The cytoskeleton precisely tunes its mechanics by altering interactions between semiflexible actin filaments, rigid microtubules, and crosslinking proteins. We use optical tweezers microrheology and confocal microscopy to characterize how varying crosslinking motifs impact the mesoscale mechanics and mobility of actin-microtubule composites. We show that, upon subtle changes in crosslinking patterns, composites can exhibit two distinct classes of force response – primarily elastic versus more viscous. For example, a composite in which actin and microtubules are crosslinked to each other but not to themselves is markedly more elastic than one in which both filaments are independently crosslinked. Notably, this distinction only emerges at mesoscopic scales in response to nonlinear forcing, whereas varying crosslinking motifs have little impact on the microscale mechanics and mobility. Our unexpected scale-dependent results not only inform the physics underlying key cytoskeleton processes and structures, but, more generally, provide valuable perspective to materials engineering endeavors focused on polymer composites. Networks of semiflexible actin filaments play critical roles in cell polarity and contractile and migratory processes8; while microtubules mediate intracellular trafficking and transport, chromosomal dynamics, and mitotic spindle alignment during cell division9. Synergistic interactions between these two filaments, which are mediated by steric and chemical interactions (i.e. entanglements and crosslinking)11, establish essential cell asymmetries and enable proliferation, differentiation, and migration14. While crosslinking of both filaments is ubiquitous in cells, serving important roles in locomotion, membrane reinforcement, and intercellular cargo transport14, there is mounting evidence of crosslinking between actin and microtubules, mediated by proteins such as tau, MAP2, APC, profilin, and plectin21. Specifically, actin-microtubule co-crosslinking has been shown to be important to cortical flow, wound healing, neuronal cone growth, cell migration, and muscle contraction25.The multifunctional mechanics of eukaryotic cells are largely determined by the cytoskeleton, a dynamic network of interacting biopolymers and binding proteins. Two principal cytoskeletal biopolymers are actin filaments and microtubules. Actin filaments polymerize from globular actin monomers to ~7 nm wide semiflexible filaments with a persistence length 27. In order to increase stiffness, strength, and toughness in composite materials, soft polymer networks are often reinforced with stiffer, load bearing fibers such as nanotubes and carbon nanofibers29. Further, varying types of crosslinking have been used to reinforce and increase the mechanical strength of flexible-stiff polymer double-networks32. Crosslinking has also been shown to preserve memory and reduce network deformation in composite polymer hydrogels33.Aside from the obvious physiological relevance, investigations of actin-microtubule composites with variable crosslinking motifs are motivated by materials engineering, as they serve as a model platform for designing and investigating flexible-stiff polymer compositesActin), only microtubules are crosslinked (Microtubule), both actin and microtubules are crosslinked (Both), and actin and microtubules are crosslinked to each other (Co-linked) , are dictated by the degree to which microtubules are crosslinked.Here, we use optical tweezers microrheology and confocal microscopy to characterize the mechanics and mobility of actin-microtubule composites with varying crosslinking motifs. We create equimolar composites of actin and microtubules in which: only actin is crosslinked (ed) Fig. . We charin vitro studies to date have focused on single-component networks of either actin or microtubules48. In response to strain, entangled actin networks have been reported to exhibit varying degrees of stiffening, softening, and yielding depending on the actin concentration as well as the scale and rate of the strain39. Crosslinked actin networks exhibit enhanced stiffness and prolonged, more pronounced elasticity compared to entangled solutions44. Entangled actin networks have also been shown to relax force via an array of mechanisms including bending, stretching, retraction, reptation, and confinement-hopping52. While many of these mechanisms are suppressed by crosslinking, crosslinked networks have been reported to exhibit relaxation and plasticity due to crosslinker unbinding/rebinding, slippage, and stretching55. Compared to entangled actin networks, entangled microtubules have been reported to respond more elastically to strain with more pronounced stiffening as well42. Further, while stretching is important to actin stress relaxation, bending plays a more dominate role in the relaxation of microtubules56. While the timescales for microtubules to relax have been suggested to be on the order of several minutes or more42, crosslinked microtubule networks have been reported to display some degree of relaxation due to temporary force-induced crosslinker unbinding events4.Despite the relevance of actin-microtubule composites to biology, physics, and engineering, most 58 due, in part, to the incompatibility of standard polymerization conditions for each protein27. However, methods have recently been introduced to co-polymerize actin and tubulin in situ to create randomly-oriented co-entangled composites of actin and microtubules27. The first study that employed these methods used microrheology and microscopy techniques to show that a surprisingly large molar fraction of microtubules (>70%) was needed to substantially increase the response force of the composites. This intriguing result was attributed to the larger mesh size of microtubule networks compared to actin networks of the same molarity. Further, actin-rich composites softened in response to strain while microtubule-rich composites stiffened. This distinction arose from actin bending (leading to softening) that was increasingly suppressed by microtubules (leading to stiffening). This result corroborated a previous study that investigated the nonlinear macrorheology of crosslinked actin networks doped with low concentrations of microtubules, in which the high bending stiffness of microtubules served to suppress actin bending and enhance stretching in response to strain43.Few studies have investigated composite networks of actin and microtubules27 to create equimolar co-entangled actin-microtubule composites. We then incorporate biotin-NeutrAvidin complexes into composites to selectively crosslink the filamentous proteins, keeping the crosslinker:protein ratio fixed at R = 0.0237. We create composites with: crosslinked actin (Actin), crosslinked microtubules (Microtubule), crosslinkers equally forming actin-actin and microtubule-microtubule bonds (Both), and crosslinkers binding actin to microtubules (Co-linked)  as well as one in which both filaments are crosslinked but R is doubled (Both 2x)  vary for the different composites, as listed in Fig. To systematically investigate the role that crosslinking plays in composites of actin and microtubules we design actin-microtubule composites with four distinct crosslinking motifs. We use our previously established protocolsed) Fig. . We comp2x) Fig. . While aF(x), as a microsphere is pulled through each type of composite. As expected, all crosslinked composites exhibit overall larger resistive forces than the composite with no crosslinkers (None). The more interesting and unexpected result that emerges is that the force curves appear to display two distinct responses dependent on the crosslinking motif: pronounced softening behavior in which the slope of the force curves approach zero at large distances, versus largely elastic behavior in which F(x) remains linear with x until the end of the strain. To better delineate between these two behaviors, we normalize F(x) by the terminal force Ft reached when x = 10 µm, which we notate as None, Actin, and Both composites while Class 2 comprises Microtubule, Co-linked, and Both 2x composites.To characterize the mechanical response of our designed composites we use optical tweezers microrheology to drag microspheres through each composite and measure the local force applied to each sphere by the composite during and following the strain. Figure F ~ x), and once the microsphere stops the force the network exerts on the sphere F(t) should be maintained with no relaxation or dissipation  ~ Ft). Conversely, a purely viscous material yields a strain-independent force response (F ~ x0) that is reached as soon as the microsphere reaches constant speed, and once the microsphere stops the network immediately and completely relaxes its force on the sphere (F(t) ~ 0). Most biopolymer networks, including entangled actin-microtubule composites, display viscoelastic behavior in between these two extremes27. However, crosslinking can lead to more elastic response by suppressing network rearrangements and polymer bending modes that can dissipate stress37. Figure For a purely elastic material we expect to see a linear relationship between the resistive force and distance the microsphere is pulled  exhibit substantial elasticity, while Actin and None force curves display similar curvature indicative of more viscous response. This result suggests that at this crosslinking density, crosslinks do not substantially prevent semiflexible actin filaments from bending and/or rearranging to dissipate stress. Further, at a given R the length between crosslinks along an actin filament is ~4x longer than that for microtubules (see Methods), so there are comparatively fewer crosslinks along an actin filament to suppress relaxation modes. The counterintuitive result presented in Fig. Both) exhibits soft/viscous behavior similar to None and Actin despite the fact that both actin and microtubules are crosslinked. Given the role that crosslinking plays in enhancing elasticity, one would expect that a network in which all filaments are crosslinked would be more elastic than one in which just half of the proteins are linked (Actin or Microtubule). However, because in this composite both actin and microtubules are crosslinked and the density of crosslinkers remains fixed (R = 0.02), the length between crosslinkers along each filament is doubled.Only composites in which microtubules are crosslinked  such that the length between crosslinkers along each actin filament and microtubule is the same as in Actin and Microtubule composites, rather than being twice as long. As shown in Fig. R, the composite exhibits Class 2 elastic-like response similar to Microtubule and Co-linked networks. Thus, it appears that the critical requirement for sustained elasticity is not only that microtubules must be crosslinked but that they must be crosslinked such that the length between crosslinkers is sufficiently small. Reducing lc,m leads to a more connected network, thereby constraining filament fluctuations and rearrangements and leading to enhanced network stiffness59.To determine if this increased ity Both x such thF(x) over different microsphere displacements xf– xi, which we denote as Fxf–xi  there is little difference between the force response the two classes exhibit, with all crosslinked composites displaying an average force of F–01 ≈ 3 ± 0.6 pN. This result indicates that variations in the crosslinking motif has little effect on the microscale, linear regime response of composites. Even at somewhat larger microscale displacements (1–4 µm), while crosslinked composites exhibit larger forces than None, the type of crosslinking has little effect on the measured force . Only at mesoscale distances, on the order of the length of filaments and substantially larger than the mesh size of composites, does the dramatic effect of crosslinking motif emerge, with Class 1 composites exhibiting an average force of F10–4 ≈ 9 ± 3 pN while Class 2 composites display F10–4 ≈ 15 ± 2 pN.To quantify the distinct behaviors of Class 1 and Class 2 composites and examine the lengthscale dependence of the response, we average –xi Fig. . As showlc reflects that of a steady-state unbinding/rebinding regime, and the response will still be dominated by stretching and/or bending modes. The varying degree to which Class 1 and Class 2 composites can undergo each mode manifests as a clear distinction between measured force values at these lengthscales.This scale-dependent variation is likely a result of both variable length between crosslinkers and a small fraction of crosslinker unlinking/relinking events. At the submicron level, the differences in crosslinker lengths only result in small differences in the density of crosslinkers encountered by the microsphere, and filament bending and stretching is minimal. As the distance becomes orders of magnitude larger than the crosslinker lengths, the effect of varying crosslinking densities, as well as the varying contributions of bending and stretching, become more appreciable. Further, at larger displacements (i.e. longer times), crosslinks that were initially ruptured (contributing to submicron softening) will have had time to re-link. While new un-linking events can occur, the force response at lengthscales much greater than K of composites, analogous to the differential modulus in bulk rheology, which we quantify as K = dF/dx  /dx, which quantifies the curvature displayed in Fig. K and K and The mechanisms described above would more clearly contribute to differences in the elasticity or stiffness of the networks rather than the absolute magnitudes of the force responses. In fact, as shown in Fig. /dx Fig. . We alsoK values for submicron scales, and exhibit softening (decreasing K) from K1–0 to K4–1. Class 1 composites do soften slightly more than Class 2 composites over the first 4 µm; however, the differing degrees of softening for Class 1 and Class 2 composites is much more substantial at larger lengthscales (>4 µm). K10–4 values drop to ~0.6 ± 0.2 pN/µm for Class 1 composites, whereas for Class 2 composites K10–4 values are indistinguishable from K4–1 values (no softening). To better quantify the extent to which composites soften or remain elastic, we turn to µm) to (4–10 µm) while Class 2 composites remain nearly constant for lengthscales beyond 1 µm.As shown in Fig. µm and 4 µm to delineate different phases of the response was motivated by visually apparent changes in the curvature of the force response as seen in Fig. µm/s. As shown in Fig µm) and (1–4 µm), as well as the magnitudes of averaged K and We note that the exact choice of 1 37. In this previous work, authors found that R > 0.05 was needed for actin networks to exhibit largely elastic response, with R < 0.05 networks displaying softening and yielding to a viscous regime over a 10 µm bead displacement of comparable speed. The authors explained the transition to elastic response as arising from actin filaments stretching in the direction of the strain rather than bending non-affinely. This study also showed that force-induced crosslinker unbinding contributed to the yielding and relaxation behavior of low R networks. Such force-induced unbinding of biotin-NeutrAvidin crosslinkers has also previously been reported for crosslinked microtubule networks4.Our results and interpretations are validated by prior measurements on actin networks crosslinked by biotin-NeutrAvidinµm at which point a more elastic response takes over. This universal softening at small scales supports the presence of force-induced unbinding of both actin and microtubule crosslinks, as the length between crosslinkers is substantially smaller than a micron for all composites, whereas the deformation lengthscales needed to induce appreciable bending or stretching are much larger60. As the strain proceeds, the contributions from bending and stretching grow, outweighing that of crosslinker-unbinding and thus minimizing its effect on the force response. Further, unbinding events are reversible, and re-binding has been shown to contribute to sustained elastic response  similar to that depicted by Class 2 composites  may not solely be due to the force the composites exert but also to transient effects arising from bringing the piezoelectric stage (which moves the trapped bead) from rest to constant speed. While the response time of the stage is 0.25 ms , the mismatch between the stage and bead velocity persists for ~25 ms  and the variation between (0–1 µm) and (1–4 µm) remains nearly constant.Finally, we note that the microscale response  (details provided in Methods). Both the magnitude and frequency dependence of η(ω) are nearly the same for all crosslinked composites, corroborating the microscale results described above. Further, the shear-thinning behavior η(ω)~ω−0.5 is indicative of a viscoelastic fluid and is comparable to previously reported scaling for entangled actin48, indicating once again that the elastic response of Class 2 composites only manifests at the mesoscale.Nonetheless, to remove transient effects entirely from the microscale analysis, we perform 1 63. To characterize the relaxation dynamics of the composites, we measure the time-dependent force F(t) exerted on the bead by each composite for 15 s following the strain  by the initial force (immediately after strain) F0 /Fo, in which Ff is the force reached at the end of the relaxation period. For reference, in a purely elastic network with no dissipation (Fo–Ff)/Fo should be 0 whereas a viscous system should exhibit a value close to 1. As shown in Fig. As shown in Fig.  F0 Fig. . Class 148. In particular, crosslinked actin networks have been shown to relax via a sum of exponential decays with well-separated decay times each corresponding to different relaxation mechanisms37. Similarly, we find that the best fit to the force relaxations for all composites is a sum of three exponential decays with well-separated time constants . The three distinct decay constants, with similar values for all composites, indicate that three different relaxation mechanisms with well-separated characteristic timescales contribute to the force relaxation of all composite types  compared to the crosslinked composites, which we discuss further in the next section. To evaluate the relative contribution of each mechanism to the force relaxation, we compare the corresponding fractional coefficients for each exponential term Ci/(C1 + C2 + C3)  64. The mesh time for our composites, computed via τm ≈ βζξ4lp−1 where is β = 1/kBT, ζ is the translational friction coefficient and ξ is the composite mesh size (see Methods)64, is ~0.086 s, which is quite close to our fast relaxation time τ1≈ 0.06 s. Thus, we can interpret our fastest relaxation mechanism as arising from hydrodynamic effects of the surrounding mesh. This timescale relies on filaments being able to fluctuate and rearrange over lengthscales comparable to the mesh size. These fluctuations are hindered by rigid crosslinkers, so for smaller crosslinker lengths (Class 2) this relaxation mode should contribute less to the force relaxation. Indeed, the average C1 value for Class 1 composites is larger than for Class 2.To understand our fast relaxation timescale, we estimate the fastest predicted relaxation mode for entangled actin networks, which is termed the mesh time 65. We estimate timescales for actin and microtubule bending using τB ≈ (γ/κ)[L/(3π/2)]4 where κ ≈ lpkBT is the bending rigidity, L is the filament length, γ = (4πη/ln(2ξ/r) is the perpendicular drag coefficient, η is the solvent viscosity, and r is the filament radius39. Using our measured lengths for actin and microtubules in composites (La≈ 8.7 µm and Lm≈ 18.8 µm)27 we compute bending relaxation times of τB,a≈ 0.54 s and τB,m≈ 0.15 s for actin and microtubules, respectively. These timescales are in close agreement with our measured τ2 values (~0.3–0.6 s), suggesting that the second relaxation mode in our experiments is due to bending of both actin and microtubules. However, Class 1 composites display larger τ2 values than Class 2, with an average value of ~0.6 s which is quite close to the predicted τB,a. Conversely, the average τ2 value for Class 2 composites is ~0.4 s, lying between τB,a and τB,m. This distinction suggests that while microtubules can freely bend in response to large strains when they are not crosslinked or minimally crosslinked (Class 1), when lc,m becomes sufficiently small (Class 2), microtubules can no longer bend to release stress. This suppression of bending modes leads to the primarily elastic response seen in Figs Another key mode of stress relaxation accessible to actin filaments and, to a lesser extent, microtubules is bending/κ)L/3π/]4 where π/4 where37. These studies reported the presence of two distinct relaxation mechanisms available to actin filaments, which both occur on similar timescales as our measured τ3 and are both due to force-induced crosslinker unbinding and rebinding: curvilinear diffusion (reptation) and lateral confinement-hopping37. More specifically, crosslinked filaments can evade the confinement of the surrounding crosslinked mesh by crosslinks momentarily unlinking and thereby releasing the constraint they impose on the filaments, allowing for reptation and lateral confinement hopping. Such force-induced temporary unbinding events have been previously reported for both actin and microtubule networks crosslinked with biotin-NeutrAvidin37. Because fast timescale fluctuations (τ1) are more suppressed in Class 2 composites, we expect this slow mode to contribute more to the relaxation of Class 2 composites compared to Class 1, which is what we see in Fig. C3 values for Class 2 composites are largely greater than for Class 1).To understand the slowest relaxation mode, which occurs on the order of ~1–10 s for all composites, we turn to previous experiments investigating the stress relaxation of crosslinked actin networks following nonlinear strain27. Briefly, for each time-series we compute the average standard deviation of the intensity over time for all pixels <δ> and normalize by the corresponding average intensity of all pixels over time <I> , we find that all crosslinking motifs reduce the mobility of both filaments by ~1.4x . This result corroborates our relaxation data in which all three decay times for None are ~1.8x faster than for crosslinked composites . Because the mobility we are measuring is at the submicron scale (each pixel is 0.41 μm) and in the steady-state (linear) regime, we expect our mobility results to more closely match our microrheology results at the submicron and microscopic scales . As described above, at these lengths and force scales there is little difference between the different crosslinking motifs, with all composites exhibiting similar force, stiffness and viscosity values  . Porcine brain tubulin, biotinylated tubulin, and rhodamine-labeled tubulin were purchased from Cytoskeleton  and stored at −80 °C in PEM-100 (100 mM PIPES (pH 6.8), 2 mM MgCl2, and 2 mM EGTA).Rabbit skeletal actin, biotinylated actin and Alexa-488-labeled actin were purchased from Cytoskeleton  and Thermofisher (A12373) and stored at −80 °C in a Ca buffer (2 mM Tris (pH 8.0), 0.2 mM ATP, 0.5 mM DTT, 0.1 mM CaCl37. As depicted in Fig. 27. In short, actin monomers, tubulin dimers, and crosslinker complexes were added to PEM-100 supplemented with 1 mM ATP, 1 mM GTP, and 5 µM Taxol. To image composites, 0.13 µM of Alexa-488-labeled actin filaments and rhodamine-labeled microtubules, as well as oxygen scavenging agents  were added ; (2) actin filaments in the composite are crosslinked to each other (Actin); (3) microtubules in the composite are crosslinked to each other (Microtubule); (4) both actin and microtubules are crosslinked but they cannot crosslink to each other (Both); (5) actin and microtubules are crosslinked to each other but not to themselves (Co-linked); and (6) a composite similar to Both but in which the densities of actin-actin and microtubule-microtubule crosslinks are both doubled (Both 2x).We prepared six different composite types that varied in their crosslinking motif as follows Fig. : (1) no µM with an equimolar ratio of actin to tubulin, and the molar ratio of crosslinker to protein was fixed at R = 0.02. The mesh size of actin and microtubule networks comprising each composite are ξa = 0.3/ca1/2 = 0.85 µm and ξm = 0.89/ct1/2 = 1.58 µm in which ca and ct are the actin and tubulin concentrations in units of mg/ml67. From these mesh sizes we calculated the effective composite mesh as ξ = (ξm−3 + ξa−3)−1/3 = 0.81 µm27. We estimated the length between crosslinkers for all three types of crosslinking used in composites  as follows  × R−1 where every 13 tubulin dimers adds lring = 7.8 nm in length to the microtubule. For Actin and Microtubule composites, lc,a = 67.5 nm and lc,m = 15 nm. In the composite where crosslinkers are equally distributed between actin-actin links and microtubule-microtubule links (Both), R remains fixed so there are half as many crosslinkers available to each network. Thus, lc,a and lc,m both double . For composites in which both networks are linked but R is doubled (Both 2x) lc,a and lc,m remain the same as in the Actin and Microtubule cases. For Co-linked composites, the length between crosslinkers that link actin to microtubules was computed as lc,a-m = 1/2 = 31 nm.For all presented data, total protein concentration was held fixed at 5.8 ows Fig. . The len68, was formed by a IX71 fluorescence microscope (Olympus) outfitted with a 1064 nm Nd:YAG fiber laser (Manlight) and focused with a 60× 1.4 NA objective (Olympus). A position-sensing detector (Pacific Silicon Sensor) measured the deflection of the trapping laser, which is proportional to the force acting on the trapped microsphere. Stokes drag method was used to calibrate trap stiffness70. A nanopositioning piezoelectric stage (Mad City Labs) was used to move the trapped microsphere relative the sample  = Fmax(ω)/3πAd where d is the bead diameter  in each channel were recorded at 16 fps for 60 seconds. For each composite type, two different samples were imaged with 3–5 time-series taken for each sample.A Nikon A1R laser scanning confocal microscope with a 60× 1.4 NA objective and QImaging QICAM CCD camera were used to collect 2D time-series of composites. The microscope is outfitted with 488 nm and 561 nm lasers and simultaneously records separate images for each laser channel (green and red) to separately visualize Alexa-488-actin (green) and rhodamine-tubulin (red) Figs , 4. Time27. In brief, every 16 frames in the time-series were averaged together to create time-series with 1 second frames27. As demonstrated and described previously27, we selected 1 second frames to average out the frame-to-frame shot noise that obscured the images of the filaments, enhancing the signal to noise without altering the trends in the data  to compare different data sets. From KS-tests, we computed probability values p for finding overlapping data and use the accepted value of p < 0.05 as the cutoff for determining when two data sets were significantly different.Time-series from each channel (green and red) were analyzed separately to determine the mobility of actin and microtubules in the composites, as previously describeddata Fig ; and becdata Fig . The avebetween actin and microtubules has received much recent attention and is thought to be responsible for maintaining cell shape and polarity, growth and structure of neurons, and spindle positioning in mitosis16. The design and characterization of composites of flexible and stiff polymers is also a topic of current interest in materials engineering66, yet how crosslinking can tune the mechanical response of these composites has remained largely unexplored.Actin and microtubules form interacting networks within the cytoskeleton, providing cells with mechanical integrity and enabling a myriad of mechanical processes such as locomotion, morphogenesis, intracellular transportation, and division. Many of these diverse functions are mediated by crosslinking proteins that can bind actin, microtubules, or both proteins. Further, the role of crosslinking Actin), microtubules are crosslinked (Microtubule), both actin and microtubules are crosslinked (Both), and actin and microtubules are crosslinked to each other (Co-linked). We use optical tweezers microrheology and dual-color fluorescence confocal microscopy to measure the nonlinear force response and mobility of each composite type. We show that composites separate into two distinct classes which are dictated by the degree to which microtubules in each composite are crosslinked. Class 1, which comprises None, Actin, and Both composites, displays largely viscoelastic response to the imposed strain with ample softening. In contrast, Class 2, comprised of Microtubule, Co-linked and Both 2x composites, elicit a substantially elastic response to perturbation. Notably, this distinction only emerges at mesoscopic scales in response to nonlinear forcing. Conversely, the crosslinking motif has little impact on the microscopic linear regime mechanics and steady-state filament mobility. These intriguing scale-dependent dynamics likely play a significant role in the ability of the composite cytoskeleton to mediate a vast array of different mechanical processes, and could be exploited to design multifunctional soft materials with scale-dependent mechanical properties. The custom-designed composites and measurement techniques demonstrated in this study further lay the groundwork for building complexity into in vitro cytoskeleton networks to determine how each component plays a role in cellular mechanics and in the design of novel biomimetic materials.Here, we characterize the mobility and mechanics – from submicron to mesoscopic scales – of custom-designed composites of actin and microtubules with distinct crosslinking patterns. We create composites in which actin is crosslinked (Supplementary Info


In addition, we make comparisons between the weighted Karcher mean and Lawson–Lim geometric mean for higher powers.This note aims to generalize the reverse weighted arithmetic–geometric mean inequality of  Let A and B, the operator geometric mean is defined by n-variable case for n-variable.Since the pioneering papers of Pusz and Woronowicz , Ando 11, and Kun positive definite matrices, and they showed that it satisfies ten important properties.In 2004, Ando et al. )LetThen the following inequality holds:U such thatDrury  recentlyLetThen, forIt is well known that For any positive integerletbe positive invertible operators on a Hilbert spacesuch thatforand some scalarsThen, forLet a map 2.3) in , we have.3 in , wean (see ). □Taking ent}p=2,  implies For any positive integerletbe positive invertible operators on a Hilbert spacesuch thatforand some scalarsThenNote that if equality  reduces equality .For any positive integerletbe positive invertible operators on a Hilbert spacesuch thatforand some scalarsThen, forandwhereLet a map (2.3) in , we havehand, by ,2.10\doPutting equality  implies Under the same conditions as in Theorem then, forWhen see that  is sharpsee that  for \docNext, we show the complements of the weighted geometric mean due to Lawson and Lim by virtue of the following lemma (see Corollary 2.12 in ) and we For any integerletbe positive invertible operators insuch thatfor alland some scalarsThenwhereis the generalized Kantorovich constant.By Corollary 2.6 in ,\documeFor any integerletbe positive invertible operators insuch thatfor alland some scalarsThenandBy the arithmetic–geometric mean inequality and , it follFor ows from  and the For ∞), from  and (2.1∞), from , we obtaIn the following remark, we present the case of Let For any integerletbe positive invertible operators insuch thatfor alland some scalarsThenfor allandandfor allandFor each equality  and (2.1equality  that2.1≤2, from  and \doc≥2, from  we haveIn the final section, we make comparisons between the weighted Karcher mean and the Lawson–Lim geometric mean for higher powers. This is a fascinating work because the order relation can be preserved between higher-power operators by the Kantorovich constant.LetandThenLetAandBbe positive invertible operators on a Hilbert spacesatisfyingandThenholds for anywhereis the generalized Kantorovich constant or the Ky Fan–Furuta constant.For any positive integerletbe positive invertible operators on a Hilbert spacesuch thatforand some scalarsThenandBy the Löewner–Heinz inequality and , we haveequality  follows equality  that\doWhen equality  reduces


Visual hallucinations are a common and often distressing feature of Parkinson’s disease; they are ephemeral and capricious, making them difficult to study but tend to be more prominent in dim illumination. Flickering stimuli can induce simple hallucinations even in healthy individuals. We tested a stroboscope and an equivalent full-screen flickering stimulus in 16 participants: 7 patients with Parkinson’s and habitual visual hallucinations, 6 Parkinson’s patients without hallucinations and 3 controls. Both flicker sources induced varied geometrical hallucinations in 4 participants (25%) and complex hallucinations in 1 but neither induced typical Parkinson’s-associated hallucinations. Visual hallucinations are a frequent and often distressing symptom of Parkinson’s disease (PD) affecting 30–70% of patients . The pheA significant impediment in studying PD hallucinations is their unpredictable occurrence. Visual hallucinations can be induced, even in healthy volunteers using a stroboscope, or by viewing a flickering stimulus . AlthougTwo stimuli were studied: a stroboscope  and a full-screen computer flicker stimulus . The strhttp://www.vislab.ucl.ac.uk/cogent_2000.php). The stimulus consisted of an alternating fully black and fully white screen at a frequency of 8 Hz; full screen presentation was chosen to achieve maximum contrast ); the stimulus was generated using MATLAB version R2014a and Cogent  . Assessmp = 0.443), disease duration (p = 0.191), MMSE (p = 0.327), MOCA (p = 0.172), visual acuity (p = 0.301), or contrast sensitivity (p = 0.138) but the two control patients were younger than the patients with PD (p < 0.001) Patients with hallucinations had higher UPDRS total score (p = 0.037), reflecting non-motor symptom burden in this population.The patients with and without hallucinations did not differ in age  only 16 consented to take part. Despite these concerns, on follow up communication, two weeks after participation, we found no adverse effects of the flickering stimuli.The demographics and clinical assessments in patients with PD in our cohort are seen in Fourteen of 16 participants (87.5%) were able to tolerate 10 cycles of each stimulus; the remaining two tested 5 cycles of each stimulus. The stroboscope induced visual hallucinations in only 4 of 16 participants; Two participants reported coloured hallucinations: one participant experienced moving blue dots, the other static neon pink and blue dots. The remaining two participants who experienced geometrical hallucinations with the stroboscope, reported white and black patterns; these also varied, including bars, squares and patterns reminiscent of “refractive diamonds”.The full screen flicker stimulus also induced hallucinations in 4 of 16 participants; two of whom had also experienced geometric hallucinations with the stroboscope. The phenotype of these was more consistent than the stroboscopic induced hallucinations, including mainly a black and white grid pattern and a “spinning tunnel” of white light. Only one participant experienced formed hallucinations which he described as “a set of squares arranged on top of each other with circles in the middle” which resembled a filling cabinet.No participants experienced typical formed hallucinations of people or animals that characterise PD-associated hallucinations .p = 0.247): geometrical hallucinations were experienced by 3 PD/VH patients (42.8%), 2 PD non VH (30%) and 1 control (33.3%). Of the 7 participants with PD who were habitual hallucinators, none experienced their habitual hallucinations or complex hallucinations with flicker. The one participant who experienced complex hallucinations with the flickering stimulus was not a habitual hallucinator and did not differ from the rest of the group in motor, visual or cognitive assessments.The rate of induced hallucinations did not differ between PD patients with and without hallucinations either on the stroboscope or the full screen flicker , light intensity decreases. A high light intensity may be crucial as the stroboscope is viewed with closed eyelids and to achieve adequate retina stimulation strong illumination of the eyelids is required. This was not an impediment in the full-screen flicker and indeed this stimulus was slightly more effective in inducing stereotypical geometrical hallucinations.It is also interesting to note that visual hallucinations tend to occur in low stimulus environments, and especially in people’s own homes . In thisWe studied the efficacy of flickering stimuli in a small cohort of patients with PD and controls. Although inferences are limited by the small number of participants, we found that less than 1 in 3 participants experienced flicker-induced hallucinations; these were almost uniformly geometrical in phenomenology and were not more prominently reported by those with habitual hallucinations. Further testing in a larger cohort, given the lack of signal in our study and the possible side effects from flicker exposure, such as migraine, would not be beneficial.Whilst our study does not provide mechanistic insights into visual hallucinations, our findings flickering stimuli, including the stroboscope are, not a reliable and predictable stress-test to induce visual hallucinations in PD.AZ is supported by an Alzheimer’s Research UK Clinical Research Fellowship (2018B-001). RSW is supported by a Wellcome Clinical Research Career Development Fellowship (201567/Z/16/Z).The authors have no conflict of interest to report.


Active colloids are a class of microparticles that ‘swim’ through fluids by breaking the symmetry of the force distribution on their surfaces. Our ability to direct these particles along complex trajectories in three-dimensional (3D) space requires strategies to encode the desired forces and torques at the single particle level. Here, we show that spherical colloids with metal patches of low symmetry self-propel along non-linear 3D trajectories when powered remotely by an alternating current (AC) electric field. In particular, particles with triangular patches of approximate mirror symmetry trace helical paths along the axis of the field. We demonstrate that the speed and shape of the particle’s trajectory can be tuned by the applied field strength and the patch geometry. We show that helical motion can enhance particle transport through porous materials with implications for the design of microrobots that can navigate complex environments. The development of functional microrobots calls for new strategies to design locomotion facilitating navigation through complex environments. Here, Lee et al. show how to realize and program helical motion in three dimensions using patchy microspheres under an alternating current electric field. At low Reynolds numbers, microorganisms and spermatozoa self-propel along helical paths by non-reciprocal motions of their chiral components such as flagella5. In these biological swimmers, helical motion facilitates chemotaxis6 whereby the rotational component enables scanning of three-dimensional (3D) space to determine the direction of an external stimulus, while the translational component drives migration toward the stimulus. The helical motions of flagellated microorganisms are known to enhance their motility4 and facilitate navigation through complex environments7. However, encoding similar helical motions in engineered colloids remains a challenge, largely due to limitations in synthesizing particles with the necessary symmetry, shape, and/or composition9.Helical motion is observed at all length scales, from the trajectory of subatomic particles in magnetic fields to the migration of interplanetary bodies in space17. For micron-scale particles, gravitational forces are often significant thereby confining the motions of self-propelled colloids to the two-dimensional environment above a planar substrate. By contrast, the propulsion of sub-micron particles is often overwhelmed by Brownian motion, which erases temporal correlations in particle orientation and position. The motion of colloids in 3D along prescribed trajectories requires propulsion mechanisms that compete favorably with both gravitational and thermal forces. In this context, alternating current (AC) electric fields provide an attractive route to power and orient particle motions by induced charge electrophoresis (ICEP) as directed by particle asymmetries22. While several studies have highlighted the role of shape25 and patchiness15 on directing particle motions, few experiments have shown how tailored asymmetries can guide complex motions in 3D28.Active colloids convert energy from their environment  into fluid flows that propel particle motions directed by asymmetries in particle shape and composition29. The details of particle motion such as the speed and radius of the trajectory can be tuned by changing the size and shape of the metal patch. Particles with triangular patches of approximate mirror symmetry perform helical motions of both right and left handedness, depending on their initial orientation in the field. We demonstrate that helical trajectories can provide a functional advantage to particles navigating through porous membranes as compared to linearly propelled particles. These results suggest strategies for designing microrobots capable of navigating structured environments such as those found in advanced materials, geological formations, and biological tissues17.Here, we show that asymmetric metal patches on the surface of spherical colloids can direct their motion along non-linear helical trajectories powered by AC-electric fields31. As detailed in the Methods, a concentrated dispersion of negatively charged microspheres is assembled into a close-packed monolayer on a glass substrate. The substrate is then transferred to a physical vapor deposition chamber, where a 10 nm layer of chromium followed by a 30 nm layer of gold is deposited onto the particles. The angle φ between the particle-coated substrate and the incident metal vapor is varied in the range 0° < φ < 20° −1, where Apatch is the patch area and a is the particle radius31. The metallodielectric particles are dispersed in deionized water and positioned between two coplanar electrodes  is applied, and the particle dynamics is monitored by an upright light microscope. Remarkably, we observe that particles with triangular metal patches perform steady helical motions along the axis of the field  and in the chirality of the trajectory (right- or left-handed) as discussed later  to the data to estimate the parameters R, Ω, and U  ≈ 0.5  increases as the cube of the particle radius a in quantitative agreement with the rotational diffusion time for a sphere, η is the viscosity of fluid, kB is the Boltzmann constant, and T is temperature  are capable of three qualitatively distinct dynamical behaviors, one of which corresponds to the helical motions observed in experiment.Application of an AC-electric field to the aqueous dispersion induces an asymmetric fluid-flow around each metallodielectric particle that propels it though the fluid. This phenomenon, known as induced charge electrophoresis (ICEP)θ  as confirmed by experiments on passive (non-patchy) particles , such that transient effects in double-layer polarization (neglected in our model) may contribute to ICEP motions. Also absent from the present model are effects due to electrostatic and hydrodynamic interactions with the walls of the chamber as well as Brownian motion of the particles  deviations from mirror symmetry in the patch geometry, 2) spatial gradients in the applied field, 3) gravitational forces and torques, 4) electro-osmotic flows within the chamber, 5) transient effects during particle polarization, (6) interactions with system boundaries, and (7) Brownian motion. The fabricated particles with triangular patches do not have perfect mirror symmetry and are therefore chiral; however, such imperfections cannot be responsible for producing both right- and left-handed helices in a single particle Fig. . Spatial electro- transien spatial  deviatio gravitatφ = 10°), rotation of the crystal monolayer can transform the triangular patches (α = 0°) described above into curved rectangular patches for α = 30°36. Particles with such asymmetric patches are observed to move along skewed helical trajectories on axes oblique to that of the applied field  is the number of particles in compartment A at time t, and ntot is the total number of particles. The number ntot is determined experimentally by fluorescence imaging of the bottom plane of compartment B containing all the particles at time t = 0 min . The number nA(t) is estimated by changing the focal plane to the bottom of compartment A and monitoring the increase in particle number with time. The corresponding coefficient KPC(t) increases from zero at the start of the experiment (since nA(0) = 0) as particles tunnel from compartment B to A.Complex particle trajectories may be useful in enhancing the transport of microrobots through structured media and crowded environments. To demonstrate this possibility, we investigate how the motion of microparticles along helical trajectories can influence their transport through a crosslinked cellulose membrane Fig. . A chambE = 2 V cm−1 is selected to drive motion with a linear speed of 5 µm s−1, comparable to that of helical ICEP motions. For both particle types, the partition coefficient KPC(t) increases in time, approaching a constant value after ca. 15 min  moving by electrophoresis along linear trajectories in a direct current (DC)-electric field directed from chamber A to B Fig. . A DC fimin Fig. . Importaa collides normal to the wall, it samples a relatively small area πa2 and stops. By contrast a helically propelled particle continues to move along a circular orbit parallel to the wall thereby sampling a larger area of ~4πaR and increasing its chances of finding the pore  were purchased from Magsphere Inc. (CA) and Molecular Probes (OR). The particles were pre-functionalized with negatively charged carboxylate groups with a measured zeta potential of −40 mV  at pH 7. Prior to use, the particles were washed three times with deionized water (DI water) and concentrated to 10% by weight. Particles monolayers were deposited onto clean glass slides by the convective assembly method30 and coated by a 10 nm chromium layer (deposition rate: 0.5 nm s−1) followed by a 30 nm gold layer (deposition rate: 0.10 nm s−1) under vacuum (1 × 10−6 Torr) in a custom-built thermal evaporator. The metal-coated particles were transferred into a plastic vial by a spatula and re-dispersed in DI water (concentration ~0.01 wt %) by gentle sonication before the experiments.Aqueous suspensions of surfactant-free polystyrene latex spheres (−1) arranged parallel to one another and perpendicular to the direction of gravity .The electrodes were prepared by gold deposition on microscope glass slides  with a 2 mm gap. The electrodes were soaked in Nochromix solution for 24 h and rinsed thoroughly with DI water before the experiments. Teflon masking tape was used to form a 2 mm × 2 mm × 100 μm chamber between the gold electrodes. The patchy particle suspension was transferred to the chamber and capped by a cover glass to create a Hele-Shaw cell type configuration. The tunneling experiments shown in Fig. ity Fig. . The thiTo characterize the patch geometry, the metallodielectric particles were sputter coated with platinum and imaged by backscattered scanning electron microscopy . Particle dynamics in the applied field were captured by a Leica DM6 B optical microscope equipped with a Leica DFC9000 GTC camera.37. For a given video, each frame was converted to a binary image that distinguished the particle from its surroundings. For each frame, the particle position  in the imaging plane was then computed as the centroid of the particle region using the “Centroid” feature in ImageJ’s “Analyze Particles” menu. The helix radius, angular velocity, and linear velocity were estimated from these data by least squares regression using the kinematic model (1).Particle motions were analyzed using the ImageJ softwareSupplementary InformationPeer Review FileDescription of Additional Supplementary FilesSupplementary Movie 1Supplementary Movie 2Supplementary Movie 3Supplementary Movie 4Supplementary Movie 5


Cells need to preserve genome integrity despite varying cellular and physical states. p53, the guardian of the genome, plays a crucial role in the cellular response to DNA damage by triggering cell cycle arrest, apoptosis or senescence. Mutations in p53 or alterations in its regulatory network are major driving forces in tumorigenesis. As multiple studies indicate beneficial effects for hyperthermic treatments during radiation- or chemotherapy of human cancers, we aimed to understand how p53 dynamics after genotoxic stress are modulated by changes in temperature across a physiological relevant range. To this end, we employed a combination of time-resolved live-cell microscopy and computational analysis techniques to characterise the p53 response in thousands of individual cells. Our results demonstrate that p53 dynamics upon ionizing radiation are temperature dependent. In the range of 33 °C to 39 °C, pulsatile p53 dynamics are modulated in their frequency. Above 40 °C, which corresponds to mild hyperthermia in a clinical setting, we observed a reversible phase transition towards sustained hyperaccumulation of p53 disrupting its canonical response to DNA double strand breaks. Moreover, we provide evidence that mild hyperthermia alone is sufficient to induce a p53 response in the absence of genotoxic stress. These insights highlight how the p53-mediated DNA damage response is affected by alterations in the physical state of a cell and how this can be exploited by appropriate timing of combination therapies to increase the efficiency of cancer treatments. To determine to which extent temperature affects the cellular capacity to preserve genome integrity, we focused on the molecular network controlling the tumour suppressor p53.Preserving genome integrity is a central function of all metazoan cells. Therefore, complex mechanisms evolved to detect and respond to DNA damage. However, the underlying molecular networks are subjected to varying physical and cellular states that limit their functionality. Among the most basic physical properties that influence molecular functions is temperature. Previous studied revealed that some cellular networks such as circadian clocks are compensated towards changes in temperatures4. In unstressed cells, p53 protein is kept at low levels by Mdm2 - mediated ubiquitination and subsequent proteasomal degradation5. Posttranslational modifications by DNA damage-activated kinases such as ATM and ATR disrupt this interaction and lead to p53 stabilization and accumulation in the nucleus. P53-mediated signalling is a highly dynamic process that integrates information from various sources to regulate the cellular stress response7. Therefore, the temporal pattern of p53 accumulation correlates with the type and quantity of the stimulus8. Ionizing radiation (IR) induces uniform pulses of p53 accumulation with comparable amplitude and duration10. The number of pulses is positively correlated with the damage dose11. These pulsatile p53 dynamics are triggered by negative feedback loops within the p53 signalling network, mainly through the ubiquitin ligases Mdm2 and the phosphatase PPM1D/Wip113. In contrast, p53 exhibits only a single sustained pulse with dose-dependent amplitude and duration in response to ultraviolet (UV) radiation8. Using pharmacological and genetic perturbation, we have previously shown that p53 dynamics contribute to cell fate choices post damage15. In most human cancers, p53 is inactivated either directly by mutations that compromise the stability of the protein or its ability to bind DNA, or indirectly by amplifications of its negative regulators such as Mdm2 or Wip116. Inactivation of p53 correlates with increased resistance to therapy and poor survival17.The transcription factor p53 is activated by cellular stresses such as DNA damage and activates the expression of downstream genes that mediate cellular responses ranging from transient cell cycle arrest and damage repair to terminal cell fates such as senescence or apoptosis19. Other factors such as age, time of day, sex, reproductive status and activity level lead to deviating body temperatures as well21. Moreover, during physical exertion, the physiological range of core temperatures extends beyond 40 °C22. Even higher core temperatures are observed in pathological settings such as vascular disease where the transport of blood and heat is perturbed, or during fever, which is associated with several different diseases including infections, autoimmune diseases23 and cancer24.As homoeothermic organisms, humans maintain a stable core body temperature of about 37 °C at rest. However, body temperature at the periphery and specifically at the extremities drops significantly to 33 °C or lower, depending on ambient temperatures25. On the cellular level, temperature changes affect metabolism, protein synthesis and cell cycle regulation26. Hyperthermia, in particular, causes membrane, DNA and protein damage and influences cell fate by triggering cell cycle arrest, senescence, apoptosis, or necrotic cell death31. On the organismic level, studies indicate that deviations in core temperature of more than 4 °C can result in physiological impairments and fatality32.Changes in temperature affect organisms on multiple levels. Its direct impact on enzyme-catalysed reactions is characterized by the Arrhenius equation, which describes that reaction velocities double when temperature increases by 10 °C until they abruptly decline due to protein denaturation33. It has been observed that hyperthermia leads to activation of human ATR inducing cell-cycle arrest at the G2/M transition34. Furthermore, activated ATR may help to stabilize arrested replication forks preventing accumulation of chromosomal lesions35. Similarly, hyperthermia induces auto-phosphorylation and activation of ATM36, which is however delayed by 1–2 hours compared to ATR activation34. Interestingly, other components of the DDR are inhibited at high temperatures: the Mre11-Rad50-Nbs1 (MRN) complex, which is essential for ATM activation by DNA double strand breaks (DSBs), translocates from the nucleus to the cytosol at high temperatures37 and the binding of 53BP1 to chromatin around DSBs is prevented38, restricting the capacity of ATM to sense this form of DNA damage.Previous studies investigating the effect of temperature changes on the DNA damage response (DDR) mainly focused on the damage-activated kinases ATM and ATR and their downstream effectors Chk1 and Chk2, which orchestrate a network of cellular processes to maintain genomic integrity39. Several randomized trials have demonstrated the benefits of hyperthermia (40–42 °C for at least 1 hour) combined with radiotherapy or chemotherapy with regard to local tumour control and survival42. Hyperthermia also amplifies the therapeutic effect of chemotherapy46. Pre-clinical and clinical studies suggest that hyperthermia is effective both in cancers with wild-type p53 and those without active p53. To our knowledge, the p53 status of cancers being treated with hyperthermia is not routinely determined in the clinic48. Molecularly, it was shown that cancer cells get arrested in different stages of the cell cycle (S/G2 or G2/M) and lose the ability to repair chromosomal lesions, which promotes cell death51.Clinically, the application of exogenous heat in combination with canonical anti-cancer treatments is an established therapeutic strategy against various human tumours54. HSF1 has been reported to interact at different levels with the p53 network by supporting post-translational modifications and acting as a transcriptional co-factor55. Furthermore, interaction of the HSF1 target Hsp90 with p53 prevents Mdm2 mediated ubiquitination56 and modulates its binding to the CDKN1A/p21 promotor55. Additional heat shock proteins such as Hsp70 and Hsp40 are as well capable of stabilizing p53-DNA complexes58.In response to temperature changes, a family of heat shock factors (HSF1-4) initiates the expression of heat shock proteins (HSP). The most well-known family member is HSF1, which is constitutively expressed and regulates the expression of HSP as well as other genes related to cell signalling, cell integrity, development, growth, fertility, senescence and apoptosis59 and followed the dynamics of p53 accumulation after ionizing radiation at the single cell level using time-resolved live-cell microscopy. Computer-aided image and data analysis indicated that the dynamic features of the pulsatile p53 response vary with temperature within the range of 33 °C to 39 °C. Above 40 °C, we observed a reversible phase transition to fundamentally different p53 accumulation dynamics, which may provide new insights how hyperthermia can be used to improve cancer therapy.We now aimed to systematically study how temperature affects p53 signalling. Is the molecular network controlling activation of the main human tumour suppressor compensated against changes in temperature or does its response to DNA damage dependent on the physical environment? To address this question, we employed an established fluorescent reporter cell line59. We irradiated cells with 10 Gy X-ray (250 kV) and monitored their p53 protein levels for 24 h by time-resolved live-cell microscopy. As previously described, p53 protein accumulated in a pulsatile manner upon damage induction . Trajectories of individual cells confirmed uniform pulsatile p53 dynamics upon damage induction  Fig. 59. We irion Fig. 8. Using ion Fig.  that werion Fig. . This leion Fig. 60.FigureTo investigate the influence of varying temperature on the p53 response to genotoxic stress, we equilibrated cells to temperatures ranging from 33 °C to 41 °C for 14 h and performed time-lapse microscopy of untreated and irradiated cells at the respective temperatures Fig. . To comp61. Interestingly, MCF10A cells tended to show sustained p53 accumulation already at 39 °C.When we analysed how untreated cells proliferated at different temperatures, we observed decreased proliferation rates below and above normothermia as expected Fig. . At 41 °As we were surprised by the strong response of untreated cells at 41 °C despite equilibrating cells to the higher temperature, we compared the p53 response in cells pre-equilibrated to 41 °C with cells that were acutely shifted to the higher temperature at the beginning of the experiment. Fig. . In pre-To further compare the strength of the p53 response at different temperatures and treatment conditions, we quantified the integrated nuclear level of p53 for the observation period. Over the temperature range from 33 °C to 39 °C, cumulative p53 levels remained similar in undamaged cells and upon irradiation Fig. . At 41 °62 to estimate the pitch of p53 pulses in single cell trajectories. The positions of the first 3 pulses varied substantially between the different temperatures res Fig. . At 33 °lse Fig. . Furtherlse Fig. . An altelse Fig. . In contlse Fig. , right. 10 temperature coefficient1, which reflects the rate of change of biological systems when temperature is raised by 10 °C assuming that reaction rates depend exponentially on temperature. For the p53 system, we determined a Q10 coefficient of 1.53 ± 0.24 based on the position of the 3rd pitch, which is on the lower end of coefficients usually observed in biology (Q10 ~ 2-3)63.A good measure to quantify temperature sensitivity is the Q64 inspired by the Smith-Waterman algorithm65 to characterized individual p53 pulses , XPC (DNA damage repair) and BAX (apoptosis), and measured corresponding RNA levels at different time points and temperatures in untreated and irradiated cells by qPCR3. For p21, GADD45 and, to a lesser extent, XPC, we observed increased expression at lower temperatures (35 °C) when p53 showed longer and less frequent accumulation pulses  supplemented with 10% fetal calf serum  as well as penicillin and streptomycin. The selective antibiotics G418  and hygromycin  were added to maintain transgene expression.The human lung carcinoma cell line A549 expressing p53-mVenus has been described before61. In brief, the coding sequence for fluorescent proteins was inserted in the endogenous gene loci using Cas9-mediated genome engineering. The chromatin associated protein Cbx5 was tagged with mCerulean to serve as a nuclear marker. Cells were maintained in DMEM/F12 with 5% horse serum, 20 ng/ml EGF, 0.5 mg/ml hydrocortisone, 100 mg/ml cholera toxin and 10 mg/ml insulin. All media contained 2 mM Glutamax, 100 U/ml penicillin and 100 mg/ml streptomycin. All cell lines were cultures at 37 °C with 5% CO2 at saturated humidity if not indicated otherwise.The female human non-transformed breast epithelial cell line MCF10A expressing p53-mVenus and p21-mCherry has been described before5 cells in ibiTreat polymer-bottom plates  2 d before experiments. When indicated, cells where equilibrated at the given temperature for 14 h. The day of the experiment, medium was replaced by FluoroBrite medium  lacking phenol red and riboflavin. Cells were treated with X-ray irradiation at a dose rate of 1 Gy/26 s . We imaged cells on a Nikon Ti inverted fluorescence microscope  with a Nikon DS‐Qi2 camera and a 20 × Plan Apo objective  using appropriate filter sets . The microscope was enclosed with an incubation chamber set to temperatures in the range from 33 °C to 41 °C as indicated. The atmosphere was maintained at 5% CO2 concentration and saturated humidity. Cells were imaged every 15 min for the duration of the experiment using Nikon Elements software59.We seeded 1 × 1080 and the CellProfiler project81. In brief, we applied flat field correction and background subtraction to raw images before segmenting individual nuclei from nuclear marker images using thresholding and seeded watershed algorithms. Segmented cells were then assigned to corresponding cells in following images using a greedy match algorithm. Only cells tracked from the first to last time point were considered. For the analyses we tracked cells in forward direction from the first to the last time point. Upon division, we followed the daughter cell closest to the last position of the mother and merged tracks from mothers and offspring. Using binary masks from nuclear marker images, we quantified mean nuclear fluorescence intensity in the p53/mVenus channel.Cells were tracked throughout the duration of the experiment using custom‐written MATLAB (MathWorks) scripts based on code developed by the Alon laboratory82.Before analysis, we pre-processed our data with custom made filters to remove technical noise and signals from biological events unrelated to the induced response. To remove spikes and sustained intensity shifts caused by segmentation and tracking errors, we identified those features based on cell specific thresholds defined by the standard deviation of the processed trajectory and replaced them by linear interpolation. Spikes and sustained shifts were defined either by a decrease followed by an increase or an increase followed by a decrease both greater than the standard deviation of the processed trajectory. Removal of spikes and sustained shifts was done iteratively. This led to an increased signal-to-noise ratio due to local smoothing, emphasizing slower changing biological responses. As the nuclear envelop breaks down during mitosis and morphological changes lead to increased auto-fluorescence, we disregarded signals measured during cell division and removed them from the trajectories by interpolation. To identify cell division, we normalized for each cell the nuclear area and the integrated fluorescence intensity of the nuclear marker to their respective means, smoothed them by the approach described above and combined the two trajectories by averaging. We then applied a 1D Prewitt filter (length 75 minutes) to the combined trajectory to amplify signal discontinuities that correspond to cell divisions. Cell divisions events corresponded to a value of the Prewitt filtered trajectory exceeding a manually selected threshold based on several hundred visually detected cell divisionsCombining different time-lapse microscopy experiments is non-trivial due to multiple sources of variability that result in different distributions of the fluorescence intensity measured even among identical experimental settings. These comprise biological sources such as different passage numbers of cell lines uses as well as technical sources such as different light sources. To overcome the limitations of comparing different experiments, we propose a method that aims to reduce the inter-experiment deviation by fitting all experiments to one reference experiment. Our approach is based on the central assumption that we have a constant set of measures for all experiments with comparable measurement distributions. In this case, all deviations of the measure can be directly related to other sources of non-biological heterogeneity in data acquisition. In our experimental setup, we have for each experiment cells incubated at 37 °C with no radiation applied at the first time point, for which we assumed similar distributions. In the following example, we also assumed equal cell numbers in all experiments. This was not the case in our data sets, which required us to employ additional interpolation or extrapolation steps.ijk be the set of our experimental measures, with i the experiment, j the time point and a cell k. We assume that all experiments have the same experimental condition at time point j = 1 and we set one experiment x as the reference. To fit another experiment y to the experiment x we use the following computation. The central part is the estimation of the coefficients weight. We start by computing the coefficient by weight = sort)./sort). In the next steps we use the weight to fit the experiment y onto x by applying the coefficient to each time point.Let EThe idea is that the non-biological error is constant over time and that we can estimate the error at the time point where we can assume identical conditions. In Supplement Fig. et al. in 197462 and is used for real time applications as it involves less computational effort83. We used window lengths between 4.5 h - 7 h and assumed a pitch period lower bound of 2 h. For robustness we computed the different pitch positions for the different window sizes and used the mean of overall window sizes for a certain pitch position.Among the different pitch detection algorithms AMDF is the most commonly used. AMDF, a variation on autocorrelation analysis, was proposed by Ross The aim of feature detection is the identification of patterns in time series data. In general, we aim to find pulses in our data. However, our approach is not limited in the kind of pattern we like to identify in the data, which can have any more or less complicated form.65 like version of the dynamic time warping64 approach. In the following we will describe both steps in detail.The proposed method works in a two-step approach. First we normalize each trajectory using a band based on local minima and maxima  at the initiation step. After filling the scoring matrix, we find the beginnings and ends of pattern occurrences by backtracking from the local minima in the last column. To improve the result, we afterwards filter overlapping occurrences.In the following feature detection step, we apply an adjusted dynamic time warping approach to find appearances of a symmetric peak pattern in the range 0–1 of length 4 h. In other applications of the method, this pattern can have a completely different shape appropriate for the specific demands. To find the defined pattern, first we initiated the scoring matrix as described in the literatureHaving the start and the end points of pulses we can straightforward extract several features  on the data matrix of the sorted time series data. On the filtered result we applied an additional median filter (31 × 31). We used the difference between the two filtered data matrices to enhance the pulses in the data as shown in Fig. ; p21 forward, TGG ACC TGT CAC TGT CTT GT and p21 reverse, TCC TGT GGG CGG ATT AG.We extracted mRNA using High Pure RNA Isolation kits . cDNA was generated using ProtoScript reverse transcriptase  and oligo-dT primers. Quantitative PCR was performed in triplicate using SYBR Green reagent  on a StepOnePlus PCR machine . Primer sequences were as follows: BAX forward, CTG ACG GCA ACT TCA ACT GG; BAX reverse, GAT CAG TTC CGG CAC CTT GG; GADD45 forward, GCA ATA TGA CTT TGG AGG AAT TCT C; GADD45 reverse, TGA CTC AGG GCT TTG CTG; XPC forward, GTC TCT ACA GCC AAT TCC TCT G; XPC reverse, CCT TTG CTG GTC TTT GGT TTGCells were plated in 6 cm dishes two days before experiments. Cells were exposed to 10 Gy X-ray radiation, harvested at indicated time points by trypsination, washed with 1xPBS, fixed with ice-cold 80% Ethanol/20% 1xPBS and stored at −20 °C until all samples were collected. For flow cytometry analysis, cells were washed with 1xPBS, stained with 25 mg/ml PI in 0.1% Triton 1xPBS with 0.2 mg/ml RNase A and analyzed on a Cytomics FC500 cytometer (Beckman Coulter). Cell cycle phases were determined based on the DNA content in FlowJo software .Supplementary Movie S1.Supplementary Movie S2.Supplementary Movie S3.Supplementary Movie S4.Supplementary Movie S5.Supplementary Movie S6.Supplementary Movie S7.Supplementary Movie S8.Supplementary Movie S9.Supplementary Movie S10.Supplementary Informatiton.


Cancer, disease and trauma to the larynx and their treatment can lead to permanent loss of structures critical to voice, breathing and swallowing. Engineered partial or total laryngeal replacements would need to match the ambitious specifications of replicating functionality, outer biocompatibility, and permissiveness for an inner mucosal lining. Here we present porous polyhedral oligomeric silsesquioxane-poly(carbonate urea) urethane (POSS-PCUU) as a potential scaffold for engineering laryngeal tissue. Specifically, we employ a precipitation and porogen leaching technique for manufacturing the polymer. The polymer is chemically consistent across all sample types and produces a foam-like scaffold with two distinct topographies and an internal structure composed of nano- and micro-pores. While the highly porous internal structure of the scaffold contributes to the complex tensile behaviour of the polymer, the surface of the scaffold remains largely non-porous. The low number of pores minimise access for cells, although primary fibroblasts and epithelial cells do attach and proliferate on the polymer surface. Our data show that with a change in manufacturing protocol to produce porous polymer surfaces, POSS-PCUU may be a potential candidate for overcoming some of the limitations associated with laryngeal reconstruction and regeneration. The manufacture and characterisation of porous silsesquioxane scaffolds for laryngeal reconstruction. •A porous polymer was created as a scaffold for laryngeal reconstruction.•Porous POSS-PCUU exhibited good tensile properties but limited surface porosity.•Primary fibroblasts and epithelial cells attach to POSS-PCUU.•POSS-PCUU may be used for larynx reconstruction by optimising manufacturing conditions. DepeThe human larynx sits at the crossroads of three critical functions: eating, breathing and talking. It has six linked cartilages, a finely controlled array of small muscles and delicate neurovascular supply . MicroscTissue engineering combines fundamental engineering theory with biological systems to create morphological, chemical and functional mimics of healthy tissue that allow better integration between the native and synthetic tissues , 17. ThiSuitable materials can be found from natural and synthetic sources , 25 and Polyhedral oligomeric silsesquioxanes (POSS) are a candidate class of materials with cage-like structures composed of silicone and oxygen. The external surface of the POSS nanocage is composed of easily modifiable organic moieties, usually hydrocarbons . Many rePOSS-PCUU has been shown to have suitable mechanical properties to retain the formed geometry in vivo . Here, w22.12.1.1trans-cyclohexanechloroydrinisobutyl-silsesquioxane  and polycarbonate polyol (2000 MW) to 130 °C. After cooling the solution to 80 °C a prepolymer solution was formed by adding flake 4,40 - methylene bis(phenyl isocyanate) and heating the mixture at 70–80 °C for 120 min. To the prepolymer solution, dimethylacetamide (DMAC) was added dropwise and cooled to 35 °C. A mixture of ethylenediamine in DMAC was then added dropwise to extend the polymer chain and form POSS-PCUU. The resulting solution was stored at room temperature until use.All chemicals for polyhedral oligomeric silsesquioxane poly(carbonate-urea) urethane (POSS-PCUU) manufacture were purchased from Sigma Aldrich Ltd. (UK) unless stated otherwise. Briefly a polyol blend was formed by heating a mixture of 2.1.210, x50, x90, Sauter Mean Diameter (SMD), Volume Mean Diameter (VMD), aspect ratio, and sphericity.Particle size distributions were measured using a QICPIC powder size analyzer, operated using VIBRI and GRADIS units . Videos were analysed frame-by-frame to yield density distributions (q3) from which the following statistical parameters were calculated according to well established procedures : x10, x52.1.33) particles sieved at 25-53 μm . Tween 20 was also added at 2% (w/w). The ratio of NaHCO3 to POSS-PCUU for each sample is shown in Scaffold solutions were created by mixing POSS-PCUU with sodium hydrogen carbonate . For polymer characterisation studies the scaffold was first washed overnight in DI H2O while for cellular studies the samples were autoclaved at 121 °C for 20 mins in DI H2O before use . For the purpose of this study we refer to precipitated polymer as 'scaffold'.The solution was mixed using a centrifugal mixer  and any air bubbles removed through a ‘degassing’ cycle (1500 rpm) on the mixer. The mixed solution was then poured onto a clean glass mould measuring 148 × 210 mm which was surrounded by a ~300 μm thick autoclave tape perimeter. To precipitate the polymer and allow NaHCO DI H2O; . The DI 2.22.2.1−1 wavenumber range at a mean spectral resolution of 3 cm−1.The surface chemical composition of the precipitated POSS-PCUU polymers was evaluated using a confocal Raman microscope  with a 0.3 W single frequency 785 nm diode laser . Data were collected via an Acton SP2300 triple grating monochromator/spectrograph  over a 200–3000 cm2.2.2−9 mbar. The C 1s (BE = 285 eV), N 1s (BE = 400 eV) and O 1s (BE = 531 eV) photoelectron peaks were analysed in detail. Three non-overlapping regions were measured for each sample. Data were fitted using the Gauss-Lorentz function, and the Shirley method was used for background subtraction. CasaXPS software was used for data processing.The composition and chemical bonds of the polymer surface were investigated using X-ray photoelectron spectroscopy (XPS). Analysis was performed using a K-alpha X-ray Photoelectron Spectrometer , operating a microfused, monochromated Al Kα X-ray source with a spot size of 400 μm and a power of 36 W. The step size in order to obtain individual peaks was 0.1 eV, whereas 1 eV was used for the acquisition of a full spectrum over the complete range of binding energies (BEs). The vacuum pressure in the analysis chamber was <102.2.32 and the samples were critical point dried at 1040 psi and 32 °C in a critical point dryer . Dried specimens were cut using a scalpel to show surface detail as well as the cross-sections. Once mounted onto stubs the samples were sputter coated with 15 nm of gold . Micrographs of polymer structure were captured at an accelerating voltage of 5 kV and a working distance of 8 mm.The microstructure of precipitated POSS-PCUU polymer samples was evaluated by field emission scanning electron microscopy . The samples were first dehydrated in graded ethanol 20%, 30%, 50%, 70%, 90% and 100% v/v ethanol in water for half an hour each. The ethanol was then exchanged for liquid CO2.2.4Profilometry was employed to evaluate the topography and roughness of polymer surfaces. Measurements were performed using a DCM3D microscope , using a white light source. Samples were imaged using a 20× objective lens, which corresponded to an analysis window of dimensions 637 μm × 477 μm. Scanning Probe Image Processor software  was employed for the analysis of acquired images, yielding the average roughness, Sa, as a measure of the surface roughness. Each value presented is the mean of a minimum of five measurements at separate locations.2.2.52O as the analyte. Samples were critical point dried prior to analysis, as outlined earlier. Droplets of volume 5 μL were deposited onto the surface through a flat-ended needle. All data were collected at temperatures in the range 20–22 °C and relative humidity in the range 40–60%.The wetting behaviour of polymer surfaces was assessed using a DSA 100 Drop Shape Analyzer , employing DI H2.2.6The true density of POSS-PCUU specimens were determined using helium pycnometry. Samples were first dried using the critical point drying method outlined earlier. Sample masses were then measured using a balance accurate to ±0.1 mg . Sample volumes were measured using a Helium Pycnometer , employing 20 measurements per sample; the sample chamber was allowed to equilibrate at 134 kPa for each measurement cycle. Hence, the true density could be calculated.2.2.7Samples were dehydrated and critical point dried as outlined earlier. POSS-PCUU porosity and pore size distribution were measured by adding the sample to a glass penetrometer , evacuating air from the penetrometer and sample, then intruding mercury under controlled pressure. A pressure range of 3 kPa–207 MPa was employed . The Washburn equation was used to determine the pore size distribution for each sample. The bulk density of the sample was estimated using the volume excluded within the penetrometer at the lowest intrusion pressure.2.2.8For tensile tests polymer sheets were cut into dumbbells with a 20 mm gauge length and 4 mm width using a Trotec Speedy 100R laser cutter  at 10 W, 0.6 V and a pulse rate of 1 kHz.2.2.9The tensile strength of dumbbell-shaped polymers (n = 6 per sample type) was measured using an Instron 5565 mechanical tester  at a rate of 50 mm/min. For each dumbbell tested the thickness was separately measured and recorded.2.32.3.1Primary porcine fibroblasts (FB) and epithelial cells (EC) were donated by Mark Lowdell, University College London. For cell culture studies on POSS-PCUU the polymer was cut into 7 mm circles using the laser cutting method outlined in 4 FB and 1.14 × 105 EC per scaffold in M-Greens.At 70%–80% confluency cells were washed with PBS and the FB feeder layer dissociated using 5 mL ethylenediaminetetraacetic acid  for 5 mins at 37 °C. The feeder layer was then removed and 6 mL TrypLE was added to digest the EC for 10 mins at 37 °C. Digested cells were diluted with equal volume modified Greens Medium , 110 mL Ham's F12 Nutrient Mixture , 50 mL foetal bovine serum , 0.4 μg/mL hydrocortisone , 10 μg/mL human recombinant epidermal growth factor , 5 μg/mL insulin , 250 μg isoproterenol , 1% Anti:Anti, 250 μg ciprofloxacin and 25 μg gentamycin and then centrifuged at 300 g for 5 mins ) before being resuspended in M-Greens containing 10 mM ROCK inhibitor Y-27632 . FB were digested with 5 mL TrypLE alone and resuspended in Dulbecco's Modified Eagle Medium (S-DMEM) supplemented with 10% v/v FBS and 1% v/v non-essential amino acid solution . Both FB and EC were used at passage 3 and 8 for FB and passage 3 for EC. The digested cells were seeded onto the polymer scaffolds at a density of 3.78 × 102.3.2For histology the samples were fixed in 10% formal saline , 0.9 g Sodium chloride and 90 mL distilled water) for a minimum of 7 h prior to processing. Samples were then dehydrated through an alcohol gradient , 95% IMS, 70% IMS, Acquascience, UK), followed by chloroform clearance on a Leica Peloris II tissue processing machine  and incubation in molten (>60 °C) paraffin wax  for 1 h prior to embedding using a Sakura Tissue-Tek tissue embedding machine . Each sample disc was bisected, with one half embedded in a vertical orientation on the cut surface, and the other half embedded horizontally. Sections were cut on a Thermo Scientific HM340E manual rotary microtome  at a section thickness of 3 μm, using Feather S35 microtome blades  before being mounted on Leica Xtra Adhesive slides  and oven dried at 70 °C for 60 min.2.3.3Sections were heated for 60 mins at 70 °C prior to staining with haematoxylin and eosin (H&E) using a Leica XL automated stainer with a Leica CV5030 automated coverslipper . The staining protocol used included 2 Xylene  dewaxing steps (2 mins each), 3 Xylene clearance steps in IMS (2 mins each) followed by staining in Harris Haematoxylin , washing the section, immersion in 1% hydrochloric acid in 50% IMS (10 s), wash 5 min), Eosin , 3 dehydration steps in IMS (2 mins each), 2 alcohol clearance steps in Xylene (2 mins each) before mounting in Pertex mountant  and covering with a coverslip.2.4Data are presented as “mean ± standard error of the mean”. Significant differences in the mean values between groups were determined by ANOVA  with post-hoc Tukey-Kramer HSD (Honestly Significant Difference) test. The significance level was set at p < 0.05.33.1The formation of solid uncontaminated POSS-PCUU was confirmed by Raman spectroscopy, specifically through the presence of expected bonds in accordance with the chemical structure A and S3.3 content in these samples varies greatly from 1% and 5% w/w (for samples 2 and 3) and 20% and 50% w/w (for samples 5 and 8). No immediate trend in PAI surface roughness and sample composition is apparent. Furthermore, while there was no clear correlation between surface roughness and sample drying technique  critical point drying was found to retain the planar sheet-like sample morphology without distorting the shape of the polymer. The surface morphology did not affect the overall water wetting behaviour of the material which was similar across sample types  surface had a smooth appearance when imaged using SEM A while t3.23; this inconsistency suggests that the incorporation of closed pores is a possible outcome of the manufacture process  had the greatest variation in porosity from both calculated and measured porosities. This indicates heterogeneity in the manufacturing process. As there is no NaHCO3 present in these samples, these data could allude to an effect of the mixing process; possibly an inefficient ‘degassing’ stage post-mixing.The true density of sample types 1–9 was in the range 1.25–1.60 g/cm process A. Sample3 concentration was increased the peak pore sizes also increased from <10 μm (samples 1–3) to approx. 20–40 μm (samples 4–7) to approx. 30–50 μm (sample 8), other than where large particle size was deliberately used (sample 9); here the majority of the pores lay between 50 and 90 μm , by day three it was evident that as the NaHCOncreased A–C; partwas used D. Cell dwas used A–B with ncreased C until increased D. Both Fncreased E–H. Histeased (3 I, the maeased (3 I and L weased (3 J and K.F43 to the polymer solution before precipitation and that the resulting scaffold contains a range of topographical features depending upon whether the interface is with air or the glass in which it was moulded. This causes a change in the material's surface morphology and roughness. Meanwhile, the internal porous structure affects the scaffold's behaviour during tensile extension. Both of these properties are associated with changes in fibroblast and epithelial cell attachment and proliferation on the scaffold.We explored whether POSS-PCUU possesses some of the characteristics ideally required for the demanding internal and external specifications of a laryngeal structural replacement. We demonstrated that porous POSS-PCUU can be formed by introducing NaHCO3 to form a sponge-like scaffold through the well-established particulate leaching method [3 dissolution within the polymer is a much slower, diffusion-governed process [co-hexafluoropropylene [3, we also note that they do not occur on the PGI in our studies. We postulate that the glass mould used in our manufacturing method presents a barrier, such that water molecules do not approach the PGI from below, preventing the formation of pores via this process. We also note that ‘protuberances’ are visible below the PAI membrane. These protuberances may be caused by a rapid thickening of the polymer surface, creating a membrane [3 under the membrane. A similar effect in a study by Wongchitphimon et al. [The formation of POSS-PCUU scaffold is a two-part process: the mixing and exchange of DMAC with water causing the polymer to precipitate out of solution and the dissolution of NaHCOg method . As withg method , and so g method , 61, whi process . We furt process , turbule process , 64. Suc process , polyeth process  and polyropylene . While wmembrane  above thn et al.  was attr3 particles [3 concentration was increased for each polymer during the manufacturing process, the pores formed from porogen leaching are likely to occupy closer spaces until some merge to form larger pores. Whilst the pore volume is expected to correspond approximately to porogen volume, this was not always the case as imaging of the internal structure shows a heterogeneity in pore size. We posit that some of the particles, as the porogen concentration is increased, begin to adhere to one another before the dissolution process is complete. This is evidenced by our analysis of particle size which showed that there is significant overlap in particle diameter between the two distributions of NaHCO3 particles used in the study; further supported by the increasingly aspherical morphology of the larger particles in the distribution. We also note that the high pressures used for mercury porosimetry, on the order 200 MPa, can lead to rupturing of thin membranes [During our studies we also noted a plateau at around 86% porosity which we attribute to limitations in the inherent packing properties of the NaHCOarticles , 70. Porarticles . Here weembranes  and thatembranes . It is p3 particle size incorporated into the POSS-PCUU solution were expected, our investigations also revealed the formation of smaller nanopores, even in the absence of porogen. It is suggested that these pores form from the DMAC leaving the system slowly via mixing and exchange with water, as the polymer precipitates [While pore sizes on a similar length-scale to the NaHCOipitates , 75 leavipitates , such asipitates , 78.3 within the scaffold being too low and the porogen particles being dispersed across the scaffold rather than coming into contact with each other, this is unlikely to be the case as even at high porosity very few cells are seen within the scaffold. We again suggest that the polymer precipitates immediately upon contact with water while NaHCO3 dissolution is a slower process leading to the formation of isolated pores. Although these observations were not investigated further for the current work, it remains an important variable to investigate for future studies, particularly as an ideal tissue engineering scaffold should promote the development of a three-dimensional tissue [The presence of micro- and nanopores resulted in foam-like scaffold interiors. Some large micropores were also seen on the surface of the polymer although the concentration of these remained low. Where these were absent cells were prevented access to the internal scaffold structure. Cells that were able to migrate through the surface pores were further inhibited by reduced interconnectivity in some areas of the scaffold. This is reflected in the cellular imaging in this study where cells appear to attach and proliferate on the surface with very little migration into the scaffold. Although the obvious assumption is that the isolated pores are created by the concentration of NaHCOl tissue ; which il tissue .Furthermore, all of the measured characteristics; the shape and dimensions of the pores, the presence or absence of interconnectivity, and the density and thickness of the polymer, will all contribute towards the mechanical behaviour of the polymer . Native The chemistry of the precipitated polymer was also investigated. There was no change in chemistry between sample types and the water contact angle behaviour of the polymer surface was in-keeping with expectations for hydrophobic materials of this type . The polIf combined with increased porosity and better interconnectivity between the pores this scaffold could serve as a suitable candidate for tissue engineering. Although increasing porogen content is likely to increase the viscosity of the polymer solution, making it difficult to handle in the current manufacturing technique an alternative method of manufacturing, such as using extrusion to deposit highly viscous solutions, which would also assist with particle alignment and spacing, could result in a more homogenous pore structure within the scaffold, and present a way of overcoming these issues.53. The porogen was easily dissolved creating a foam-like scaffold. The scaffold exhibited a non-linear relationship between load and extension under tensile deformation. Pores present within the scaffolds varied in their size distribution which contributed to this behaviour.We present a porogen-leaching technique for manufacturing porous POSS-PCUU using NaHCOThe scaffold chemistry remained consistent and supported the proliferation of fibroblasts and epithelial cells over three days, although the formation of a skin on the surface of the polymer prevented the migration of cells into the scaffold. Furthermore, we observed differences in topography between the two surfaces of the solid polymer which result from the presence of liquid/solid and liquid/air interfaces during the manufacture process. This manufacturing technique presents a potential method for designing scaffold surface topographies using one or more liquid/solid interfaces. However, in order to meet the considerable demands of a structural laryngeal replacement using POSS-PCUU, it is vital that future studies target optimisation of the manufacturing method to improve cellular access to the internal structure. This would provide routes to functional integration with surrounding tissues, including the development of vascular netoworks and extracellular matrices, in turn supporting long-term functionality and internal epithelialization. Although much work is still required, POSS-PCUU has some promising features for the fabrication or coating of advanced bio-integrated implants for unmet healthcare needs.