distancethe 0 fr
01 10
eight
on geneous
of and with
of 2slopes,
the µm, the concentration
we can slopesoutside.
shaped ofSince
cells
by in becomes
the states uniform.
1⇤and =@ 2 thee↵ect
beads by + assuming 0
01 10 confined
are 12 2
After
es eject
of =about
a beads twenty
andminutes,
0.5 outside.
µm b =to2 beµmthe collecting
(Fig. structures are from 3 probability
0min the two for a bead
to within the same distance 12 walls, 21 +
nding energy
olloidal beads, barrier
shown infor thermally ac-
it is reasonable to 1.5 min that 12 = 23 = out and
assume +
sting
20 and
kB T ejecting
meaningstruc-that in the 21 =absence
10 = inand S = (0, 0,
. However, wes)can a source
expectterm, that where 01 is s is
cles
after are the strictly confined
introduction of by the walls.lowerper
significantly than unit12timeas beads
that in 0 are enters
a bead on average the stru
ngof the
beads is still homo-
direction of the slopes,at a larger
we candistance from Since
outside. the wall.in the Westates
correct 1 and for 2this the be
fare
cellsexpected
becomes to uniform.
eject beads e↵ect by assuming
outside. to be 01 = ↵ outthe
within , with same ↵Curvature effect KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013)
Two-photon lithography
TWO PHOTON ABSORPTION
TWO PHOTON POLYMERIZATION
SOLLER, MICROSCFig.
RES 2.
TECH. (1999)
Fig. 2.
PHOTORESIST
SPATIAL LIGHT MODULATOR
G. VIZSNYICZAI, UNPUBLISHEDSTOCHASTIC DYNAMICS IN ACTIVE BATHS II a bacterial ratchet motor
Work from fluctuations
UNBIASED RANDOM FLUCTUATIONS
WORK?Work from fluctuations
UNBIASED RANDOM FLUCTUATIONS
?
WORK?Work from fluctuations
UNBIASED RANDOM FLUCTUATIONS
“C’est la dissymétrie qui crée le
phénomène” P. CURIE, J. PHYS 3, 393, (1894)
WORK?Brownian ratchets
1903 Full P
M. SMOLUCHOWSKI
1913 1 st Göttingen Lecture (Wolfskeh
1913 May, full Professor Jagellonian U
1916 2 nd Lecture series in Göttingen
3 lectures on diffusion, Brown
[(Phys. Z. 17: 557 – 571; 585
“So it is impossible to design a machine which, in the long run,
is more likely to be going one way than the other,
if the machine is sufficiently complicated”
“It is based on the fact that the laws of mechanics
are reversible”Bacterial dynamics violates detailed balance
Micro-fabrication
E. Di FABRIZIO BIONEM LAB, CATANZARO
48 μm
10 μm2D geometries
Type I a) b)
48 µm
10 µm
Type II Type IV
48 µm
Type III 80 µm
48 µm2D geometries
Type I a) b)
48 µm
10 µm
Type II Type IV
48 µm
Type III 80 µm
48 µm2D geometries
Type I a) b)
48 µm
10 µm
Type II Type IV
48 µm
Type III 80 µm
48 µm R. DI LEONARDO, et al. PNAS (2010)Bacteria-boundary interaction
High concentration regime
10 11
BACTERIA/ML
/Summary 2
STOCHASTIC DYNAMICS IN ACTIVE BATHS
• persistent (non FDT) forces due to bacteria generate stationary states
characterized by probability distributions that strongly deviate from Boltzmann
• these stationary states are also microscopically not invariant under time reversal
• these peculiar properties of active matter allow to exploit bacteria as a workforce
in miniaturized environmentsb e m ir r o p re v e n t t he p a
r than the pro S L M b l o ck s th e b e a m , t o
o c u s lig h t f o m t h e b a
r DELLE RICERCHE - NANOTEC c k -
fi c i e n t l y h a r d p b y o u t -o f -f CONSIGLIO NAZIONALE
e su f u t of t h e t r a SOFT AND LIVING MATTER LABORATORY
y d o n o t o DIPARTIMENTO DI FISICA SAPIENZA
) t h a t th e g b e a m . P.le A. Moro 2, 00185 ROMA, ITALY
p ropagatin
e using.AT THE MICRON SCALE
e arPHYSICS
a g a t i n g o p t ic al
propPEOPLE HYDRO SYNC IN ROTATING LANDSCAPES
e f o c i s l i g h t l y KOUMAKIS & RDL, PRL (2013)
th t h
c t s b e t w e e n t h e
obje
t o d e s c r i b e TRAPPING AT GPa
ufficient s
BOWMAN, GIBSON, PADGETT,
ric a l o b j e c t i SAGLIMBENI, RDL PRL (2013).
sphR. DIeLEONARDO C. MAGGI
b y t h e N. KOUMAKIS M. PAOLUZZI
hat direction e
i r e s a f o r c
tion requ d
o n t h e b e a
to this l
cal a x i s . A x i a
e optS.iBIANCHI A. LEPORE
f
F. SAGLIMBENI
i G. VIZSNYICZAI
IMAGING THROUGH OPTICAL FIBERS
t h e b e a d : BIANCHI & RDL LAB CHIP (2011)
red from i s
COLLABORATIONS o r e
er, mCNR-IPCF SAPIENZA l i g h t
otL.hANGELANI, s
T h i s m e a n
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hat EfDIoFABRIZIO,
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