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Over the past decades, active matter systems have attracted the attention of scientists from different areas, including physics, engineering, biology, and the human sciences. These systems involve agents that convert some type of energy into directed motion. Examples range from swimming microorganisms to crawling cells to synthetic active colloids. A striking feature of active materials is that they are strongly driven out of equilibrium and therefore display a variety of unusual phenomena at the single as well as collective level, which differ drastically from their passive counterparts. In this preface, we provide an overview of the main avenues of research in active matter and bring together the topics addressed in our book. We conclude by discussing future research directions in this rapidly-evolving, interdisciplinary research field.

Soft condensed matter research is concerned with the physics of materials that lie in between simple liquids and solids1–3  [Figure 1.1A]. While the latter states of matter are perhaps more widely known to everyone, our everyday life is in fact full of soft materials, ranging from food products to cosmetics to display devices. Furthermore, human tissues, muscles, and bodily fluids fall into this category, making our body a ‘soft machine’, a term which already appeared in the novel by William Burroughs in the 1960s.4  One outstanding feature of soft, or squishy, materials is their intricate response to external stresses. Unraveling the underlying physics lays the foundation for our knowledge of biological processes and the development of novel technological devices.

Figure 1.1

(A) Overview of soft materials.(i) Polymers: simulation snapshot of the structure of a styrene-butadiene chain; (ii) liquid crystals: nematic ordering of anisotropic constituents; (iii) colloids: self-assembly of hard core/soft shell Ag–PNIPAM particles to Moiré microstructures; (iv) membranes: molecular dynamics simulation of membranes composed of lipid molecules with a hydrophilic head and a hydrophobic tail; (v) biological tissues: stained lung tissue; (vi) active matter: swarming fish; (vii) granular matter: ball pit; (viii) fracture: crevasse at the Exit Glacier in Alaska; (ix) interfaces: drop at a liquid–air interface; (x) glasses: windows of the United Nations Secretariat Building in New York City. (B) Overview of active matter systems.(i) Microorganisms: Escherichia coli bacterium; (ii) synthetic agents: sketch of a Janus colloid and simulation snapshot of positions of active Brownian particles at subsequent times (indicated by different colors) starting to move from the left to the right; (iii) granular matter: millimeter-sized tapered brass rods move persistently on a vibrating surface; (iv) macroscopic systems: swarming fish; (v) programmable materials: self-assembly of self-spinning microgears; (vi) mammalian cells and tissues: eukaryotic cells on patterned substrates; (vii) active nematics: active liquid crystals composed of microtubule-motor protein suspensions; (viii) phase separation: spinodal decomposition of quorum-sensing active Brownian particles; (ix) molecular machineries: mitotic spindle; (x) filaments and carpets: wild-type node of a mouse, where cilia emanate from the posterior part of the cells. The book chapters, which cover the different topics, are indicated as: C [chapter number]. Permissions: Panel (A) was inspired by the graph by Jesse L. Silverberg on the back page of the APS NEWS magazine, May 2015, Volume 24, Number 5 (https://www.aps.org/publications/apsnews/201505/backpage.cfm). (A-i) Adapted from https://commons.wikimedia.org/wiki/File:Styrene-butadiene_chain2.png under the CC BY-SA 4.0 license, https://creativecommons.org/licenses/by-sa/4.0/deed.en. (A-iii) Adapted from ref. 10 with permission from the Royal Society of Chemistry. (A-iv) Adapted from ref. 11 with permission from the American Chemical Society, Copyright 2019. (A-v) Adapted from https://commons.wikimedia.org/wiki/File:Emphysema_H_and_E.jpg under terms of the CC BY 2.0 license, https://creativecommons.org/licenses/by/2.0/deed.en. (A-vii) Adapted from https://commons.wikimedia.org/wiki/File:Granular_matter_examples.PNG under the CC BY-SA 3.0 license, https://creativecommons.org/licenses/by-sa/3.0/deed.en. (A-ix) Adapted from ref. 12 with permission from Cambridge University Press. (B-i) Adapted from ref. 13 with permission from John Wiley & Sons, Copyright © 2011 John Wiley & Sons, Ltd. (B-iii) Reproduced from ref. 14 with permission from Springer Nature, Copyright 2014. (B-v) Reproduced from ref. 15 with permission from Springer Nature, Copyright 2018. (B-vi) Reproduced from ref. 16 with permission from National Academy of Sciences, U.S.A., Copyright 2005. (B-vii) Reproduced from ref. 17 with permission from Springer Nature, Copyright 2012. (B-viii) Adapted from Figure 4.2 of Chapter 4 with permission from Julien Tailleur. (B-ix) Adapted from ref. 18, https://doi.org/10.1038/s41598-018-27008-w under the terms of the CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/. (B-x) Adapted from ref. 19, https://doi.org/10.1371/journal.pbio.0030268 under the terms of the CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/.

Figure 1.1

(A) Overview of soft materials.(i) Polymers: simulation snapshot of the structure of a styrene-butadiene chain; (ii) liquid crystals: nematic ordering of anisotropic constituents; (iii) colloids: self-assembly of hard core/soft shell Ag–PNIPAM particles to Moiré microstructures; (iv) membranes: molecular dynamics simulation of membranes composed of lipid molecules with a hydrophilic head and a hydrophobic tail; (v) biological tissues: stained lung tissue; (vi) active matter: swarming fish; (vii) granular matter: ball pit; (viii) fracture: crevasse at the Exit Glacier in Alaska; (ix) interfaces: drop at a liquid–air interface; (x) glasses: windows of the United Nations Secretariat Building in New York City. (B) Overview of active matter systems.(i) Microorganisms: Escherichia coli bacterium; (ii) synthetic agents: sketch of a Janus colloid and simulation snapshot of positions of active Brownian particles at subsequent times (indicated by different colors) starting to move from the left to the right; (iii) granular matter: millimeter-sized tapered brass rods move persistently on a vibrating surface; (iv) macroscopic systems: swarming fish; (v) programmable materials: self-assembly of self-spinning microgears; (vi) mammalian cells and tissues: eukaryotic cells on patterned substrates; (vii) active nematics: active liquid crystals composed of microtubule-motor protein suspensions; (viii) phase separation: spinodal decomposition of quorum-sensing active Brownian particles; (ix) molecular machineries: mitotic spindle; (x) filaments and carpets: wild-type node of a mouse, where cilia emanate from the posterior part of the cells. The book chapters, which cover the different topics, are indicated as: C [chapter number]. Permissions: Panel (A) was inspired by the graph by Jesse L. Silverberg on the back page of the APS NEWS magazine, May 2015, Volume 24, Number 5 (https://www.aps.org/publications/apsnews/201505/backpage.cfm). (A-i) Adapted from https://commons.wikimedia.org/wiki/File:Styrene-butadiene_chain2.png under the CC BY-SA 4.0 license, https://creativecommons.org/licenses/by-sa/4.0/deed.en. (A-iii) Adapted from ref. 10 with permission from the Royal Society of Chemistry. (A-iv) Adapted from ref. 11 with permission from the American Chemical Society, Copyright 2019. (A-v) Adapted from https://commons.wikimedia.org/wiki/File:Emphysema_H_and_E.jpg under terms of the CC BY 2.0 license, https://creativecommons.org/licenses/by/2.0/deed.en. (A-vii) Adapted from https://commons.wikimedia.org/wiki/File:Granular_matter_examples.PNG under the CC BY-SA 3.0 license, https://creativecommons.org/licenses/by-sa/3.0/deed.en. (A-ix) Adapted from ref. 12 with permission from Cambridge University Press. (B-i) Adapted from ref. 13 with permission from John Wiley & Sons, Copyright © 2011 John Wiley & Sons, Ltd. (B-iii) Reproduced from ref. 14 with permission from Springer Nature, Copyright 2014. (B-v) Reproduced from ref. 15 with permission from Springer Nature, Copyright 2018. (B-vi) Reproduced from ref. 16 with permission from National Academy of Sciences, U.S.A., Copyright 2005. (B-vii) Reproduced from ref. 17 with permission from Springer Nature, Copyright 2012. (B-viii) Adapted from Figure 4.2 of Chapter 4 with permission from Julien Tailleur. (B-ix) Adapted from ref. 18, https://doi.org/10.1038/s41598-018-27008-w under the terms of the CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/. (B-x) Adapted from ref. 19, https://doi.org/10.1371/journal.pbio.0030268 under the terms of the CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/.

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The nature of soft materials is determined by a variety of different components of mesoscopic size, which exceed the atomic level but are usually smaller than the macroscopic scale. These constituents encompass colloidal particles, bubbles, droplets, granular matter, polymers, lipids, living microorganisms, and mammalian cells, to name a few. The typical energy scale of these systems is set by the thermal energy, such that due to thermal fluctuations the single constituents continuously jiggle around and perform Brownian motion. In addition to ordinary diffusion, biological living systems, such as microorganisms or biofilament-protein suspensions in cells, convert chemical energy into directed motion, which drives them strongly out of equilibrium and leads to a wealth of new phenomena that differ drastically from their passive counterparts. These systems, which can intrinsically, without the need of external fields, generate transport, are referred to as active materials5–9  [Figure 1.1B]. They have also been designed and synthesized in the laboratory and, besides their potential application for biomedical and environmental settings, serve as tools for the study of non-equilibrium physics.

In these active materials, intriguing physical phenomena arise at the collective level due to the non-reciprocal interactions between the different components. While in equilibrium systems self-assembly and nematic ordering occurs, for instance, due to chemical properties or anisotropy of the constituents, in living systems active transport can generate a variety of dynamic patterns, which underlies different biological functions, and leads to tissue formation. Due to the non-equilibrium nature of these materials, the development of new theoretical tools is required as the well-established framework of equilibrium statistical physics breaks down.

This book provides insights into different topics relevant to the field of active matter. These include the hydrodynamics of cell swimming (Chapter 2), active nematics (Chapter 3), the physics of motility-induced phase separation (Chapter 4), active transport in complex environments (Chapter 5), the mitotic spindle (Chapter 6), self-propelled droplets (Chapter 7), photothermally-driven transport (Chapter 8), the rheology of active fluids (Chapter 9), and computational studies on active matter (Chapter 10). Below we discuss these topics in the context of active matter and point towards other directions within the rapidly-evolving research area.

Nature provides several examples of self-propelling agents, commonly addressed as swimmers in aqueous-based environments, ranging from biomacromolecules in the nanoscale to large organisms in the meter scale, passing through micro-, meso-, and macro-organisms, Figure 1.2A–G. Biological swimmers are generally driven by out-of-equilibrium dynamics through chemical-to-mechanical energy conversion. Several microswimmers are also subjected to Brownian motion and background flows at a low Reynolds number, consequently, the motion can be simulated using Brownian dynamics based on the active Brownian particle (ABP) model,20  for further details see chapters 2 and 5. Several attempts to fabricate microscopic artificial devices to emulate the swimming of bio-based self-propelling agents have been made21  adopting as an energy source magnetic and electrical properties or by inducing swimming through the presence of external fields, Figure 1.2H–J. Robotic organisms able to swim in aqueous-based environments generally use built-in external energy sources such as lithium polymer batteries, Figure 1.2K. A swimmer having both biological and artificial constituents is defined as a hybrid swimmer,22  for which generally a passive synthetic constituent is attached or encapsulated into living microorganisms, Figure 1.2L–N. The energy source of hybrid swimmers can vary depending on their fabrication.

Figure 1.2

An overview of individual biological, synthetic, and hybrid swimmers. (A) The Canavalia ensiformis (Jack bean urease) complex. Reproduced from ref. 23 (10.2210/pdb4H9M/pdb) under the terms of the CC0 1.0 license (https://creativecommons.org/publicdomain/zero/1.0/). (B) Kinesin and dynein motor proteins translocate along the microtubules in the positive and negative direction, respectively. Reproduced from ref. 24 with permission of IOP Publishing, Copyright 1989. (C) Escherichia coli bacteria with cell body of approximately 2 µm and total length 10 µm. Reproduced from ref. 25, https://doi.org/10.3389/fmicb.2020.01042, under the terms of the CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/. (D) Eukaryotic unicellular algae Chlamydomonas reinhardtii with a cell body of approximately 10 µm. Scale bar = 5 µm. Reproduced from ref. 26 with permission from Elsevier, Copyright 2013. (E) A swimming sperm, adapted from ref. 27, https://doi.org/10.7554/eLife.02403, under the terms of the CC BY 3.0 license, https://creativecommons.org/licenses/by/3.0/. (F) A 1 mm long multi-cellular organism Caenorhabditis elegans. Reproduced from ref. 28 with permission of PNAS. (G) A swimming fish under pixabay.com license. (H) A nanohelix with Au nanodots produced via micellar nanolithography, spacings around 135 nm, and a magnetic nickel section with a thickness around 40 nm. Reproduced from ref. 29 with permission of the American Chemical Society, Copyright 2014. (I) Schematic Janus particle in a half cycle of an AC electric field where the conductive (gold) side is more strongly polarized and thus drives a stronger electroosmotic slip than the dielectric side, resulting in induced-charge electrophoresis motion in the direction of the dielectric side. Reproduced from ref. 30 with permission of the American Physical Society, Copyright 2008. (J) Magnetically-driven artificial bacterial flagella made of InGaAs/GaAs/Cr trilayer patterned in a ribbon-like shape for the helical tail and Cr/Ni/Au metal thin films patterned for the soft-magnetic head of the artificial flagella. Reproduced from ref. 31 with permission of the American Chemical Society, Copyright 2009. (K) Robotic fish presented by Katzschmann et al.;32  the photo is reproduced with permission of Joseph DelPreto, MIT CSAIL. (L) Liposomes attached to the surface of a magnetotactic bacterium, Magnetococcus marinus. Reproduced from ref. 33 with permission of the American Chemical Society, Copyright 2014. (M) Tetrahymena pyriformis after magnetization of internalized iron oxide particles. Scale bar = 10 µm. Reproduced from ref. 34 with permission of AIP Publishing. (N) A biohybrid fish with a synthetic body and human stem cell-derived cardiomyocytes providing spontaneous muscle activation rhythms;35  the photo is reproduced with permission of Kevin Kit Parker, Harvard University.

Figure 1.2

An overview of individual biological, synthetic, and hybrid swimmers. (A) The Canavalia ensiformis (Jack bean urease) complex. Reproduced from ref. 23 (10.2210/pdb4H9M/pdb) under the terms of the CC0 1.0 license (https://creativecommons.org/publicdomain/zero/1.0/). (B) Kinesin and dynein motor proteins translocate along the microtubules in the positive and negative direction, respectively. Reproduced from ref. 24 with permission of IOP Publishing, Copyright 1989. (C) Escherichia coli bacteria with cell body of approximately 2 µm and total length 10 µm. Reproduced from ref. 25, https://doi.org/10.3389/fmicb.2020.01042, under the terms of the CC BY 4.0 license, https://creativecommons.org/licenses/by/4.0/. (D) Eukaryotic unicellular algae Chlamydomonas reinhardtii with a cell body of approximately 10 µm. Scale bar = 5 µm. Reproduced from ref. 26 with permission from Elsevier, Copyright 2013. (E) A swimming sperm, adapted from ref. 27, https://doi.org/10.7554/eLife.02403, under the terms of the CC BY 3.0 license, https://creativecommons.org/licenses/by/3.0/. (F) A 1 mm long multi-cellular organism Caenorhabditis elegans. Reproduced from ref. 28 with permission of PNAS. (G) A swimming fish under pixabay.com license. (H) A nanohelix with Au nanodots produced via micellar nanolithography, spacings around 135 nm, and a magnetic nickel section with a thickness around 40 nm. Reproduced from ref. 29 with permission of the American Chemical Society, Copyright 2014. (I) Schematic Janus particle in a half cycle of an AC electric field where the conductive (gold) side is more strongly polarized and thus drives a stronger electroosmotic slip than the dielectric side, resulting in induced-charge electrophoresis motion in the direction of the dielectric side. Reproduced from ref. 30 with permission of the American Physical Society, Copyright 2008. (J) Magnetically-driven artificial bacterial flagella made of InGaAs/GaAs/Cr trilayer patterned in a ribbon-like shape for the helical tail and Cr/Ni/Au metal thin films patterned for the soft-magnetic head of the artificial flagella. Reproduced from ref. 31 with permission of the American Chemical Society, Copyright 2009. (K) Robotic fish presented by Katzschmann et al.;32  the photo is reproduced with permission of Joseph DelPreto, MIT CSAIL. (L) Liposomes attached to the surface of a magnetotactic bacterium, Magnetococcus marinus. Reproduced from ref. 33 with permission of the American Chemical Society, Copyright 2014. (M) Tetrahymena pyriformis after magnetization of internalized iron oxide particles. Scale bar = 10 µm. Reproduced from ref. 34 with permission of AIP Publishing. (N) A biohybrid fish with a synthetic body and human stem cell-derived cardiomyocytes providing spontaneous muscle activation rhythms;35  the photo is reproduced with permission of Kevin Kit Parker, Harvard University.

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Self-propelling biomacromolecules are protein-powered motors able to achieve physiological functions by converting chemical energy into mechanical energy.36  The metalloenzyme urease, Figure 1.2A, converts urea into ammonia and hydroxamic acid, the latter which is further hydrolyzed to ammonia and bicarbonate.37  The asymmetric gradient of products upon catalysis was initially proposed as a self-propulsion mechanism, self-diffusiophoresis,38  leading to Purcell’s model for motion at low Reynolds number and to the random walk of proteins.39,40  At this time, the self-propelling mechanism of urease is related to a gradient of ionic products, e.g., to a self-electrokinetic mechanism.41,42  Myosins, kinesins, or dyneins convert adenosine triphosphate (ATP) hydrolysis resulting in a conformational modification in the globular motor domain, which leads to directed motion.43,44  These three proteins are classified as cytoskeletal motor proteins. Myosin motors move along actin filaments transporting a wide variety of cargo, while dynein and kinesin motors use microtubules to transport vesicles across the cell, Figure 1.2B.45–47 

In the prokaryotic organisms, bacteria and archaea, locomotion is due to a gradient of protons generated by the electron transport chain, known as proton motive force, generated across the cell membrane.48  In some cases a concentration gradient leads to the rotation of the bacteria flagella, through a rotating molecular joint that connects them to the main body.22,49–51  The flagella, due to their elasticity, form a helical shape upon rotation subject to the anisotropic drag of the fluidic surrounding, which leads to a corkscrew-like motion of a cell.39,50  Typical bacteria swimming in Newtonian suspensions exhibit the so-called ‘run-and-tumble’ locomotion, where ‘run’ refers to straight trajectories combined with ‘tumbles’, e.g., shorter, random reorientations.52  The bacteria can be classified as peritrichous, such as Escherichia coli (E. coli), adopting many flagella,53 Figure 1.2C, in their self-propelling locomotion leading to a swimming velocity of 10–35 µm s−1.54  Those bacteria having one single flagellum, e.g., Vibrio cholera with a swimming velocity of 74.5 µm s−1,55  are classified as monotrichous bacteria.

The other large family of flagellated microorganisms is eukaryotic swimmers. Eukaryotic flagella and cilia are cellular organelles having a complex, yet well-ordered internal structure known as the ‘9 + 2’ axoneme. In the ‘9 + 2’ structure, nine ‘doublet’ microtubules surround the central pair. Each of the nine doublet microtubules presents two dynein extensions, the so-called arms.56,57  Further details are provided in chapter 2. Flagella and cilia are identical in internal structure, but flagella are commonly longer than cilia. The axonemal motor proteins that generate the force that slides the microtubules are the dynein ATPases, leading flagella to undulate like a whip with symmetrical traveling waves, while cilia beat with an oar-like action with alternation of so-called ‘effective’ and ‘recovery’ strokes.22,39,56,58,59  The damped, wave-like beating pattern due to the flagellum elasticity generates a non-reciprocal motion at a low Reynolds number, even though the molecular motor unit’s initial power stroke is reciprocal.22,39,60 Chlamydomonas reinhardtii (C. reinhardtii), Figure 1.2D, is a widely investigated eukaryotic microalgae with two flagella61  having at least two types of locomotion, i.e., swimming locomotion in the liquid bulk and a crawling locomotion on a surface.62–66 

One of the most life-relevant cell swimmers is the sperm cell, Figure 1.2E, in which the single flagellum is made of a ‘9 + 2’ axoneme covered by a thin cell membrane, with mitochondria arranged spirally around the axoneme at the sperm middle-part.67  The mitochondria synthesize ATP transported to the dynein ATPase motors by an adenylate kinase (AK) shuttle. The activation of the dynein ATPases in the mitochondria is modulated by pH, ATP, ADP, Ca2+, and phosphorylation.68,69  Consequently, ion transport plays a key role in sperm motility regulation.70 

The previous view on the human sperm cell swimming process was based on the symmetrical movement of the flagellum from side-to-side.72–75  Gadelha et al. demonstrated that the human sperm flagellum [Figure 1.3A] beating is asymmetrical in one plane (b plane), with a symmetric out-of-plane (z plane) component, Figure 1.3B. The coordinated 360° rotation, around the rolling axis, of asymmetric one-sided bends, drives symmetrical arrangement of the flagellum with respect to the rolling axis, Figure 1.3C and D. This rolling motion enables sperm cells to swim in a straight trajectory.71 

Figure 1.3

(A) Schematic of a sperm flagellum covered by a thin cell membrane (highlighted with a blue color) that protects the axoneme (yellow). (B) The flagellar beating anisotropy in 3D showing the b plane and z plane. (C) 3D flagellar beating of a human sperm cell near to and (D) far from a microscope coverslip. The color progression of the waveform through the flagellar rolling cycle is indicated by the cyclic color map inset, with periods of 285 ms. The red curves depict the trajectory of the mid-flagellar point, indicated by the red plane cross-section. Reproduced from ref. 71 (10.1126/sciadv.aba5168) under the terms of the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

Figure 1.3

(A) Schematic of a sperm flagellum covered by a thin cell membrane (highlighted with a blue color) that protects the axoneme (yellow). (B) The flagellar beating anisotropy in 3D showing the b plane and z plane. (C) 3D flagellar beating of a human sperm cell near to and (D) far from a microscope coverslip. The color progression of the waveform through the flagellar rolling cycle is indicated by the cyclic color map inset, with periods of 285 ms. The red curves depict the trajectory of the mid-flagellar point, indicated by the red plane cross-section. Reproduced from ref. 71 (10.1126/sciadv.aba5168) under the terms of the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

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In the Caenorhabditis elegans, Figure 1.2F, the ATP synthase is the primary cellular energy-generating machinery76,77  of the mitochondrial respiratory chain. The lengthening of the lifespan of C. elegans is associated with reduced mitochondrial function, in particular with a decrease in rotenone-sensitive NADH ubiquinone oxidoreductase activity due to genetic inhibition of the Y82E9BR.3 protein.78 C. elegans presents adaptive undulatory locomotion that produces articulate locomotion behavior. Two kinematically distinct locomotion behaviors of C. elegans are swimming and crawling in liquids and gel-like media, respectively. The crawling locomotion is due to strong and extensive contractions of the worm’s body64  allowed by the four-quadrant muscle arrangement that is anatomically capable of generating the articulated body deformations needed.28 

For fish, the swimming energy to overcome pressure drag arises from active muscle contraction, which is driven by myosin molecular motors that hydrolyze ATP.79  The muscles of a fish contract and expand, during undulatory and oscillatory motions, to produce ‘S’ wave-like undulations in their bodies. These waves allow the fish to exert a force through its body and tail with a positive angle-of-attack of the tail against the water, which pushes the water backwards.80 

Natural swimmers are usually driven out of equilibrium by internal energy sources even though chemotaxis can play a considerable role in locomotion, while synthetic swimmers can be driven by internal or external energy sources. Synthetic swimmers’ propulsion mechanisms include bubble propulsion, self-electrophoresis, and self-diffusiophoresis.81  The bubble propulsion consists of the recoil force of bubbles generated from the decomposition reaction used to propel the synthetic swimmers.82,83  The self-electrophoresis is based on a local electric field generated by an asymmetric formation of ionic products like in the case of Janus particles,84 Figure 1.2I, while in self-diffusiophoresis, the gradient of substrate concentration is used to propel synthetic swimmers.85  The propulsion can also be driven by external fields, for instance, by applying oscillating or rotating magnetic fields to magnetically modified swimmers. However, the structural motion must be non-reciprocal in order to gain a net forward movement (scallop theorem).39  To create non-reciprocal motion, rotating helical microstructures propelling at low Reynolds number can be prepared.31  Further details on their propulsion mechanisms are provided in Subsection 1.3. The robotic fish locomotion is due to the tail undulation, which is allowed by the cyclic flow of a displacement pump and adjusting the relative amount of liquid pumped into each side of the tail.32 

Biological swimmers can act as active vehicles to promote the transport of synthetic passive elements becoming the so-called hybrid swimmers. For instance, a magnetotactic bacterium, such as Magnetococcus marinus, was adopted as an active transport agent for synthetic passive liposomes,33 Figure 1.2L, by providing the advantage to control the swimming direction by an external magnetic field. Likewise, the most common protozoan model used in toxicological studies, Tetrahymena pyriformis, can be artificially modified by adding iron-oxide nanoparticles providing magnetotactic properties,34 Figure 1.2M. The initial idea of Montemagno and Bachand86  consists of a hybrid swimmer made by the catalytic complex of the ATP synthase, a molecular motor that can consume ATP to drive rotation of the γ-subunit inside the ring of three αβ-subunit heterodimers in 120° power strokes, namely F1-ATPase,87  attached to lithographic-made nanostructured gold-, copper-, and nickel-coated substrates. The interaction between the active biomacromolecule agents and the substrate allows movement in the presence of the ATP energy source; like in the case of the hybrid fish in which human stem cell derived cardiomyocytes generate the pulse that bends the synthetic body allowing functional locomotion.

A ratchet placed in a bath of Brownian particles cannot display any net motion without the addition of an external energy source. This perpetuum mobile, pioneered by Richard Feynman, has been revisited in the realm of active matter. In particular, replacing the Brownian particles by swimming Escherichia coli bacteria leads to a net motion of the ratchet due to the non-reciprocal interactions of the bacteria with the asymmetric object88  (see Figure 1.4A). In this study, bacteria effectively convert chemical energy from the environment into directed motion of the gear (it rotates roughly one round per minute), which could in principle allow for the extraction of work. This study demonstrates that active constituents can produce work and overcome the limitations of the second law of thermodynamics in equilibrium physics. In what follows we discuss machineries at the molecular scale, which translate chemical energy into biological function, as well as synthetic processes.

Figure 1.4

Active machines. (A) Bacterial ratchet motor. A ratchet is placed in a bath of Escherichia coli bacteria, which drive the ratchet by interacting with its boundaries. Reproduced from ref. 88 with permission from PNAS. (B) Development of the mitotic spindle. Reproduced from ref. 18 (https://doi.org/10.1038/s41598-018-27008-w) under the terms of the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/). (C) Illustration of filopodia used for migration in mammalian cells. Reproduced from ref. 89 with permission from Springer Nature, Copyright 2008.

Figure 1.4

Active machines. (A) Bacterial ratchet motor. A ratchet is placed in a bath of Escherichia coli bacteria, which drive the ratchet by interacting with its boundaries. Reproduced from ref. 88 with permission from PNAS. (B) Development of the mitotic spindle. Reproduced from ref. 18 (https://doi.org/10.1038/s41598-018-27008-w) under the terms of the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/). (C) Illustration of filopodia used for migration in mammalian cells. Reproduced from ref. 89 with permission from Springer Nature, Copyright 2008.

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Each cell relies on the functioning of various different non-equilibrium processes at the subcellular scale to proliferate, move, and perform its specific tasks, which makes it an ‘active machinery’ by itself.90–93  These subcellular machineries vary among cell types, such as bacteria or mammalian cells. Prominent examples represent the mitotic spindle for the separation of chromosomes in the cell94–96  and filopodia for cell migration and growth,89,97–99  which we briefly address below.

Mitotic spindle The micro-scale filamentous molecular machinery that a cell self-assembles from a soluble pool of nanometer-scale tubulin dimers during the process of cell division, in order to capture and separate chromosomes, is called the mitotic spindle94–96  (see Figure 1.4B). This structure consists of growing (polymerization) and retracting (depolymerization) bipolar filaments of microtubules, which are nucleated at the growing end. The evolving structure and relative motion of the many filaments that make up the spindle are driven by motor proteins, the two main ones being kinesis-5 100,101  and dynein.102,103  The energy for the different steps in the process comes from ATP and GTP hydrolysis and the active processes include ‘check points’ that enable sequential processes of growth, chromosome capture, chromosome separation, and eventual cell division to form two genetically identical daughter cells.

There are two possible main types of spindle assemblies:96  (i) those that organize from two distinct centers (centrosomes) in a cell and (ii) acentrosomal spindles that originate from other sites within a cell. For more details about the active processes that enable this robust cell machinery to assemble and function, we refer to Chapter 6.

Filopodia are thin protrusions with a diameter of 0.1–0.3 µm emanating from the leading edge of the membrane of eukaryotic cells,89  where they may be (depending on the cell) connected to the lamellipodia, i.e., a network of actin filaments. They serve as cellular ‘antennae’ for probing the environment and thereby, for example, enable cell migration on substrates (see Figure 1.4B). Filopodia contain a tight, cross-linked bundle of parallel, polar actin filaments, which grow towards the cell membrane via actin polymerization. As the protrusions grow, new adhesions, with the underlying substrate near the edge, form. The additional presence of myosin motors, which move along the polar actin filaments via ATP hydrolysis, and focal adhesions may lead to the generation of contractile stresses and hence traction forces inducing cell movement. Details of the generation of traction forces required for cell motion depend on the different cells and are still being investigated.

In addition to cell migration, filopodia (or similar protrusions) play important roles in other areas of cell biology, ranging from the growth of neurites and dendritic spines to wound repair to the invasion of cancer cells. We refer to ref. 89, 97–99, 104 and 105 for excellent reviews on these topics.

Additional examples include the cytokinetic ring dividing the cell into two,106,107  complex motors rotating connected cellular appendages as well as deforming flagella and cilia carpets for the self-propulsion of microorganisms108–110  (see Section 1.2.1). The latter topics are addressed in Chapters 2, 5, 9, and 10.

Many mechanisms for designing active machines rely on non-equilibrium processes of components much smaller than the self-propelled agents themselves, such as the transport of ions, micelles,111  and organic compounds.112  In contrast to biological systems, these out-of-equilibrium processes lead to active transport of, e.g., colloids or droplets only, and, to our knowledge, no synthetic counterparts for more complicated functions, such as the division of compounds, exist to date. As our book lacks a chapter on these types of self-driven systems, we describe some of them here in more detail.

Diffusiophoresis refers to the phenomenon that chemical gradients can induce the directed motion of suspended particles as a consequence of the interaction of a solute with the surface of the particle.114  Experimental demonstrations of this kind of active motion, where the energy is effectively stored in the gradient that is established initially, have been reported for nanometer and micron-diameter spheres, droplets, vesicles, and macromolecules such as DNA, bacteria, etc.115  Often the liquids studied are dilute (e.g., millimolar) salt solutions, though molar concentrations have also been reported.116  In addition, surfactant solutions have also been studied.117 

Typically, there are two contributions to the driving force for motion. In a chemical gradient of ions, when the cations and anions have different diffusion coefficients, denoted D+ and D, respectively, then a chemical gradient gives rise to a local electric field that is proportional to the ratio (D+D)/(D+ + D). Since most objects in liquid obtain some surface change, then there is an electrically-driven relative motion of a particle and the fluid, which is electrophoresis. In addition, the presence of the chemical gradient means that adjacent to the surface there are osmotic pressure differences that give rise to relative motion, which is termed chemiphoresis. The two effects together give rise to diffusiophoretic transport. When a surface is stationary, such as the walls of a container, and the liquid moves, then the motion is termed diffusioosmosis.

Because the origin of this effect is the ions in solutions, effectively a suspended particle is responding to diffusive transport of ions. Thus, a consequence is that micron dimension particles, which ordinarily are expected to spread diffusively with a diffusivity of magnitude O(10−12 m2 sec−1), instead spread diffusively possible as fast as O(10−9 m2 sec−1). Thus, the chemically-driven transport enhancement can be substantial.118 

As the relative motion of the particle and liquid depends on the interaction of the solute and the surface, the motion can be associated with a surface stress, and so is similar to Marangoni motions. It has also been observed that Janus colloids, e.g., particles that are surface-coated with one catalytic material on one half, when placed in a solution with a reactive solute, e.g., hydrogen peroxide, can undergo directed transport38,41  (see Figure 1.5A for a sketch). It is believed that chemical decomposition of the solute creates a chemical gradient that drives the motion, i.e., self-generated diffusiophoresis.

Figure 1.5

Synthetic machines. (A) Self-diffusiophoresis of a catalytic Janus colloid (half-coated with an ‘active’, i.e., reactive, material) in a chemical suspension (gray particles). Chemical reactions occur at the catalytic surface of the sphere decomposing the larger (gray) reactant into three smaller (orange) product particles. (B) Self-propelled liquid droplets in liquid media with surfactants moving due to the generation of Marangoni flows via chemical reactions with the surfactants at the droplet interface or depletion of surfactants. Reproduced from ref. 113 with permission of the Royal Society of Chemistry. (C) A microswimmer moving with an artificial flagellum. Reproduced from ref. 21 with permission from Springer Nature, Copyright 2005.

Figure 1.5

Synthetic machines. (A) Self-diffusiophoresis of a catalytic Janus colloid (half-coated with an ‘active’, i.e., reactive, material) in a chemical suspension (gray particles). Chemical reactions occur at the catalytic surface of the sphere decomposing the larger (gray) reactant into three smaller (orange) product particles. (B) Self-propelled liquid droplets in liquid media with surfactants moving due to the generation of Marangoni flows via chemical reactions with the surfactants at the droplet interface or depletion of surfactants. Reproduced from ref. 113 with permission of the Royal Society of Chemistry. (C) A microswimmer moving with an artificial flagellum. Reproduced from ref. 21 with permission from Springer Nature, Copyright 2005.

Close modal

Marangoni flows are a central aspect for the self-propulsion of liquid droplets, covered by a surfactant layer, in aqueous media111  (see Figure 1.5B). These flows can be induced by chemical reactions of chemicals (present in the droplet or the surrounding medium) with the surfactants on the droplet surface or by inhomogeneous depletion of the surfactants. Both processes locally change the surface tension of the droplet and generate a surface tension gradient, which leads to Marangoni flows towards regions of higher tension inside the droplet. Due to the stress balance at the interface, flows in the outer medium are created leading to self-propulsion of the droplet. Conditions under which these surface tension gradients are stable are discussed in ref. 111. Overall, the droplet displays self-sustained directed motion by ‘consuming’ chemical energy from its surroundings, making it a great exemplar of a synthetic active machinery.

Synthetic flagella, mimicking flagellated propulsion in microorganisms,119  rely on the presence of external forces and operate without requiring chemical fuel. Flexible flagella, as used by, e.g., sperms, have been designed as a chain of magnetic colloids:21  in response to an external, oscillatory magnetic field, the flagellum, which is attached to a red blood cell, deforms and beats in a non-reciprocal manner in a viscous medium, allowing the composite object to swim [see Figure 1.5C]. In addition, rigid, helical flagella have been manufactured at the nano-scale.29,120  The flagella have been attached to a colloid with a permanent magnetic moment, which couples with an external rotating magnetic field leading to self-propulsion. The latter represent a synthetic example of bacteria or archaea, whose propulsion rely on the rotation of the motor and a helical appendage.

Self-propelled agents display fascinating non-equilibrium physics at the collective level. Examples range from the flocking of birds and schools of fish at the macroscopic scale to the emergence of a plethora of new phenomena at the microscopic scale, which are determined by the intricate non-reciprocal interactions of biological filament-protein suspensions, microorganisms, synthetic agents, and mammalian cells.

Microorganisms make up about 90% of the biomass in the ocean, account for 1–3% of the human body, and are omnipresent in soils and sediments. Hence, there is a large variety of different species, many of which rely on their motility to optimize their survival strategies. These microorganisms, beside their importance for biology, have been widely studied in the realm of out-of-equilibrium physics and a range of interesting collective behaviors have been discovered. Here, we discuss a few selected examples to illustrate the rich underlying physics.

Collective behaviors can occur when active agents slow down as they interact with others. Theories have predicted that this leads to the formation of small aggregates and eventually to phase separation.125  The latter has been demonstrated in computer simulations to occur for active Brownian particles (as well as other active particle models) interacting via repulsive forces and quorum sensing, where the particle speed depends on local density (see Chapter 4 for details). Experimentally, the development of clusters has been observed in suspensions of the surface-gliding soil bacterium Myxococcus xanthus,126  however, a fully phase-separated system, as predicted by the theory, has not been found. Densely packed suspensions of Myxococcus xanthus form active nematic crystals, which can evolve to three-dimensional fruiting bodies at the topological defects of the active fluid121  (see Figure 1.6). At high concentrations Bacillus subtilis suspensions exhibit dynamic flocks127  and patterns reminiscent of turbulent flows at high Reynolds number, referred to as ‘active turbulence’, which are dominated by short-range interactions between the cells and characterized by vorticities and flow jets.128  The topic of active nematics and topological defects is also particularly relevant for biofilament-motor protein suspensions.17  We refer the reader to Chapter 3 for more details.

Figure 1.6

Self-organization in active matter. (A) Dense suspensions of Myxococcus xanthus form active nematic crystals and fruiting bodies near the topological defects. Reproduced from ref. 121 with permission from Springer Nature, Copyright 2020. (B) Light-controlled pattern formation of Escherichia coli. In the upper panel dark colors correspond to dense and light colors to dilute bacterial suspensions. The lower panel is color coded according to cell speed. Reproduced from ref. 122 (https://doi.org/10.7554/eLife.36608) under the terms of the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/). (C) Emergence of flocking patterns of colloidal rollers. Reproduced from ref. 123 with permission from PNAS. (D) Wound healing by the movement of epithelial cells towards the ruptured area. Green and red arrows indicate the traction forces. Reproduced from ref. 124 with permission from Springer Nature, Copyright 2014.

Figure 1.6

Self-organization in active matter. (A) Dense suspensions of Myxococcus xanthus form active nematic crystals and fruiting bodies near the topological defects. Reproduced from ref. 121 with permission from Springer Nature, Copyright 2020. (B) Light-controlled pattern formation of Escherichia coli. In the upper panel dark colors correspond to dense and light colors to dilute bacterial suspensions. The lower panel is color coded according to cell speed. Reproduced from ref. 122 (https://doi.org/10.7554/eLife.36608) under the terms of the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/). (C) Emergence of flocking patterns of colloidal rollers. Reproduced from ref. 123 with permission from PNAS. (D) Wound healing by the movement of epithelial cells towards the ruptured area. Green and red arrows indicate the traction forces. Reproduced from ref. 124 with permission from Springer Nature, Copyright 2014.

Close modal

In nature these collective behaviors are affected by the presence of environmental cues. The ability of cells to perform chemotaxis, i.e., adapt their swimming motion to follow chemical gradients, underlies a range of collective phenomena, such as aggregation129  or the formation of traveling bands130  (see Chapter 6). While at low and intermediate cell densities the chemotactic drift can be enhanced compared to that of an individual cell, the drift of high cell densities is strongly suppressed due to cell reorientations resulting from interactions with neighboring cells.131  In addition, light sources can be exploited to control pattern formation in bacterial suspensions.122,132  For example, Escherichia coli, whose speed can be tuned by the light intensity, can display a pattern reminiscent of the gray-scale image of the Mona Lisa, where dense suspensions accumulate at low-light intensity regions, as cells move slowly, and dilute suspensions are present in high-intensity regions, as cells move fast122  (see Figure 1.6).

It is worth noting that bacterial growth becomes important at time scales longer than those relevant for the examples discussed above and represents a process (in addition to self-propulsion), which drives the system far from equilibrium. The physics of growth is interesting at the single cell level, where transport processes at the molecular scale play a major role (see Section 1.3), as well as on the collective level, where bacterial communities, such as swarms and biofilms, i.e., a bacterial community embedded in a polymeric matrix, form.133  Bacteria have evolved numerous strategies to survive under different environmental conditions. Their growth behavior and the shape of the entire bacterial community are strongly affected, amongst others, by the shape of the cell bodies,134  the intrinsic cell cycle,135  confinement,136  and hydrodynamic flows.137 

Active colloids exhibit a wealth of collective phenomena and thus represent a fascinating playground for physicists. The emergence of living colloidal crystals, which continuously form, break, and rearrange due to the interplay of self-propulsion and details of particle–particle interactions, have been found in photoactivated colloids,138  in (attractive) Janus particles moving in a H2O2 solution,139  and in (repulsive) Janus colloids suspended in a critical binary mixture of water and lutidine.140  A single cluster, and hence a phase-separated system, was observed in a colloidal suspension interacting via quorum sensing rules.141  Besides clustering, suspensions of colloidal rollers display coherent flocks123,142  (see Figure 1.6), which develop as defects of the active flows and annihilate over time, in contrast to the active nematic crystals formed by dense solutions of anisotropic microorganisms (see Chapter 3). Interestingly, the flocks evolve into correlated flows in the presence of frozen disorder in the environment, which indicates the importance of unraveling these collective phenomena in complex surroundings resembling natural environments rather than perfect laboratory conditions.

Collective cell migration lies at the heart of many biological processes, such as embryonic development, morphogenesis, regeneration, wound healing, and cancer invasion.143–148  Recent advances in experimental methods (e.g., optical, phase-contrast, and fluorescent microscopy, traction force microscopy) as well as imaging methods (e.g., time-lapse imaging, particle imaging velocimetry) together with the development of new active matter theories (e.g., continuum theories, particle-based simulations, cellular Pott models, phase field models), have enabled the study and characterization of the physics of different biological systems. While the motion of individual cells relies on the generation of protrusions, such as filopodia, (see Section 1.3), the behavior of cells immersed between other cells is crucially affected by cell-to-cell interactions, which include adhesion via transmembrane protein complexes connecting the actomyosin cortices of neighboring cells, cell-to-cell repulsion mediated by the elastic properties of the cytoskeleton, and regulatory processes as cells get in contact. The latter can generate intercellular mechanical forces, which couple both position as well as orientations of the neighboring cells. Hence, the overall collective migration is determined by the motion of individual cells, each being polarized, and the contraction of multicellular actin-myosin structures.145 

This area of research spans several length scales, from the molecular scale of chemical reactions for signaling, to the cellular scale and cell-to-cell interactions, to the macroscopic scale of collective cell behavior, which makes it a particularly exciting research area at the interface of life sciences, biology, and physics. Interesting phenomena at the cell and tissue level represent the collective motion of smaller groups and jamming in cell monolayers, the emergence of leader cells and ‘fingering’ instabilities, collective motion for wound repair124  (see Figure 1.6C), and directed cell motion in response to chemical gradients, electric fields, and changes in substrate stiffness, to name a few. For more references and information, we refer the reader to the excellent reviews on collective cell migration143–148  and to Chapter 5, which provides a review of cell motion in complex environments.

Another topic in the realm of active matter concerns mechanisms of ‘active’ stirring and mixing of fluids. For example, the beating of flagella, the cyclic motion of individual cilia, and the metachronal waves of cilia carpets can generate complex fluid flows,119,151  which enable swimming and feeding of microorganisms,152,153  impact early stages of embryogenesis,19,154–156  facilitate the clearance of our airways,157  and enhance mass transport in coral reefs149  (see Chapter 2 for more details). These systems are rather complex and operate over several orders in space and time. For example, the cyclic motion of the cilia of the protozoan Tetrahymena is determined by the motion of molecular motors on microtubules at the nanometer scale. The cilia, which have a length of ∼10 µm, coordinate their behavior over several hundreds of micrometers, which can lead to complex dynamics, such as swimming, at the millimeter scale.119 

An interesting feature of cilia is their ability to synchronize158  and perform metachronal waves.119,151  The latter refers to self-organized, rhythmic motion of many filaments, which exhibit repeated cyclic motion at a phase lag with respect to their neighbors. This phenomenon also occurs among organisms of larger scale, such as worms and shrimp,151  and has been programmed with magnetically activatable soft filaments150  (see Figure 1.7B). It is, in fact, fascinating that such complex biological systems can lead to patterns that remain very stable to perturbations159  and generate fluid flows enabling different biological functions or fluid pumping and mixing in microfluidic devices, which are topics of current research.

Figure 1.7

Stirring and mixing with filamentous appendages. (A) Vortical flows are driven by motile epidermal cilia, which cover the surface of the coral Pocillopora damicornis. These flows lead to up to 400% enhanced mass transport and guide the exchange of nutrients and oxygen of the coral with its environment. Reproduced from ref. 149 with permission from PNAS. (B) Synthetic carpets of magnetically activatable soft filaments perform metachronal waves for different densities of filaments in the presence of an oscillatory magnetic field. The distance between filaments in (a) is 10 mm, 7 mm, 5 mm, 4 mm, 2 mm, and 1 mm (from left to right), respectively. The direction of the magnetic field is shown at the left side of panel (b). Panel (c) shows average displacements of nearby suspended particles. Reproduced from ref. 150 (https://doi.org/10.1038/s41467-020-16458-4) under the terms of the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

Figure 1.7

Stirring and mixing with filamentous appendages. (A) Vortical flows are driven by motile epidermal cilia, which cover the surface of the coral Pocillopora damicornis. These flows lead to up to 400% enhanced mass transport and guide the exchange of nutrients and oxygen of the coral with its environment. Reproduced from ref. 149 with permission from PNAS. (B) Synthetic carpets of magnetically activatable soft filaments perform metachronal waves for different densities of filaments in the presence of an oscillatory magnetic field. The distance between filaments in (a) is 10 mm, 7 mm, 5 mm, 4 mm, 2 mm, and 1 mm (from left to right), respectively. The direction of the magnetic field is shown at the left side of panel (b). Panel (c) shows average displacements of nearby suspended particles. Reproduced from ref. 150 (https://doi.org/10.1038/s41467-020-16458-4) under the terms of the CC BY 4.0 license (https://creativecommons.org/licenses/by/4.0/).

Close modal

Active matter represents a rapidly-evolving research direction at the interface of physics, engineering, chemistry, biology, and the life sciences. These systems convert some type of energy into directed motion, which drives them far from equilibrium and calls for new theoretical approaches that go beyond the well-established framework of equilibrium statistical mechanics. Recent advances in experimental techniques allow quantifying microbiological processes and provide insights into the mechanics of individual entities, their intricate transport behaviors, and the self-organization of cells, e.g., to form biofilms, tissues, and organs. In addition, new microfabrication tools enable the design of synthetic active materials, which represent both a playground for the controlled study of new non-equilibrium phenomena and a toolbox for new biomimetic materials and machineries, which are expected to perform complex functions. The multi-disciplinary nature of active matter research makes it an exciting area, spanning processes operating over several orders of magnitude in space and time, and holds great potential for discovering universal physical features of a collective of interacting components, such as complex biological and synthetic systems. Future research directions include, but are not limited to, the following topics:

  1. The transport behavior of biofilament-protein suspensions, microorganisms, and mammalian cells is dictated by their surrounding complex medium, such as the interior of cells, the human body, soils and sediments, and the ocean. While the transport behavior of typical microswimmers in dilute environments is relatively well understood, the study of spatial heterogeneity due to confinement, chemical fields, and external flows on the motion of the active agents and collective phenomena is only at the beginning. It is desirable to achieve a comprehensive view of these phenomena and identify common as well as distinct features among the different systems. The design of problem-specific microfluidic devices160  could be used to test theories and suggest new mechanisms for large-scale modeling of environmental processes.

  2. Much is known about typical spherical model swimmers, such as the squirmer. Unraveling the effect of shape, such as ellipsoidal bodies or time-varying shapes of many microorganisms, remains an important research topic, covering motion in Newtonian and non-Newtonian fluids.

  3. At a smaller scale, the diffusion of enzymes has been observed to become enhanced due to their catalytic activity,161  which represents another interesting class of active systems. Building kinetic models for such systems will be important to unravel the physics of this type of active motion.

  4. At larger length and time scales, cell division plays a role. The growth of bacterial colonies and mammalian cells in complex surroundings is important for many biomedical topics as well as the prevention of bio-fouling in industrial processes and thus entails a variety of open research questions.

  5. The interactions between different types of cells and entire communities, despite their importance for microbiology, remain elusive so far. First, the interactions between different cells, such as mammalian cells and bacteria in the context of bacterial infection, is an open research question. Second, how bacterial shape, different propulsion mechanisms, and swim gait (e.g., run-and-tumble mechanisms) impact the classical picture of equilibrium statistical physics, such as phase transitions, pressure, or surface tension, represents an interesting future research avenue.162–164  In this respect, the overall aim is to identify universal principles that govern the interplay of thermal fluctuations, activity, and shape.

  6. Biofilament-motor protein suspensions, many microorganisms, and mammalian cells move in three dimensions, yet quantitative methods for measuring dynamical processes in three dimensions are still sparse. While three-dimensional transport behavior of microorganisms has been measured using advanced tracking methods165–168  as well as the recent framework of differential dynamic microscopy,169  the behavior of mammalian cells has hardly been explored in three dimensions. Hence, future research should focus on the development of experimental tools and models for crawling and swimming cells in three dimensions.

  7. The design of smart materials, such as synthetic cells, relies on relating details of the interactions between the individual (chiral) biofilaments and motor proteins to the rheological properties of homogeneous and heterogeneous mixtures of, e.g., actin and microtubule filaments, as well as establishing tools for controlled and dynamic self-assembly.170  This opens another exciting future research direction.

  8. Advances in rheometry from specially designed geometry tools for rotational rheometers to microfluidic-based rheometers171–173  might allow overcoming of issues in pushers’ suspensions measurements where sensitivity limits are relevant. Future analysis of oscillatory measurements could also provide interesting insights into the flow dynamics of the active agents in the non-Newtonian matrix.

  9. Future progress in data analysis methods from artificial intelligence and machine learning are also expected to reveal new insights into the collective interactions important to the world of active matter.174 

Establishing a physical understanding of these topics is, amongst others, expected to (1) provide fundamental insights into microbiological and ecological processes, such as the role of microbial communities on crop growth or the carbon cycle in the ocean; (2) allow us to identify the mechanical properties and physical mechanisms of biomedical applications, such as bacterial infection, progression of cancer cells, wound healing, and morphogenesis; and (3) enable the design of smart materials, e.g., synthetic cells and microrobots for tissue repair, bioremediation, and drug delivery.

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