Swimming in complex environments: from biofilms to bacteria powered micro-devices

Swimming in complex environments: from biofilms to bacteria powered micro-devices

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

Swimming in complex environments: from biofilms to bacteria powered micro-devices

Outline A SELF-PROPELLED MICRO-MACHINE b) CONFINED SWIMMING a) SELF PROPELLING BACTERIA + TUESDAY Microhydrodynamics TODAY Statistical Mechanics c) STOCHASTIC DYNAMICS IN ACTIVE BATHS d) BACTERIA POWERED MICRODEVICES

Swimming in complex environments: from biofilms to bacteria powered micro-devices

STOCHASTIC DYNAMICS IN ACTIVE BATHS I targeted delivery of colloidal cargos

Swimming in complex environments: from biofilms to bacteria powered micro-devices

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 must exist both in liquids and solids” GIOVANNI CANTONI MEAN-SQUARE DISPLACEMENT DIFFUSION COEFFICIENT h r2 (t)i = 6Dt A. EINSTEIN Theory of Brownian motion Theory of Brownian motion W.

Sutherland (1858-1911) A. Einstein (1879-1955) M. Smoluchowski (1872-1917) Source: www.theage.com.au Source: wikipedia.org Source: wikipedia.org Source: www.theage.com.au Source: wikipedia.org Source: wikipedia.org 1905 W. SUTHERLAND D = kBT/ = 6⇡µa STOKES DRAG

Swimming in complex environments: from biofilms to bacteria powered micro-devices

Langevin equation 1908 PAUL LANGEVIN: IT IS EASY TO GIVE A DEMONSTRATION THAT IS INFINITELY MORE SIMPLE BY MEANS OF A METHOD THAT IS ENTIRELY DIFFERENT 0 = f(x) ẋ(t ⌘ ( t) LANGEVIN EQUATION FRICTION RANDOM FORCE EXTERNAL INTERACTION WITH SOLVENT h⌘(t)⌘(t0 )i = kBT 2 (t t0 ) h⌘(t)i = 0 UNBIASED WHITE NOISE mẍ ⇠ ẋ(t) = Z t 2 (t t0 ) ẋ(t0 )dt0 FRICTION FLUCTUATION DISSIPATION ⇢B ⇢A = exp "Z B A f(x) kBT dx # exp  UB UA kBT + = BOLTZMANN DISTRIBUTION

Swimming in complex environments: from biofilms to bacteria powered micro-devices

Colloidal delivery at equilibrium A B ENERGY DENSITY FLAT CONCENTRATION (MAXIMUM ENTROPY) A B EXTERNAL FIELD PEAKED CONCENTRATION (DELIVERY TO B) EXTERNAL WORK ENTROPY DECREASE ! x U (x) A B ASYMMETRIC BARRIER NO NET WORK ⇢B ⇢A = exp "Z B A f(x) kBT dx # exp  UB UA kBT = BOLTZMANN DISTRIBUTION

Swimming in complex environments: from biofilms to bacteria powered micro-devices

Transport with external fields ELECTRIC FIELDS SULLIVAN et al. PRL (2006) TEMPERATURE FIELDS (LASER HEATING) DUHR & BRAUN, APL (2005) MAGNETIC, FLOW ...

Swimming in complex environments: from biofilms to bacteria powered micro-devices

SPATIAL LIGHT MODULATOR MICROSCOPE OBJECTIVE SLM 8 bit, 0-2π phase modulation 1 Megapixel resolution LIQUID CRYSTALS SLM 100x NA 1.4 GRIER, NATURE (2003) PADGETT & DI LEONARDO, Lab Chip (2011) R. DI LEONARDO 2 µm SILICA BEADS IN WATER 5 µm GRAPHICS PROCESSING UNIT (GPU) DI LEONARDO et al., Opt. Express (2006) BIANCHI & DI LEONARDO Comp. Phys. Comm. (2010) DIGITAL PARALLEL HOLOGRAPHY Highly optimized holograms in real time SPONSORED BY ACADEMIC PARTNERSHIP Optical micromanipulation: Holographic Tweezers

Swimming in complex environments: from biofilms to bacteria powered micro-devices

Using active particles as micro-oxen WEIBEL ET AL. PNAS (2005) SWIMMING CELLS C. reinhardtii particle speed, and me is the electrophoretic bimetallic particle (a function of the dielectric n viscosity, particle dimension, and particle Jþ is the current density due to the electron, and s is the conductivity of the bulk solution. et al. recently showed that in the case of silver f the p In another method of cargo drop-off, a bifunctional, photocleavable o-nitrobenzylbased linker (PCL) was used to attach the motor to the cargo. The photolysis of o-nitrobenzyl-group-based linkers is widely employed in combinatorial organic synthesis for the release of moieties from solid supports.[14] Whitesides et al.

demonstrated the release of cargo from phototactic bacteria using such linkers.[15,16] Figure 2A shows a schematic image of PCL-assisted cargo drop-off. Pt"Au"PPy rods were synthesized incorporating carboxylic acid groups in the polymer segment. This was accomplished by electropolymerizing pyrrole and 4-(3-pyrrolyl) butyric acid to yield a copolymer, PPyPPyCOOH. Figure 2B shows a TEM image of a Pt"Au"PPyPPyCOOH motor. Figure 3 shows the structure of PCL in which the photocleavable moiety is flanked by an amine functionality on one side and biotin on the other. The carboxyl acid groups on the polymer end of the rod were bound to the amine terminus of the bifunctional PCL via 3-(ethyliminomethyleneamino)-N,Ndimethyl-propan-1-amine coupling (EDC).

The biotin end of the PCL was used to link the motor unications ematic image of motor design for silver-assisted cargo drop-off. Pt"Au"Ag" tached to positively charged 0.8-mm-diameter PS–amidine cargo. The blue he Ag section of the rod that dissolves in the presence of UV light (365 nm), go. B) TEM images of Pt"Au"Ag"Au–Ppy rods. C) Screen-capture images ssolution-assistedcargodrop-off.TheimageontheleftisbeforeUVexposure the right is post UV exposure where the cargo dissociates from the motor. For ow points to the motor and the black arrow to the cargo. where, n is the particle speed, and me is the electrophoretic mobility of the bimetallic particle (a function of the dielectric constant, solution viscosity, particle dimension, and particle zeta potential), Jþ is the current density due to the electrochemical reaction, and s is the conductivity of the bulk solution.

However, Wang et al. recently showed that in the case of silver ions, the speed of the pa In another method of cargo drop-off, a bifunctional, photocleavable o-nitrobenzylbased linker (PCL) was used to attach the motor to the cargo. The photolysis of o-nitrobenzyl-group-based linkers is widely employed in combinatorial organic synthesis for the release of moieties from solid supports.[14] Whitesides et al. demonstrated the release of cargo from phototactic bacteria using such linkers.[15,16] Figure 2A shows a schematic image of PCL-assisted cargo drop-off. Pt"Au"PPy rods were synthesized incorporating carboxylic acid groups in the polymer segment.

This was accomplished by electropolymerizing pyrrole and 4-(3-pyrrolyl) butyric acid to yield a copolymer, PPyPPyCOOH. Figure 2B shows a TEM image of a Pt"Au"PPyPPyCOOH motor. Figure 3 shows the structure of PCL in which the photocleavable moiety is flanked by an amine functionality on one side and biotin on the other. The carboxyl acid groups on the polymer end of the rod were bound to the amine terminus of the bifunctional PCL via 3-(ethyliminomethyleneamino)-N,Ndimethyl-propan-1-amine coupling (EDC). The biotin end of the PCL was used to link the motor s communications Figure 1. A) Schematic image of motor design for silver-assisted cargo drop-off.

Pt"Au"Ag" Au"PPy motor attached to positively charged 0.8-mm-diameter PS–amidine cargo. The blue arrow points to the Ag section of the rod that dissolves in the presence of UV light (365 nm), releasing the cargo. B) TEM images of Pt"Au"Ag"Au–Ppy rods. C) Screen-capture images depictingsilver-dissolution-assistedcargodrop-off.Theimageontheleftisbefore UVexposure and the image on the right is post UV exposure where the cargo dissociates from the motor. For clarity, the red arrow points to the motor and the black arrow to the cargo. e is the In another method of cargo drop-off, a bifunctional, photocleavable o-nitrobenzylbased linker (PCL) was used to attach the motor to the cargo.

The photolysis of o-nitrobenzyl-group-based linkers is widely employed in combinatorial organic synthesis for the release of moieties from solid supports.[14] Whitesides et al. demonstrated the release of cargo from phototactic bacteria using such linkers.[15,16] Figure 2A shows a schematic image of PCL-assisted cargo drop-off. Pt"Au"PPy rods were synthesized incorporating carboxylic acid groups in the polymer segment. This was accomplished by electropolymerizing pyrrole and 4-(3-pyrrolyl) butyric acid to yield a copolymer, PPyPPyCOOH. Figure 2B shows a TEM image of a Pt"Au"PPyPPyCOOH motor.

Figure 3 shows the structure of PCL in which the photocleavable moiety is flanked by sign for silver-assisted cargo drop-off. Pt"Au"Ag" ged 0.8-mm-diameter PS–amidine cargo. The blue hat dissolves in the presence of UV light (365 nm), Au"Ag"Au–Ppy rods. C) Screen-capture images drop-off.TheimageontheleftisbeforeUVexposure ure where the cargo dissociates from the motor. For nd the black arrow to the cargo.

SUNDARARAJAN et al. SMALL (2010) SYNTHETIC SWIMMERS CATALYTIC Pt-Au NANOMOTOR MICROSWIMMERS TRANSPORT DELIVERY PICKUP EXTERNAL FIELDS

Swimming in complex environments: from biofilms to bacteria powered micro-devices

Colloids in active baths 5 µm LATEX BEADS IN E.coli 0 = f(x) ẋ(t t) h⇠(t)i = 0 COLORED NOISE ACTIVE NOISE h⇠(0)⇠(t)i = h⇠2 ie t/⌧ oes nor any modulator with computer-generated holograms. Thus, (s) MSD (µm 2 ) 10–2 10–2 10–1 100 10–1 100 101 0.6 0.4 0.2 0.0 MSD/4t 10–2 10–1 100 t ξ 3 A schematic representation of the main geometric and dynamic features of transition ning electron microscopy image of a square structure that gathers particles to the c r, 10 mm in length.

(c) The mean squared displacements (MSD) of the beads in the and in the bacterial bath (filled symbols). Solid and dashed lines are fits to the data ve system. Inset depicts the same data as an effective diffusivity (divided by 4t), cl + D = kBT D⇤ = kBT⇤

Non-equilibrium random walks COLORED DICOTOMOUS(1D) NOISE t RUN LENGTH 1D RUN AND TUMBLE SCHNITZER, PRE (1993) TAILLEUR & CATES, PRL (2008) ANGELANI, COSTANZO, RDL, EPL (2011) ⇠0 ⇠0 h⇠(t)i = 0 BOLTZMANN-LIKE STATISTICS WHITE NOISE LIMIT ⇢(x) / exp  U(x) KBT⇤ RUN & TUMBLE IN EXTERNAL FIELD (J=0) SPACE DEPENDENT TEMPERATURE ⇢(x) ⇢(0) = T⇤ (0) T⇤(x) exp Z x f(x) kBT⇤(x) dx MOBILITY FREE PARTICLE f0v0 1 h r(t)2 i = 2v2 2D⇤ t ẋ(t ⇠ ( t)/ v0 = ⇠0/ v2 0t2 BALLISTIC DIFFUSIVE D⇤ = v2 = KBT⇤ / h⇠(0)⇠(t)i = ⇠2 0e t/⌧ T⇤ (x) = T⇤ f(x)2 ⌧/ ⇠0 ⇠0 ⌧ ⇠(t) T(x) ! T⇤

Holographic microfabrication N.

J. JENNESS, ET AL. OPT. EXPRESS 16, 15942 (2008). SPATIAL LIGHT MODULATOR MICROSCOPE OBJECTIVE SLM 100x NA 1.4 OPTICAL UV GLUE COVERGLASS (a) Fig. 6. SEM images of four simultaneo and (b) 45± from the surface. Examining the results, the desired struct sive. The average side length and height o A B # GRAVITY A MICROPATTERNED SURFACE WITH A 3D TOPOGRAPHY ACTS AS A STATIC (GRAVITATIONAL) ENERGY LANDSCAPE

OUT IN Collecting and ejecting structures 5 µ m 2µm~20 kBT KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013)

Targeted delivery of colloids t=0 t=20 min IN OUT KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013)

Average particle densities ACTIVE BATH THERMAL BATH KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013)

Fitting transition rates + = 0.66 min 1 = 0.36 min 1 3 min 1.5 min KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013) a b with a finite persistence ng a di↵ractive maskless coherent laser light fojective and shaped by a omputer-generated holor spots can be projected or micron-featured polySEM image of a device quare boundaries having the inner region.

Struco collect particles in the tructures approximately with slopes shaped by µm and b = 2 µm (Fig. barrier for thermally acning that in the absence y confined by the walls. on of the slopes, we can to eject beads outside. olloidal beads, shown in ting and ejecting strucafter the introduction of of beads is still homof cells becomes uniform. of beads in the three internal regions of all structures. Averaged data, corresponding to the collecting and ejecting structures, are reported in fig. 3. As a starting model we assume that the number of beads in each region is governed by a coupled set of linear rate equations.

Calling N = (n0, n1, n2) the array of particle numbers we have: Ṅ(t · N(t) + S (1) with ⇤ the rate matrix: ⇤ = @ 01 10 0 01 10 + 12 21 0 12 21 + 23 1 A (2) and S = (0, 0, s) a source term, where s is the probability per unit time that a bead enters the structures from the outside. Since in the states 1 and 2 the beads are confined to be within the same distance from the two walls, it is reasonable to assume that 12 = 23 = out and 21 = 10 = in. However, we can expect that 01 is significantly lower than 12 as beads in 0 are on average at a larger distance from the wall. We correct for this e↵ect by assuming 01 = ↵ out, with ↵ < 1 being the cting on sedimenting beads translates the surface into an energy landscape.

e bacteria to drive colloidal beads with ochastic forces with a finite persistence were built using a di↵ractive maskless ique, utilizing coherent laser light fomicroscope objective and shaped by a dulator with computer-generated holoh intensity laser spots can be projected mer allowing for micron-featured polyig. 1b shows a SEM image of a device ries of three square boundaries having ointing towards the inner region. Strucare designed to collect particles in the er. The final structures approximately eight of 2 µm, with slopes shaped by es of a = 0.5 µm and b = 2 µm (Fig. nding energy barrier for thermally acs 20 kBT meaning that in the absence cles are strictly confined by the walls.

ng the direction of the slopes, we can are expected to eject beads outside. compartments (fig. 2d).

In order to get a quantitative estimate rates we have recorded the time evolutio of beads in the three internal regions o Averaged data, corresponding to the colle ing structures, are reported in fig. 3. As a we assume that the number of beads in ea erned by a coupled set of linear rate equ N = (n0, n1, n2) the array of particle nu Ṅ(t · N(t) + S with ⇤ the rate matrix: ⇤ = @ 01 10 0 01 10 + 12 2 0 12 21 + and S = (0, 0, s) a source term, where s is per unit time that a bead enters the stru outside. Since in the states 1 and 2 the be to be within the same distance from onto a photopolymer allowing for micron-featured polymerization [20].

Fig. 1b shows a SEM image of a device composed by a series of three square boundaries having the larger slope pointing towards the inner region. Structures of this kind are designed to collect particles in the innermost chamber. The final structures approximately have a vertical height of 2 µm, with slopes shaped by horizontal distances of a = 0.5 µm and b = 2 µm (Fig. 1a). The corresponding energy barrier for thermally activated particles is 20 kBT meaning that in the absence of bacteria, particles are strictly confined by the walls. By simply reversing the direction of the slopes, we can build devices that are expected to eject beads outside.

In fig. 2a we digitally track colloidal beads, shown in green, on a surface with collecting and ejecting structures. We set time t = 0 soon after the introduction of bacteria, while the distribution of beads is still homogeneous and the concentration of cells becomes uniform. After about twenty minutes, the collecting structures are Ṅ(t) with ⇤ the rate ma ⇤ = @ 01 01 and S = (0, 0, s) a sou per unit time that a b outside. Since in the st to be within the sam it is reasonable to as 21 = 10 = in. Ho significantly lower tha at a larger distance fr e↵ect by assuming 0 probability for a bead +

Curvature effect KOUMAKIS, LEPORE, MAGGI, RDL, Nature Comm. (2013)

Two-photon lithography TWO PHOTON ABSORPTION Fig. 2. Fig. 2. SOLLER, MICROSC RES TECH. (1999) TWO PHOTON POLYMERIZATION SPATIAL LIGHT MODULATOR PHOTORESIST G. VIZSNYICZAI, UNPUBLISHED

STOCHASTIC DYNAMICS IN ACTIVE BATHS II a bacterial ratchet motor

Work from fluctuations UNBIASED RANDOM FLUCTUATIONS WORK?

Work from fluctuations WORK? ? UNBIASED RANDOM FLUCTUATIONS

Work from fluctuations WORK? “C’est la dissymétrie qui crée le phénomène” P.

CURIE, J. PHYS 3, 393, (1894) UNBIASED RANDOM FLUCTUATIONS

Brownian ratchets “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” 1903 Full P 1913 1 st Göttingen Lecture (Wolfskeh 1913 May, full Professor Jagellonian U 1916 2 nd Lecture series in Göttingen 1916 2 nd Lecture series in Göttingen 3 lectures on diffusion, Brown [(Phys. Z. 17: 557 – 571; 585 M. SMOLUCHOWSKI

Bacterial dynamics violates detailed balance

Micro-fabrication 10 μm 48 μm E.

Di FABRIZIO BIONEM LAB, CATANZARO

2D geometries Type III Type IV Type II 48 µm 48 µm 48 µm 80 µm Type I 10 µm a) b)

2D geometries Type III Type IV Type II 48 µm 48 µm 48 µm 80 µm Type I 10 µm a) b)

2D geometries Type III Type IV Type II 48 µm 48 µm 48 µm 80 µm Type I 10 µm a) b) R. DI LEONARDO, et al. PNAS (2010)

Bacteria-boundary interaction

High concentration regime / 2 1011 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 environments

M. PAOLUZZI R. DI LEONARDO C. MAGGI S. BIANCHI A. LEPORE F. SAGLIMBENI PHYSICS AT THE MICRON SCALE CONSIGLIO NAZIONALE DELLE RICERCHE - NANOTEC SOFT AND LIVING MATTER LABORATORY DIPARTIMENTO DI FISICA SAPIENZA P.le A. Moro 2, 00185 ROMA, ITALY PEOPLE N. KOUMAKIS COLLABORATIONS L. ANGELANI, CNR-IPCF SAPIENZA E DI FABRIZIO, C. LIBERALE, KAUST, SAUDI ARABIA r than the probe e sufficiently hard ) that they do not e are using. propagating optical th the foci slightly objects between the ufficient to describe spherical object is hat direction by the tion requires a force to this on the bead e optical axis.

Axial red from the bead: if other, more light is hat focus. This means adiation pressure from the midpoint of the optical traps use a mirds the trapping site as a mirro SLM blocks the beam, to prevent the pa out of the trap by out-of-focus light from the backpropagating beam.

(color online). The optical system used to trap at h d using a liquid cry BOWMAN, GIBSON, PADGETT, SAGLIMBENI, RDL PRL (2013). TRAPPING AT GPa BIANCHI & RDL LAB CHIP (2011) IMAGINGTHROUGH OPTICAL FIBERS FUNDING KOUMAKIS & RDL, PRL (2013) HYDRO SYNC IN ROTATING LANDSCAPES G.VIZSNYICZAI

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