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A precise representation of the spatial distribution of hydrophobicity, hydrophilicity and charges on the molecular surface of proteins is critical for the understanding of the interaction with small molecules and larger systems. The representation of hydrophobicity is rarely done at atom-level, as this property is generally assigned to residues. A new methodology for the derivation of atomic hydrophobicity from any amino acid-based hydrophobicity scale was used to derive 8 sets of atomic hydrophobicities, one of which was used to generate the molecular surfaces for 35 proteins with convex structures, 5 of which, i.e., lysozyme, ribonuclease, hemoglobin, albumin and IgG, have been analyzed in more detail. Sets of the molecular surfaces of the model proteins have been constructed using spherical probes with increasingly large radii, from 1.4 to 20 Å, followed by the quantification of (i) the surface hydrophobicity; (ii) their respective molecular surface areas, i.e., total, hydrophilic and hydrophobic area; and (iii) their relative densities, i.e., divided by the total molecular area; or specific densities, i.e., divided by property-specific area. Compared with the amino acid-based formalism, the atom-level description reveals molecular surfaces which (i) present an approximately two times more hydrophilic areas; with (ii) less extended, but between 2 to 5 times more intense hydrophilic patches; and (iii) 3 to 20 times more extended hydrophobic areas. The hydrophobic areas are also approximately 2 times more hydrophobicity-intense. This, more pronounced \"leopard skin\"-like, design of the protein molecular surface has been confirmed by comparing the results for a restricted set of homologous proteins, i.e., hemoglobins diverging by only one residue (Trp37). These results suggest that the representation of hydrophobicity on the protein molecular surfaces at atom-level resolution, coupled with the probing of the molecular surface at different geometric resolutions, can capture processes that are otherwise obscured to the amino acid-based formalism.

The combinatorial nature of many important mathematical problems, including nondeterministic-polynomial-time (NP)-complete problems, places a severe limitation on the problem size that can be solved with conventional, sequentially operating electronic computers. There have been significant efforts in conceiving parallel-computation approaches in the past, for example: DNA computation, quantum computation, and microfluidics-based computation. However, these approaches have not proven, so far, to be scalable and practical from a fabrication and operational perspective. Here, we report the foundations of an alternative parallel-computation system in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. Exploring the network in a parallel fashion using a large number of independent, molecular-motor-propelled agents then solves the mathematical problem. This approach uses orders of magnitude less energy than conventional computers, thus addressing issues related to power consumption and heat dissipation. We provide a proof-of-concept demonstration of such a device by solving, in a parallel fashion, the small instance {2, 5, 9} of the subset sum problem, which is a benchmark NP-complete problem. Finally, we discuss the technical advances necessary to make our system scalable with presently available technology.

Understanding the motility behavior of bacteria in confining microenvironments, in which they search for available physical space and move in response to stimuli, is important for environmental, food industry, and biomedical applications. We studied the motility of five bacterial species with various sizes and flagellar architectures (Vibrio natriegens, Magnetococcus marinus, Pseudomonas putida, Vibrio fischeri, and Escherichia coli) in microfluidic environments presenting various levels of confinement and geometrical complexity, in the absence of external flow and concentration gradients. When the confinement is moderate, such as in quasi-open spaces with only one limiting wall, and in wide channels, the motility behavior of bacteria with complex flagellar architectures approximately follows the hydrodynamics-based predictions developed for simple monotrichous bacteria. Specifically, V. natriegens and V. fischeri moved parallel to the wall and P. putida and E. coli presented a stable movement parallel to the wall but with incidental wall escape events, while M. marinus exhibited frequent flipping between wall accumulator and wall escaper regimes. Conversely, in tighter confining environments, the motility is governed by the steric interactions between bacteria and the surrounding walls. In mesoscale regions, where the impacts of hydrodynamics and steric interactions overlap, these mechanisms can either push bacteria in the same directions in linear channels, leading to smooth bacterial movement, or they could be oppositional (e.g., in mesoscale-sized meandered channels), leading to chaotic movement and subsequent bacterial trapping. The study provides a methodological template for the design of microfluidic devices for single-cell genomic screening, bacterial entrapment for diagnostics, or biocomputation.

Filamentous fungi that colonize microenvironments, such as animal or plant tissue or soil, must find optimal paths through their habitat, but the biological basis for negotiating growth in constrained environments is unknown. We used time-lapse live-cell imaging of Neurospora crassa in microfluidic environments to show how constraining geometries determine the intracellular processes responsible for fungal growth. We found that, if a hypha made contact with obstacles at acute angles, the Spitzenkörper (an assembly of vesicles) moved from the center of the apical dome closer to the obstacle, thus functioning as an internal gyroscope, which preserved the information regarding the initial growth direction. Additionally, the off-axis trajectory of the Spitzenkörper was tracked by microtubules exhibiting “cutting corner” patterns. By contrast, if a hypha made contact with an obstacle at near-orthogonal incidence, the directional memory was lost, due to the temporary collapse of the Spitzenkörper–microtubule system, followed by the formation of two “daughter” hyphae growing in opposite directions along the contour of the obstacle. Finally, a hypha passing a lateral opening in constraining channels continued to grow unperturbed, but a daughter hypha gradually branched into the opening and formed its own Spitzenkörper–microtubule system. These observations suggest that the Spitzenkörper–microtubule system is responsible for efficient space partitioning in microenvironments, but, in its absence during constraint-induced apical splitting and lateral branching, the directional memory is lost, and growth is driven solely by the isotropic turgor pressure. These results further our understanding of fungal growth in microenvironments relevant to environmental, industrial, and medical applications.

The bacterial flagellar switch that controls the direction of flagellar rotation during chemotaxis has a highly cooperative response. This has previously been understood in terms of the classic two-state, concerted model of allosteric regulation. Here, we used high-resolution optical microscopy to observe switching of single motors and uncover the stochastic multistate nature of the switch. Our observations are in detailed quantitative agreement with a recent general model of allosteric cooperativity that exhibits conformational spread— the stochastic growth and shrinkage of domains of adjacent subunits sharing a particular conformational state. We expect that conformational spread will be important in explaining cooperativity in other large signaling complexes.

Exact cover is a non-deterministic polynomial time (NP)—complete problem that is central to optimization challenges such as airline fleet planning and allocation of cloud computing resources. Solving exact cover requires the exploration of a solution space that increases exponentially with cardinality. Hence, it is time- and energy consuming to solve large instances of exact cover by serial computers. One approach to address these challenges is to utilize the inherent parallelism and high energy efficiency of biological systems in a network-based biocomputation (NBC) device. NBC is a parallel computing paradigm in which a given combinatorial problem is encoded into a graphical, modular network that is embedded in a nanofabricated planar device. The network is then explored in parallel using a large number of biological agents, such as molecular-motor-propelled protein filaments. The answer to the combinatorial problem can then be inferred by measuring the positions through which the agents exit the network. Here, we (i) show how exact cover can be encoded and solved in an NBC device, (ii) define a formalization that allows to prove the correctness of our approach and provides a mathematical basis for further studying NBC, and (iii) demonstrate various optimizations that significantly improve the computing performance of NBC. This work lays the ground for fabricating and scaling NBC devices to solve significantly larger combinatorial problems than have been demonstrated so far.

Garlic is a well-known example of natural self-defence system consisting of an inactive substrate (alliin) and enzyme (alliinase) which, when combined, produce highly antimicrobial allicin. Increase of alliinase stability and its activity are of paramount importance in various applications relying on its use for in-situ synthesis of allicin or its analogues, e.g., pulmonary drug delivery, treatment of superficial injuries, or urease inhibitors in fertilizers. Here, we discuss the effect of temperature, pH, buffers, salts, and additives, i.e. antioxidants, chelating agents, reducing agents and cosolvents, on the stability and the activity of alliinase extracted from garlic. The effects of the storage temperature and relative humidity on the stability of lyophilized alliinase was demonstrated. A combination of the short half-life, high reactivity and non-specificity to particular proteins are reasons most bacteria cannot deal with allicin’s mode of action and develop effective defence mechanism, which could be the key to sustainable drug design addressing serious problems with escalating emergence of multidrug-resistant (MDR) bacterial strains.

Quantitative modelling is increasingly important in cancer research, helping to integrate myriad diverse experimental data into coherent pictures of the disease and able to discriminate between competing hypotheses or suggest specific experimental lines of enquiry and new approaches to therapy. Here, we review a diverse set of mathematical models of cancer cell plasticity (a process in which, through genetic and epigenetic changes, cancer cells survive in hostile environments and migrate to more favourable environments, respectively), tumour growth, and invasion. Quantitative models can help to elucidate the complex biological mechanisms of cancer cell plasticity. In this review, we discuss models of plasticity, tumour progression, and metastasis under three broadly conceived mathematical modelling techniques: discrete, continuum, and hybrid, each with advantages and disadvantages. An emerging theme from the predictions of many of these models is that cell escape from the tumour microenvironment (TME) is encouraged by a combination of physiological stress locally (e.g., hypoxia), external stresses (e.g., the presence of immune cells), and interactions with the extracellular matrix. We also discuss the value of mathematical modelling for understanding cancer more generally.

Gas embolism is a rare but life-threatening process characterized by the presence of gas bubbles in the venous or arterial systems. These bubbles, if sufficiently large or numerous, can block the delivery of oxygen to critical organs, in particular the brain, and subsequently they can trigger a cascade of adverse biochemical reactions with severe medical outcomes. Despite its critical nature, gas embolism remains poorly understood, necessitating extensive investigation, particularly regarding its manifestations in the human body and its modulation by various biological conditions. However, given its elusive nature, as well as potential lethality, gas embolism is extremely difficult to study in vivo, and nearly impossible to be the subject of clinical trials. To this end, we developed a microfluidic device designed to study in vitro the impact of blood properties and vascular geometries on the formation and evolution of gas bubbles. The system features a biomimetic vascular channel surrounded by two pressure chambers, which induce the genesis of bubbles under varying circumstances. The bubble parameters were correlated with different input parameters, i.e., channel widths, wall thicknesses, viscosities of the artificial blood, and pressure levels. Smaller channel widths and higher equivalent hematocrit concentrations in synthetic blood solutions increased the nucleation density and bubble generation frequencies. Small channel widths were also more prone to bubble formation, with implications for the vulnerability of vascular walls, leading to increased risks of damage or compromise to the integrity of the blood vessels. Larger channel widths, along with higher equivalent hematocrit concentrations, translated into larger bubble volumes and decreased bubble velocities, leading to an increased risk of bubble immobilization within the blood vessels. This biomimetic approach provides insights into the impact of patient history and biological factors on the incidence and progression of gas embolism. Medical conditions, such as anemia, along with anatomical features related to age and sex—such as smaller blood vessels in women and children or larger vascular widths in adult men—affect the susceptibility to the initiation and progression of gas embolism, explored here in vitro through the development of a controlled, physiological-like environment. The analysis of the videos that recorded gas embolism events in vitro for systems where pressure is applied laterally on the microvasculature with thin walls, i.e., 50 μm or less, suggests that the mechanism of gas transfer for the pressure area to the blood is based on percolation, rather than diffusion. These findings highlight the importance of personalized approaches in the management and prevention of gas embolism.

All known algorithms to solve nondeterministic polynomial (NP) complete problems, relevant to many real-life applications, require the exploration of a space of potential solutions, which grows exponentially with the size of the problem. Since electronic computers can implement only limited parallelism, their use for solving NP-complete problems is impractical for very large instances, and consequently alternative massively parallel computing approaches were proposed to address this challenge. We present a scaling analysis of two such alternative computing approaches, DNA computing (DNA-C) and network biocomputing with agents (NB-C), compared with electronic computing (E-C). The Subset Sum Problem (SSP), a known NP-complete problem, was used as a computational benchmark, to compare the volume, the computing time, and the energy required for each type of computation, relative to the input size. Our analysis shows that the sequentiality of E-C translates in a very small volume compared to that required by DNA-C and NB-C, at the cost of the E-C computing time being outperformed first by DNA-C (linear run time), followed by NB-C. Finally, NB-C appears to be more energy-efficient than DNA-C for some types of input sets, while being less energy-efficient for others, with E-C being always an order of magnitude less energy efficient than DNA-C. This scaling study suggest that presently none of these computing approaches win, even theoretically, for all three key performance criteria, and that all require breakthroughs to overcome their limitations, with potential solutions including hybrid computing approaches.