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Abstract Bacterial biofilms are highly complex communities in which isogenic bacteria display different gene expression patterns and organize in a three-dimensional mesh gaining enhanced resistance to biocides. The molecular mechanisms behind such increased resistance remain mostly unknown, also because of the technical difficulties in biofilm investigation at the sub-cellular and molecular level. In this work we focus on the AcrAB-TolC protein complex, a multidrug efflux pump found in Enterobacteriaceae, whose overexpression is associated with most multiple drug resistance (MDR) phenotypes occurring in Gram-negative bacteria. We propose an optical method to quantify the expression level of the AcrAB-TolC pump within the biofilm volume at the sub-cellular level, with single-molecule sensitivity. Through a combination of super-resolution PALM with single objective light sheet and precision genome editing, we can directly quantify the spatial distribution of endogenous AcrAB-TolC pumps expressed in both planktonic bacteria and, importantly, within the bacterial biofilm volume. We observe a gradient of pump density within the biofilm volume and over the course of biofilm maturation. Notably, we propose an optical method that could be broadly employed to achieve volumetric super-resolution imaging of thick samples.

By using laser tweezers, the authors show that a single α-catenin molecule does not resist force on F-actin. However, clustering of multiple molecules and force applied toward F-actin pointed end engage a molecular switch in α-catenin, which unfolds and strongly binds F-actin.

Deep anterior lamellar keratoplasty (DALK) is considered a valuablealternative to penetrating keratoplasty (PK) for treatingcorneal disordersthat do not involve theendothelium. DALK preserves the host endothelium, eliminating the risk of endothelial rejection and reducing the risk of late graft failure due to endothelial decay. Despite its not recent introduction, DALK has been considered a difficult, lengthy, and poorly reproducible procedure, limiting its adoption worldwide. With the introduction of the big-bubble technique (BBT) the reproducibility and the time required to complete the procedure were significantly improved, encouraging many surgeons to approach DALK. With BBT air is injected into the stroma to induce separation between the layers of the cornea, facilitating the separation of the diseased or scarred stroma from the healthy endothelium; this allows the creation of a graft-host interface of pristine optical quality, granting clinical results equal to those obtained with PK.Understanding the anatomy and physics behind the big bubble (BB) formation is crucial for thesurgical success of this technique. The discovery of the pre-Descemet's layer (Dua's layer)played a significant role in understanding the principles behindBBformation, considerablyimpacting the safety and reproducibility of the technique. BB formation is influenced by preoperative pathology, trephination size, and instruments used for air injection.Continue advancements have helped to refine BBT's efficacy and reproducibility, broadening its applicability in corneal transplantation whenever the endothelium is healthy.This review provides a detailed account of the procedural steps involved in DALK using the BBT, addressing the most common challenges, highlightingtechnical innovations, and handlingthe most frequent complications., (Copyright © 2024. Published by Elsevier Inc.)

Proliferative vitreoretinopathy (PVR) has traditionally been managed with vitreoretinal surgery. Although there have been several recent innovations in this surgery to make the retinal approach as uninvasive as possible, the outcomes remain unsatisfactory. Significant complications remain and the complexity of the surgical approach is challenging. The focus of this review was to investigate and discuss the effectiveness of nanomedicine, featuring a wide range of drugs and molecules, as a novel potential treatment for PVR. To date, ocular drug delivery remains a significant issue due to the physiological and anatomical barriers, dynamic or static, which prevent the entry of exogenous molecules. We tried to summarize the nanotechnology-based ophthalmic drugs and new nanoparticles currently under research, with the intention of tackling the onset and development of PVR. The purpose of this review was to thoroughly and analytically examine and assess the potential of nano-based techniques as innovative strategies to treat proliferative vitreoretinopathy (PVR). This study aimed to emphasize the breakthroughs in nanomedicine that provide promising therapeutic options to enhance the results of vitreoretinal surgery and halt disease progression, considering the complexity and difficulty of PVR treatment. The future directions of the nanoparticles and nanotherapies applied to PVR highlight the importance of investing in the development of better designs and novel ophthalmic formulations in order to accomplish a mini-invasive ocular approach, replacing the standard-of-care vitreoretinal surgery.

The mitogen-activated protein kinase (MAPK) extracellular signal-regulated kinase 5 (ERK5) is emerging as a promising target in cancer. Indeed, alterations of the MEK5/ERK5 pathway are present in many types of cancer, including melanoma. One of the key events in MAPK signalling is MAPK nuclear translocation and its subsequent regulation of gene expression. Likewise, the effects of ERK5 in supporting cancer cell proliferation have been linked to its nuclear localization. Despite many processes regulating ERK5 nuclear translocation having been determined, the nuclear transporters involved have not yet been identified. Here, we investigated the role of importin subunit alpha (α importin) and importin subunit beta-1 (importin β1) in ERK5 nuclear shuttling to identify additional targets for cancer treatment. Either importin β1 knockdown or the α/β1 importin inhibitor ivermectin reduced the nuclear amount of overexpressed and endogenous ERK5 in HEK293T and A375 melanoma cells, respectively. These results were confirmed in single-molecule microscopy in HeLa cells. Moreover, immunofluorescence analysis showed that ivermectin impairs epidermal growth factor (EGF)-induced ERK5 nuclear shuttling in HeLa cells. Both co-immunoprecipitation experiments and proximity ligation assay provided evidence that ERK5 and importin β1 interact and that this interaction is further induced by EGF administration and prevented by ivermectin treatment. The combination of ivermectin and the ERK5 inhibitor AX15836 synergistically reduced cell viability and colony formation ability in A375 and HeLa cells and was more effective than single treatments in preventing the growth of A375 and HeLa spheroids. The increased reduction of cell viability upon the same combination was also observed in patient-derived metastatic melanoma cells. The combination of ivermectin and ERK5 inhibitors other than AX15836 provided similar effects on cell viability. The identification of importin β1 as the nuclear transporter of ERK5 may be exploited for additional ERK5-inhibiting strategies for cancer therapy., (© 2024 The Author(s). Molecular Oncology published by John Wiley & Sons Ltd on behalf of Federation of European Biochemical Societies.)

Background: An increasing amount of people are globally affected by retinal diseases, such as diabetes, vascular occlusions, maculopathy, alterations of systemic circulation, and metabolic syndrome., Aim: This review will discuss novel technologies in and potential approaches to the detection and diagnosis of retinal diseases with the support of cutting-edge machines and artificial intelligence (AI)., Methods: The demand for retinal diagnostic imaging exams has increased, but the number of eye physicians or technicians is too little to meet the request. Thus, algorithms based on AI have been used, representing valid support for early detection and helping doctors to give diagnoses and make differential diagnosis. AI helps patients living far from hub centers to have tests and quick initial diagnosis, allowing them not to waste time in movements and waiting time for medical reply., Results: Highly automated systems for screening, early diagnosis, grading and tailored therapy will facilitate the care of people, even in remote lands or countries., Conclusion: A potential massive and extensive use of AI might optimize the automated detection of tiny retinal alterations, allowing eye doctors to perform their best clinical assistance and to set the best options for the treatment of retinal diseases., Competing Interests: The authors declare no conflicts of interest.

Bacterial biofilms are highly complex communities in which isogenic bacteria display different gene expression patterns and organize in a three-dimensional mesh gaining enhanced resistance to biocides. The molecular mechanisms behind such increased resistance remain mostly unknown, also because of the technical difficulties in biofilm investigation at the sub-cellular and molecular level. In this work we focus on the AcrAB-TolC protein complex, a multidrug efflux pump found in Enterobacteriaceae, whose overexpression is associated with most multiple drug resistance (MDR) phenotypes occurring in Gram-negative bacteria. We propose an optical method to quantify the expression level of the AcrAB-TolC pump within the biofilm volume at the sub-cellular level, with single-molecule sensitivity. Through a combination of super-resolution PALM with single objective light sheet and precision genome editing, we can directly quantify the spatial distribution of endogenous AcrAB-TolC pumps expressed in both planktonic bacteria and, importantly, within the bacterial biofilm volume. We observe a gradient of pump density within the biofilm volume and over the course of biofilm maturation. Notably, we propose an optical method that could be broadly employed to achieve volumetric super-resolution imaging of thick samples., (© 2024. The Author(s).)

The dynamics of cellular membrane tension and its role in mechanosensing, which is the ability of cells to respond to physical stimuli, remain incompletely understood, mainly due to the lack of appropriate tools. Here, we report a force-controlled nanopipette-based method that combines fluidic force microscopy with fluorescence imaging for precise manipulation of the cellular membrane tension while monitoring the impact on single-cell mechanosensitivity. The force-controlled nanopipette enables control of the indentation force imposed on the cell cortex as well as of the aspiration pressure applied to the plasma membrane. We show that this setup can be used to concurrently monitor the activation of Piezo1 mechanosensitive ion channels via calcium imaging. Moreover, the spatiotemporal behavior of the tension propagation is assessed with the fluorescent membrane tension probe Flipper-TR, and further dissected using molecular dynamics modeling. Finally, we demonstrate that aspiration and indentation act independently on the cellular mechanobiological machinery, that indentation induces a local pre-tension in the membrane, and that membrane tension stays confined by links to the cytoskeleton., (© 2024. The Author(s).)

We develop a foreign exchange market model in which a market maker adjusts the exchange rate with respect to the trading behavior of chartists, fundamentalists and a central bank. While chartists bet on the persistence of bull and bear markets, fundamentalists speculate on mean reversion. The central bank seeks to stabilize the foreign exchange market by placing buy (sell) orders when the undervaluation (overvaluation) of the exchange rate exceeds a certain threshold. Since a one-dimensional piecewise-linear discontinuous map with three branches determines the evolution of the exchange rate, we use a combination of analytical and numerical tools to explore the extent to which the central bank is able to tame the behavior of the foreign exchange market.

Purpose: We describe the management of a case of severe corneal melting after corneal cross-linking (CXL) treated with a staged approach using a conjunctival flap followed by deep anterior lamellar keratoplasty (DALK)., Methods: A 12-year-old male developed severe corneal melting with pending perforation after an accelerated epithelium-off CXL protocol. We initially treated the patient with a conjunctival flap to prevent perforation. Three months later, we performed DALK to restore vision., Results: Conjunctival flap surgery allowed us to avoid corneal perforation and penetrating keratoplasty (PK) à chaud. Once the inflammation had resolved, we recessed the conjunctiva and performed DALK for optical purposes. Twelve months later, the graft was clear and the corrected visual acuity was 20/25 (Snellen). No complications occurred after surgery., Conclusions: Although CXL is considered a safe procedure, in rare cases it can lead to serious complications, such as corneal haze, infectious and non-infectious keratitis, stromal melting and perforation. Corneal melting and perforation are usually managed by emergency PK. Herein we suggest a staged approach involving an emergency conjunctival flap followed by DALK at a later time that allowed us to avoid PK à chaud., (© 2024. The Author(s).)

In HILO microscopy, a highly inclined and laminated light sheet is used to illuminate the sample, thus drastically reducing background fluorescence in wide-field microscopy, but maintaining the simplicity of the use of a single objective for both illumination and detection. Although the technique has become widely popular, particularly in single molecule and super-resolution microscopy, a limited understanding of how to finely shape the illumination beam and of how this impacts on the image quality complicates the setting of HILO to fit the experimental needs. In this work, we build up a simple and comprehensive guide to optimize the beam shape and alignment in HILO and to predict its performance in conventional fluorescence and super-resolution microscopy. We model the beam propagation through Gaussian optics and validate the model through far- and near-field experiments, thus characterizing the main geometrical features of the beam. Further, we fully quantify the effects of a progressive reduction of the inclined beam thickness on the image quality of both diffraction-limited and super-resolution images and we show that the most relevant impact is obtained by reducing the beam thickness to sub-cellular dimensions (< 3 µm). Based on this, we present a simple optical solution that exploits a rectangular slit to reduce the inclined beam thickness down to 2.6 µm while keeping a field-of-view dimension suited for cell imaging and allowing an increase in the number of localizations in super-resolution imaging of up to 2.6 folds.

Purpose: To analyze epidemiology, clinical features, and surgical outcomes of type III acute acquired concomitant esotropia (Bielschowsky esotropia (BE))., Methods: The medical charts of patients diagnosed with acquired concomitant esotropia between 2013 and 2021 were reviewed. Assessed data were age, gender, age at diplopia onset, age at the diagnosis, refraction, visual acuity, neuroimaging, diplopia onset, angle of deviation, stereopsis, surgical procedure, amount of surgery, and relapse of diplopia after surgery. Moreover, we investigated the correlation between the use of electronic devices and the onset of diplopia., Results: One hundred seventeen patients (mean age 35.07 ± 15.81 years) were included in the study. The mean delay to the diagnosis was 3.29 ± 3.62 years. Myopia range was 0 to 17 diopters spherical equivalent. 66,3% spent more than 4 hours a day using laptops, tablets, or smartphones at the onset of diplopia, and 90,6% presented a subacute onset. None showed neurologic signs or symptoms. Patients who underwent surgery were ninety-three, with a rate of surgical success of 93.6%, and a relapse rate of 17.2%. A negative correlation resulted between pre-operative deviation and age at diagnosis (ρ = -0.261; p<0.05), whereas factors associated with surgical failure were older age at diplopia onset (p = 0.042) and longer delay between onset and diagnosis (p = 0.002)., Conclusion: We registered an outstanding increase in prevalence of BE, which could be related to the exponential increase in the use of electronic devices for professional, educational, and recreational purposes. A prompt diagnosis and an augmented dose of surgery allows good motor and sensory results., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Roda et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Intraoperative OCT is an innovative and promising technology which allows anterior and posterior segment ocular surgeons to obtain a near-histologic cross-sectional and tomographic image of the tissues. Intraoperative OCT has several applications in ocular surgery which are particularly interesting in the context of corneal transplantation. Indeed, iOCT images provide a direct and meticulous visualization of the anatomy, which could guide surgical decisions. In particular, during both big-bubble and manual DALK, the visualization of the relationship between the corneal layers and instruments allows the surgeon to obtain a more desirable depth of the trephination, thus achieving more type 1 bubbles, better regularity of the plane, and a reduced risk of DM perforation. During EK procedures, iOCT supplies information about proper descemetorhexis, graft orientation, and interface quality in order to optimize the postoperative adhesion and reduce the need for re-bubbling. Finally, mushroom PK, a challenging technique for many surgeons, can be aided through the use of iOCT since it guides the correct apposition of the lamellae and their centration. The technology of iOCT is still evolving: a larger field of view could allow for the visualization of all surgical fields, and automated tracking and iOCT autofocusing guarantee the continued centration of the image.

Particle localization plays a fundamental role in advanced biological techniques such as single-molecule tracking, superresolution microscopy, and manipulation by optical and magnetic tweezers. Such techniques require fast and accurate particle localization algorithms as well as nanometer-scale stability of the microscope. Here, we present a universal method for three-dimensional localization of single labeled and unlabeled particles based on local gradient calculation of particle images. The method outperforms state-of-the-art localization techniques in high-noise conditions, and it is capable of 3D nanometer accuracy localization of nano- and microparticles with sub-millisecond calculation time. By localizing a fixed particle as fiducial mark and running a feedback loop, we demonstrate its applicability for active drift correction in sensitive nanomechanical measurements such as optical trapping and superresolution imaging. A multiplatform open software package comprising a set of tools for local gradient calculation in brightfield, darkfield, and fluorescence microscopy is shared for ready use by the scientific community.

Background: Corneal transplantation in keratoconus (KC) patients is generally considered to be successful with a high grade of patient satisfaction. Long-term studies suggest a 6% to 11% probability of KC recurrence manifested by keratometric instability and progressive corneal ectasia., Methods: We propose to review the frequency, risk factors for the development, and the surgical options for the correction of high irregular astigmatism due to late graft ectasia following penetrating keratoplasty (PK)., Results: Post-keratoplasty ectasia is characterized by increasing corneal steepening with myopic shift and high irregular astigmatism, developing years or decades after PK, mostly occurring in KC patients. Contact lenses may adequately improve the visual acuity; however, because these patients are often elderly and intolerant to hard contact lenses, ultimately a surgical correction is proposed to the patient. Compressive suture and corneal wedge resection may improve corneal astigmatism, but the outcomes are unpredictable and often temporary. For this reason, a larger PK graft is often proposed for surgical rehabilitation with the consequence of removing more of the recipient's healthy endothelium and exposing the patient to a renewed immunogenic stimulus and short-term graft failure for endothelial decompensation. More recently, lamellar keratoplasty using various techniques has been proposed as an alternative to PK in order to maximize the visual outcomes and minimize the complications., Conclusions: Management of advanced corneal ectasia is a significant challenge for corneal surgeons. Many surgical approaches have been developed, so there is a large arsenal of surgical operations to correct post-PK ectasia. Among them, large-diameter anterior lamellar keratoplasty may be a viable, safer, and effective alternative to PK for the correction of post-keratoplasty ectasia.

This paper contributes to studying the bifurcations of closed invariant curves in piecewise-smooth maps. Specifically, we discuss a border collision bifurcation of a repelling resonant closed invariant curve (a repelling saddle-node connection) colliding with the border by a point of the repelling cycle. As a result, this cycle becomes attracting and the curve is destroyed, while a new repelling closed invariant curve appears (not in a neighborhood of the previously existing invariant curve), being associated with quasiperiodic dynamics. This leads to a global restructuring of the phase portrait since both curves mentioned above belong to basin boundaries of coexisting attractors.

α-catenin is a crucial protein at cell junctions that provides connection between the actin cytoskeleton and the cell membrane. At adherens junctions (AJs), α-catenin forms heterodimers with β-catenin that are believed to resist force on F-actin. Outside AJs, α-catenin forms homodimers that regulates F-actin organization and directly connect the cell membrane to the actin cytoskeleton, but their mechanosensitive properties are inherently unknown. By using ultra-fast laser tweezers we found that a single α-β-catenin heterodimer does not resist force but instead slips along F-actin in the direction of force. Conversely, the action of 5 to 10 α-β-catenin heterodimers together with force applied toward F-actin pointed end engaged a molecular switch in α-catenin, which unfolded and strongly bound F-actin as a cooperative catch bond. Similarly, an α-catenin homodimer formed an asymmetric catch bond with F-actin triggered by protein unfolding under force. Our data suggest that α-catenin clustering together with intracellular tension engage a fluid-to-solid phase transition at the membrane-cytoskeleton interface., (© 2022. The Author(s).)

Background: MDR in bacteria is threatening to public health. Overexpression of efflux pumps is an important cause of MDR. The co-administration of antimicrobial drugs and efflux pump inhibitors (EPIs) is a promising approach to address the problem of MDR., Objectives: To identify new putative EPIs and to characterize their mechanisms of action., Methods: The effects of four selected piperazine derivatives on resistance-nodulation-cell division (RND) pumps was evaluated in Escherichia coli strains overexpressing or not expressing RND pumps by assays aimed at evaluating antibiotic potentiation, membrane functionality, ethidium bromide accumulation and AcrB expression. The cytotoxicity of selected piperazines towards primary cultures of human dermal fibroblasts was also investigated., Results: Four molecules enhanced levofloxacin activity against strains overexpressing RND efflux pumps (AcrAB-TolC and AcrEF-TolC), but not against RND pump-deficient strains. They had little effects on membrane potential. Molecule 4 decreased, whereas the other three increased, membrane permeability compared with untreated control cells. The four molecules showed differences in the specificity of interaction with RND efflux pumps, by inactivating the transport of one or more antibiotics, and in the levels of ethidium bromide accumulation and of acrB expression inhibition., Conclusions: Piperazine derivatives are good candidates as inhibitors of RND efflux pumps. They decreased the activity of RND pumps by mixed mechanisms of action. Small structural differences among the molecules can be critical in defining their behaviour., (© The Author(s) 2021. Published by Oxford University Press on behalf of the British Society for Antimicrobial Chemotherapy. All rights reserved. For permissions, please email: journals.permissions@oup.com.)

Interactions between biological molecules occur on very different time scales, from the minutes of strong protein-protein bonds, down to below the millisecond duration of rapid biomolecular interactions. Conformational changes occurring on sub-ms time scales and their mechanical force dependence underlie the functioning of enzymes (e.g., motor proteins) that are fundamental for life. However, such rapid interactions are beyond the temporal resolution of most single-molecule methods. We developed ultrafast force-clamp spectroscopy (UFFCS), a single-molecule technique based on laser tweezers that allows us to investigate early and very fast dynamics of a variety of enzymes and their regulation by mechanical load. The technique was developed to investigate the rapid interactions between skeletal muscle myosin and actin, and then applied to the study of different biological systems, from cardiac myosin to processive myosin V, microtubule-binding proteins, transcription factors, and mechanotransducer proteins. Here, we describe two different implementations of UFFCS instrumentation and protocols using either acousto- or electro-optic laser beam deflectors, and their application to the study of processive and non-processive motor proteins., (© 2022. The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature.)

Introduction: Post-radiation fractures of the femur (PRF) are difficult to treat and are associated with a high risk of delayed union and non-union. We report a series of patients affected by soft tissue sarcoma (STS) of the thigh, treated with limb-sparing surgery and perioperative radiotherapy (RT), to analyse post-radiotherapy femur fracture (FF) rate and its management., Material and Methods: 547 patients treated with surgery and RT for a deep primary STS of the thigh were included. "Periosteal stripping" and "bone tangential resection" were performed in case of tumor invasion. In the case of complete bone involvement, the patient received its complete resection and econstruction., Results: Twenty-three (4.3%) patients underwent surgical procedures involving periosteum and cortical bone. In 11 (2.0%) patients a bone resection was required because of massive bone involvement. Six out of these 11 (54.5%) patients developed major complications (infection and aseptic loosening). At the time of STS excision, 11 patients (2.0%) underwent prophylactic intramedullary nailing (PIN). PRF occurred in 15 patients (3.0%) at a median follow up of 52 months (range 3-151). Among patients who developed PRF, three were treated with a prosthesis (no complications) and eight nailing (7/8, 87.5% did not heal and developed a non-union)., Conclusions: Given the potentially devastating complication of a PRF, PIN should be considered. We suggest prophylactic IM nail in patients at higher risk the time of STS excision. In other cases, IM nail can be postponed in the following years considering the prognosis., (© 2020. Springer-Verlag GmbH Germany, part of Springer Nature.)

Ultrafast force-clamp spectroscopy (UFFCS) is a single molecule technique based on laser tweezers that allows the investigation of the chemomechanics of both conventional and unconventional myosins under load with unprecedented time resolution. In particular, the possibility to probe myosin motors under constant force right after the actin-myosin bond formation, together with the high rate of the force feedback (200 kHz), has shown UFFCS to be a valuable tool to study the load dependence of fast dynamics such as the myosin working stroke. Moreover, UFFCS enables the study of how processive and non-processive myosin-actin interactions are influenced by the intensity and direction of the applied force. By following this protocol, it will be possible to perform ultrafast force-clamp experiments on processive myosin-5 motors and on a variety of unconventional myosins. By some adjustments, the protocol could also be easily extended to the study of other classes of processive motors such as kinesins and dyneins. The protocol includes all the necessary steps, from the setup of the experimental apparatus to sample preparation, calibration procedures, data acquisition and analysis.

Aim: To investigate the action mechanism of 1-benzyl-1,4-diazepane (1-BD) as efflux pump inhibitor (EPI) in Escherichia coli mutants: Δ acrAB or overexpressing AcrAB and AcrEF efflux pumps. Materials & methods: Effect of 1-BD on: antibiotic potentiation, by microdilution method; membrane functionality, by fluorimetric assays; ethidium bromide accumulation, by fluorometric real-time efflux assay; AcrB expression, by quantitative photoactivated localization microscopy. Results: 1-BD decreases the minimal inhibitory concentration of levofloxacin and other antibiotics and increase ethidium bromide accumulation in E. coli overexpressing efflux pumps but not in the Δ acrAB strain. 1-BD increases membranes permeability, without sensibly affecting inner membrane polarity and decreases acrAB transcription. Conclusion: 1-BD acts as an EPI in E. coli with a mixed mechanism, different from that of major reference EPIs.

After the seminal works by Schelling, several authors have considered models representing binary choices by different kinds of agents or groups of people. The role of the memory in these models is still an open research argument, on which scholars are investigating. The dynamics of binary choices with impulsive agents has been represented, in the recent literature, by a one-dimensional piecewise smooth map. Following a similar way of modeling, we assume a memory effect which leads the next output to depend on the present and the last state. This results in a two-dimensional piecewise smooth map with a limiting case given by a piecewise linear discontinuous map, whose dynamics and bifurcations are investigated. The map has a particular structure, leading to trajectories belonging only to a pair of straight lines. The system can have, in general, only attracting cycles, but the related periods and periodicity regions are organized in a complex structure of the parameter space. We show that the period adding structure, characteristic for the one-dimensional case, also persists in the two-dimensional one. The considered cycles have a symbolic sequence which is obtained by the concatenation of the symbolic sequences of cycles, which play the role of basic cycles in the bifurcation structure. Moreover, differently from the one-dimensional case, the coexistence of two attracting cycles is now possible. The bistability regions in the parameter space are investigated, evidencing the role of different kinds of codimension-two bifurcation points, as well as in the phase space and the related basins of attraction are described.

Myosin is a large family of actin-based molecular motors, which includes efficient intracellular transporters that move cargoes and material essential for cell's life. Here, we describe protocols for labelling single myosin motors with quantum dots, tracking them in an in vitro reconstituted single-molecule motility assay, acquiring image stacks and analyzing them. We describe the required steps to obtain trajectories of single myosin motors from which fundamental biophysical parameters such as the motor velocity, run length and step size can be derived. We also describe protocols for an ensemble actin gliding assay, which is valuable to test the motor viability and its ensemble properties. The protocols allow probing the effect of changes in nucleotides, ions, and buffer composition on the motor properties and are easily generalizable to track the movements of different motor proteins.

Myosin-5B is one of three members of the myosin-5 family of actin-based molecular motors fundamental in recycling endosome trafficking and collective actin network dynamics. Through single-molecule motility assays, we recently demonstrated that myosin-5B can proceed in 36-nm steps along actin filaments as single motor. By analyzing trajectories of single myosin-5B along actin filaments we showed that its velocity is dependent on ATP concentration, while its run length is independent on ATP concentration, as a landmark of processivity. Here, we share image stacks acquired under total internal reflection fluorescence (TIRF) microscopy and representative trajectories of single myosin-5B molecules labelled with Quantum Dots (QD-myo-5B) moving along actin filaments at different ATP concentrations (0.3-1000 μM). Localization of QD-myo-5B was performed with the PROOF software, which is freely available [1]. The data can be valuable for researchers interested in molecular motors motility, both from an experimental and modeling point of view, as well as to researchers developing single particle tracking algorithms. The data is related to the research article "Dissecting myosin-5B mechanosensitivity and calcium regulation at the single molecule level" Gardini et al., 2015.

The mechanism by which proteins are able to find small cognate sequences in the range from few to few tens of base pairs amongst the millions of non-specific chromosomal DNA has been puzzling researchers for decades. Single molecule techniques based on fluorescence have been successfully applied to investigate this process but are inherently limited in terms of spatial and temporal resolution. We previously showed that ultrafast force-clamp spectroscopy, a single molecule technique based on laser tweezers, can be applied to the study of protein-DNA interaction attaining sub-millisecond and few base-pair resolution. Here, we share experimental records of interactions between a single lactose repressor protein and DNA collected under different forces using our technique [1]. The data can be valuable for researchers interested in the study of protein-DNA interaction and the mechanism of DNA target search, both from an experimental and modeling point of view. The data is related to the research article " Sliding of a single lac repressor protein along DNA is tuned by DNA sequence and molecular switching " [2].

Myosin-5B is one of three members of the myosin-5 family of actin-based molecular motors. Despite its fundamental role in recycling endosome trafficking and in collective actin network dynamics, the molecular mechanisms underlying its motility are inherently unknown. Here we combine single-molecule imaging and high-speed laser tweezers to dissect the mechanoenzymatic properties of myosin-5B. We show that a single myosin-5B moves processively in 36-nm steps, stalls at ~2 pN resistive forces, and reverses its directionality at forces >2 pN. Interestingly, myosin-5B mechanosensitivity differs from that of myosin-5A, while it is strikingly similar to kinesin-1. In particular, myosin-5B run length is markedly and asymmetrically sensitive to force, a property that might be central to motor ensemble coordination. Furthermore, we show that Ca 2+ does not affect the enzymatic activity of the motor unit, but abolishes myosin-5B processivity through calmodulin dissociation, providing important insights into the regulation of postsynaptic cargoes trafficking in neuronal cells.

In any living cell, genome maintenance is carried out by DNA-binding proteins that recognize specific sequences among a vast amount of DNA. This includes fundamental processes such as DNA replication, DNA repair, and gene expression and regulation. Here, we study the mechanism of DNA target search by a single lac repressor protein (LacI) with ultrafast force-clamp spectroscopy, a sub-millisecond and few base-pair resolution technique based on laser tweezers. We measure 1D-diffusion of proteins on DNA at physiological salt concentrations with 20 bp resolution and find that sliding of LacI along DNA is sequence dependent. We show that only allosterically activated LacI slides along non-specific DNA sequences during target search, whereas the inhibited conformation does not support sliding and weakly interacts with DNA. Moreover, we find that LacI undergoes a load-dependent conformational change when it switches between sliding and strong binding to the target sequence. Our data reveal how DNA sequence and molecular switching regulate LacI target search process and provide a comprehensive model of facilitated diffusion for LacI.

Time traces obtained from a variety of biophysical experiments contain valuable information on underlying processes occurring at the molecular level. Accurate quantification of these data can help explain the details of the complex dynamics of biological systems. Here, we describe PLANT (Piecewise Linear Approximation of Noisy Trajectories), a segmentation algorithm that allows the reconstruction of time-trace data with constant noise as consecutive straight lines, from which changes of slopes and their respective durations can be extracted. We present a general description of the algorithm and perform extensive simulations to characterize its strengths and limitations, providing a rationale for the performance of the algorithm in the different conditions tested. We further apply the algorithm to experimental data obtained from tracking the centroid position of lymphocytes migrating under the effect of a laminar flow and from single myosin molecules interacting with actin in a dual-trap force-clamp configuration., (Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.)

The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents benefit from integration. Despite the differences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilibrium, while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dynamic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several different kinds of bifurcations, smooth, and border collision, in a complicated interplay. Our global analysis can give intuitions to be used by a social planner to maximize integration through social policies that manipulate people's preferences for integration.

We consider a discrete-time version of the continuous-time fashion cycle model introduced in Matsuyama, 1992. Its dynamics are defined by a 2D discontinuous piecewise linear map depending on three parameters. In the parameter space of the map periodicity, regions associated with attracting cycles of different periods are organized in the period adding and period incrementing bifurcation structures. The boundaries of all the periodicity regions related to border collision bifurcations are obtained analytically in explicit form. We show the existence of several partially overlapping period incrementing structures, that is, a novelty for the considered class of maps. Moreover, we show that if the time-delay in the discrete time formulation of the model shrinks to zero, the number of period incrementing structures tends to infinity and the dynamics of the discrete time fashion cycle model converges to those of continuous-time fashion cycle model.

Mechanical transitions in molecular motors often occur on a submillisecond time scale and rapidly follow binding of the motor with its cytoskeletal filament. Interactions of nonprocessive molecular motors with their filament can be brief and last for few milliseconds or fraction of milliseconds. The investigation of such rapid events and their load dependence requires specialized single-molecule tools. Ultrafast force-clamp spectroscopy is a constant-force optical tweezers technique that allows probing such rapid mechanical transitions and submillisecond kinetics of biomolecular interactions, which can be particularly valuable for the study of nonprocessive motors, single heads of processive motors, or stepping dynamics of processive motors. Here we describe a step-by-step protocol for the application of ultrafast force-clamp spectroscopy to myosin motors. We give indications on optimizing the optical tweezers setup, biological constructs, and data analysis to reach a temporal resolution of few tens of microseconds combined with subnanometer spatial resolution. The protocol can be easily generalized to other families of motor proteins.

Here, we describe protocols for three-dimensional tracking of single quantum dot-conjugated molecules with nanometer accuracy in living cells using conventional fluorescence microscopy. The technique exploits out-of-focus images of single emitters combined with an automated pattern-recognition open-source software that fits the images with proper model functions to extract the emitter coordinates. We describe protocols for targeting quantum dots to both membrane components and cytosolic proteins.

Introduction: In routine colonoscopy, diverticulosis is the most commonly found feature, but only a minority of these cases show symptoms of diverticular disease.From June 2014 to December 2014, we enrolled prospectively 178 patients affected by symptomatic uncomplicated diverticular disease (Male/Female=0.47, mean age 71.7±11.5 y, range 41 to 95 y) from 15 General Pratictioners patient files. All patients were symptomatic; in all cases, diagnosis was been confirmed by a colonoscopy performed at least 1 year before. Patients with acute diverticulitis were excluded.On the basis of the predominant symptoms (abdominal complaints or constipation), patients were addressed to 4 different therapeutic approaches using mesalamine, rifaximine, probiotics (in a consortium of different species of Lactobacillus and Bifidobacterium), and fibers (Plantago Ovata Husk). All treatments lasted 3 months., Results: Sixty-three patients were enrolled in group A (rifaximine), 43 in group A1 (rifaximine+fibers+probiotics), 23 in group B (mesalamine), and 31 in group B1 (mesalamine+fibers).Analysis of variance suggested a statistically significant difference (P<0.003) among groups at the end of the observation period, with Groups A1 and B1 showing a higher number of bowel movement per week. Global linear measurement confirmed the role of treatment as a significant factor (F=2.858; P=0.039) associated with body mass index (F=6.972; P<0.009)., Conclusions: In accordance with the baseline clinical presentation, the supplementation of fiber and/or probiotics is associated with a statistically significant improvement in the clinical pattern of symptoms in patients with diverticular disease in a primary-care/family physician setting.

Live cells are three-dimensional environments where biological molecules move to find their targets and accomplish their functions. However, up to now, most single molecule investigations have been limited to bi-dimensional studies owing to the complexity of 3d-tracking techniques. Here, we present a novel method for three-dimensional localization of single nano-emitters based on automatic recognition of out-of-focus diffraction patterns. Our technique can be applied to track the movements of single molecules in living cells using a conventional epifluorescence microscope. We first demonstrate three-dimensional localization of fluorescent nanobeads over 4 microns depth with accuracy below 2 nm in vitro. Remarkably, we also establish three-dimensional tracking of Quantum Dots, overcoming their anisotropic emission, by adopting a ligation strategy that allows rotational freedom of the emitter combined with proper pattern recognition. We localize commercially available Quantum Dots in living cells with accuracy better than 7 nm over 2 microns depth. We validate our technique by tracking the three-dimensional movements of single protein-conjugated Quantum Dots in living cell. Moreover, we find that important localization errors can occur in off-focus imaging when improperly calibrated and we give indications to avoid them. Finally, we share a Matlab script that allows readily application of our technique by other laboratories.

Supported by experiments on a power electronic DC/AC converter, this paper considers an unusual transition from the domain of stable periodic dynamics (corresponding to the desired mode of operation) to chaotic dynamics. The behavior of the converter is studied by means of a 1D stroboscopic map derived from a non-autonomous ordinary differential equation with discontinuous right-hand side. By construction, this stroboscopic map has a high number of border points. It is shown that the onset of chaos occurs stepwise, via irregular cascades of different border collisions, some of which lead to bifurcations while others do not.

In recent years, the study of chaotic and complex phenomena in electronic circuits has been widely developed due to the increasing number of applications. In these studies, associated with the use of chaotic sequences, chaos is required to be robust (not occurring only in a set of zero measure and persistent to perturbations of the system). These properties are not easy to be proved, and numerical simulations are often used. In this work, we consider a simple electronic switching circuit, proposed as chaos generator. The object of our study is to determine the ranges of the parameters at which the dynamics are chaotic, rigorously proving that chaos is robust. This is obtained showing that the model can be studied via a two-dimensional piecewise smooth map in triangular form and associated with a one-dimensional piecewise linear map. The bifurcations in the parameter space are determined analytically. These are the border collision bifurcation curves, the degenerate flip bifurcations, which only are allowed to occur to destabilize the stable cycles, and the homoclinic bifurcations occurring in cyclical chaotic regions leading to chaos in 1-piece.

When homoclinic orbits to an expanding periodic point exist, the point is called a snap-back repeller. Here, we consider the two-dimensional piecewise-linear map in canonical form, continuous and discontinuous, showing how snap-back repellers may be associated with robust chaotic attracting sets (not only with chaotic repellers). Examples are given both for the continuous and discontinuous maps.

This paper is devoted to the study of the global dynamical properties of a two-dimensional noninvertible map, with a denominator which can vanish, obtained by applying Bairstow's method to a cubic polynomial. It is shown that the complicated structure of the basins of attraction of the fixed points is due to the existence of singularities such as sets of nondefinition, focal points, and prefocal curves, which are specific to maps with a vanishing denominator, and have been recently introduced in the literature. Some global bifurcations that change the qualitative structure of the basin boundaries, are explained in terms of contacts among these singularities. The techniques used in this paper put in evidence some new dynamic behaviors and bifurcations, which are peculiar of maps with denominator; hence they can be applied to the analysis of other classes of maps coming from iterative algorithms (based on Newton's method, or others). (c) 1999 American Institute of Physics.