Foraging success under uncertainty: search tradeoffs and optimal space use

Understanding the structural complexity and the main drivers of animal search behaviour is pivotal to foraging ecology. Yet, the role of uncertainty as a generative mechanism of movement patterns is poorly understood. Novel insights from search theory suggest that organisms should collect and assess new information from the environment by producing complex exploratory strategies. Based on an extension of the first passage time theory, and using simple equations and simulations, we unveil the elementary heuristics behind search behaviour. In particular, we show that normal diffusion is not enough for determining optimal exploratory behaviour but anomalous diffusion is required. Searching organisms go through two critical sequential phases (approach and detection) and experience fundamental search tradeoffs that may limit their encounter rates. Using experimental data, we show that biological search includes elements not fully considered in contemporary physical search theory. In particular, the need to consider search movement as a non‐stationary process that brings the organism from one informational state to another. For example, the transition from remaining in an area to departing from it may occur through an exploratory state where cognitive search is challenged. Therefore, a more comprehensive view of foraging ecology requires including current perspectives about movement under uncertainty.     

Monte Carlo Simulation of Tetrahedral Chains II: Properties of “First Self-avoiding Walks” and their Usability as Starting Configurations for Dynamic Relaxation Mechanisms

Very long model chains may be produced in a highly efficient manner using dynamic Monte Carlo methods. As any dynamic Monte Carlo procedure transforms one chain into another one, some starting configuration is necessary. This might be an unbiased self-avoiding walk (SAW) obtained by any static method, or an arbitrary configuration, e.g. a rodlike chain, equilibrated by a sufficiently large number of relaxations, the corresponding chains not being used for data sampling. An alternative method is to start with a non reversal random walk (NRRW) and to apply a dynamic Monte Carlo procedure under the constraint that the new chain must have a smaller (or at least an equal) number of double occupancies than the old one. The properties of those chains that are free of overlaps for the first time (FSAWs) are strongly dependent on the relaxation mechanism chosen. Whereas FSAWs obtained by local motions are very similar to the (initial) NRRWs on a macroscopic scale, pivot algorithms and reptation yield configurations with properties comparable to unbiased self-avoiding chains. When reptation is used and the relaxation is continued until each bond of the initial NRRW is replaced by a new bond (if the chain is self-avoiding earlier) no further equilibration is necessary prior to data sampling.     

High accuracy 3D quantum dot tracking with multifocal plane microscopy for the study of fast intracellular dynamics in live cells

Single particle tracking in three dimensions in a live cell environment holds the promise of revealing important new biological insights. However, conventional microscopy-based imaging techniques are not well suited for fast three-dimensional (3D) tracking of single particles in cells. Previously we developed an imaging modality multifocal plane microscopy (MUM) to image fast intracellular dynamics in three dimensions in live cells. Here, we introduce an algorithm, the MUM localization algorithm (MUMLA), to determine the 3D position of a point source that is imaged using MUM. We validate MUMLA through simulated and experimental data and show that the 3D position of quantum dots can be determined over a wide spatial range. We demonstrate that MUMLA indeed provides the best possible accuracy with which the 3D position can be determined. Our analysis shows that MUM overcomes the poor depth discrimination of the conventional microscope, and thereby paves the way for high accuracy tracking of nanoparticles in a live cell environment. Here, using MUM and MUMLA we report for the first time the full 3D trajectories of QD-labeled antibody molecules undergoing endocytosis in live cells from the plasma membrane to the sorting endosome deep inside the cell.     

A spatio-temporal mining approach towards summarizing and analyzing protein folding trajectories

Understanding the protein folding mechanism remains a grand challenge in structural biology. In the past several years, computational theories in molecular dynamics have been employed to shed light on the folding process. Coupled with high computing power and large scale storage, researchers now can computationally simulate the protein folding process in atomistic details at femtosecond temporal resolution. Such simulation often produces a large number of folding trajectories, each consisting of a series of 3D conformations of the protein under study. As a result, effectively managing and analyzing such trajectories is becoming increasingly important.     

The microenvironmental determinants for kidney epithelial cyst morphogenesis

Although epithelial morphogenesis is tightly controlled by intrinsic genetic programs, the microenvironment in which epithelial cells proliferate and differentiate also contributes to the morphogenetic process. The roles of the physical microenvironment in epithelial morphogenesis, however, have not been well dissected. In this study, we assessed the impact of the microenvironment on epithelial cyst formation, which often marks the beginning or end step of morphogenesis of epithelial tissues and the pathological characteristic of some diseases. Previous studies have demonstrated that Madin-Darby canine kidney (MDCK) epithelial cells form cysts when grown in a three-dimensional (3D) extracellullar matrix (ECM) environment. We have now further demonstrated that the presence of ECM in the 3D scaffold is required for the formation of properly polarized cysts. Also, we have found that the full interface of epithelial cells with the ECM environment (in-3D) is not essential for cyst formation, since partial contact (on-3D) is sufficient to induce cystogenesis. In addition, we have defined the minimal ECM environment or the physical threshold for cystogenesis under the on-3D condition. Only above the threshold can the morphological cues from the ECM environment induce cyst formation. Moreover, cyst formation under the on-3D condition described in this study defines a novel and more feasible model to analyze in vitro morphogenesis. Finally, we have found that, during cystogenesis, MDCK cells generate basal microprotrusions and produce vesicle-like structures to the basal extracellular space, which are specific to and correlated with cyst formation. For the first time, we have systematically and quantitatively elucidated the microenvironmental determinants for epithelial cystogenesis.     

Molecular dynamics of substrate complexes with hamster cytochrome P450c17 (CYP17): mechanistic approach to understanding substrate binding and activities

The cytochrome P450c17 isoforms from various animal species have different substrate selectivity, especially for 17,20-lyase activity. In particular, the human P450c17 selectively produces dehydroepiandrosterone with little androstenedione (AD). Hamster P450c17, on the other hand, produces both of these steroids at comparable rates. We thus investigated if computational analysis could explain the difference in activity profiles. Therefore, we inserted the four P450c17 substrates-pregnenolone, progesterone, and their 17alpha-hydroxylated forms-inside our hamster P450c17 model, which we derived from our human P450c17 model based on the crystal structure of P450BMP. We performed molecular dynamics (MD) simulations on the complexes and analyzed the resultant trajectories to identify amino acids that interact with substrates. Starting with substrates in two different orientations, we obtained two sets of binding trajectories in each case. The first set of trajectories reveal structural rearrangements that occur during binding, whereas the second set of trajectories reflects substrate orientations during catalysis. Our modeling suggests that three distinct steps are required for substrate selectivity and binding to the hamster P450c17: (1) recognition of the substrate at the putative substrate entrance, characterized by a pocket at the surface of the hamster P450c17 containing charged residues R96 and D116; (2) entry of the substrate into the active site, in an intermediate position directed by possible hydrogen bonding of the substrates with the heme D-ring propionate group, R96, R440, and T306; followed by (3) 90 degrees counterclockwise rotation of the substrates, positioning them in optimal position for reactivity, a process that may be directed by hydrogen bonding to the 110-112 region of the hamster P450c17. With some substrates, we obtained trajectories which suggest that major distortions in the I-helix and opening of the H-I loop occur during substrate binding. In conclusion, these modeling exercises provide insight to possible structural reorganizations that occur during substrate binding and suggest that amino acids that participate in three distinct steps of this process may all contribute to substrate binding and activity.     

Plasma 24,25-dihydroxyvitamin D concentration of Dahl salt-sensitive rats decreases during high salt intake

Dahl salt-sensitive rats, but not salt-resistant rats, develop hypertension in response to high salt intake. We have previously shown an inverse relationship between plasma 25-hydroxyvitamin D (25-OHD) concentration and blood pressure of Dahl salt-sensitive rats during high salt intake. In this study, we report on the relationship between high salt intake and plasma 24,25-dihydroxyvitamin D (24,25-(OH)(2)D) concentration of Dahl salt-sensitive and salt-resistant rats. Rats were fed a high salt diet (8%) and sacrificed at day 2, 7, 14, 21, and 28. Plasma 24,25-(OH)(2)D concentrations of salt-sensitive rats were reduced to 50% of that at baseline at day 2-when blood pressure and plasma 25-OHD concentration were unchanged, but 25-OHD content in the kidney was 81% of that at baseline. Plasma 24,25-(OH)(2)D concentration was reduced further to 10% of that at baseline from day 7 to 14 of high salt intake, a reduction that was prevented in rats switched to a low salt (0.3%) diet at day 7. Exogenous 24,25-dihydroxycholecalciferol (24,25-(OH)(2)D(3)), administered at a level that increased plasma 24,25-(OH)(2)D concentration to five times normal, did not attenuate the salt-induced hypertension of salt-sensitive rats. Plasma 24,25-(OH)(2)D concentration of salt-resistant rats was gradually reduced to 50% of that at baseline at day 14 and returned to baseline value at day 28 of high salt intake. We conclude that the decrease in plasma 24,25-(OH)(2)D concentration in salt-sensitive rats during high salt intake is caused by decreased 25-OHD content in the kidney and also by another unidentified mechanism.     

Prediction of Three-Dimensional Arm Trajectories Based on ECoG Signals Recorded from Human Sensorimotor Cortex

Brain-machine interface techniques have been applied in a number of studies to control neuromotor prostheses and for neurorehabilitation in the hopes of providing a means to restore lost motor function. Electrocorticography (ECoG) has seen recent use in this regard because it offers a higher spatiotemporal resolution than non-invasive EEG and is less invasive than intracortical microelectrodes. Although several studies have already succeeded in the inference of computer cursor trajectories and finger flexions using human ECoG signals, precise three-dimensional (3D) trajectory reconstruction for a human limb from ECoG has not yet been achieved. In this study, we predicted 3D arm trajectories in time series from ECoG signals in humans using a novel preprocessing method and a sparse linear regression. Average Pearson’s correlation coefficients and normalized root-mean-square errors between predicted and actual trajectories were 0.44∼0.73 and 0.18∼0.42, respectively, confirming the feasibility of predicting 3D arm trajectories from ECoG. We foresee this method contributing to future advancements in neuroprosthesis and neurorehabilitation technology.     

Quantitative underwater 3D motion analysis using submerged video cameras: accuracy analysis and trajectory reconstruction

In this study we aim at investigating the applicability of underwater 3D motion capture based on submerged video cameras in terms of 3D accuracy analysis and trajectory reconstruction. Static points with classical direct linear transform (DLT) solution, a moving wand with bundle adjustment and a moving 2D plate with Zhang's method were considered for camera calibration. As an example of the final application, we reconstructed the hand motion trajectories in different swimming styles and qualitatively compared this with Maglischo's model. Four highly trained male swimmers performed butterfly, breaststroke and freestyle tasks. The middle fingertip trajectories of both hands in the underwater phase were considered. The accuracy (mean absolute error) of the two calibration approaches (wand: 0.96 mm – 2D plate: 0.73 mm) was comparable to out of water results and highly superior to the classical DLT results (9.74 mm). Among all the swimmers, the hands' trajectories of the expert swimmer in the style were almost symmetric and in good agreement with Maglischo's model. The kinematic results highlight symmetry or asymmetry between the two hand sides, intra- and inter-subject variability in terms of the motion patterns and agreement or disagreement with the model. The two outcomes, calibration results and trajectory reconstruction, both move towards the quantitative 3D underwater motion analysis.     

Ultra High Content Image Analysis and Phenotype Profiling of 3D Cultured Micro-Tissues

In many situations, 3D cell cultures mimic the natural organization of tissues more closely than 2D cultures. Conventional methods for phenotyping such 3D cultures use either single or multiple simple parameters based on morphology and fluorescence staining intensity. However, due to their simplicity many details are not taken into account which limits system-level study of phenotype characteristics. Here, we have developed a new image analysis platform to automatically profile 3D cell phenotypes with 598 parameters including morphology, topology, and texture parameters such as wavelet and image moments. As proof of concept, we analyzed mouse breast cancer cells (4T1 cells) in a 384-well plate format following exposure to a diverse set of compounds at different concentrations. The result showed concentration dependent phenotypic trajectories for different biologically active compounds that could be used to classify compounds based on their biological target. To demonstrate the wider applicability of our method, we analyzed the phenotypes of a collection of 44 human breast cancer cell lines cultured in 3D and showed that our method correctly distinguished basal-A, basal-B, luminal and ERBB2+ cell lines in a supervised nearest neighbor classification method.     

Tracking sperm in three-dimensions

Sperm motility, crucial for fertilization, has been mostly studied in two dimensions (2D) by recording their swimming trajectories near a flat surface. However, spermatozoa swim in three-dimensions (3D) to find eggs, with their speed being the main impediment to track them under realistic conditions. Here, we describe a novel method allowing 3D tracking and analysis of the trajectories of multiple free-swimming sperm. The system uses a piezo-electric device displacing a large focal distance objective mounted on a microscope to acquire 70 image stacks per second, each stack composed of 60 images that span a depth of 100 μm. With this method, 3D paths of multiple sperm in the same field could be visualized simultaneously during 1 s . Within the same sample we found that surface-confined sperm swam 25% slower, produced 3-fold fewer circular revolutions per second, and had trajectories of 134% greater radius of curvature than those sperm swimming freely in 3D.     

A 3D pattern matching algorithm for DNA sequences

MOTIVATION: Biologists usually work with textual DNA sequences (succession of A, C, G and T). This representation allows biologists to study the syntax and other linguistic properties of DNA sequences. Nevertheless, such a linear coding offers only a local and a one-dimensional vision of the molecule. The 3D structure of DNA is known to be very important in many essential biological mechanisms. By using 3D conformation models, one is able to construct a 3D trajectory of a naked DNA molecule. From the various studies that we performed, it turned out that two very different textual DNA sequences could have similar 3D structures. RESULTS: In this article, we address a new research work on 3D pattern matching for DNA sequences. The aim of this work is to enhance conventional pattern matching analyses with 3D-augmented criteria. We have developed an algorithm, based on 3D trajectories, which compares angles formed by these trajectories and thus quantifies the difference between two 3D DNA sequences. This analysis performs from a global scale to al local one. AVAILABILITY: Available on request from the authors.     

The influence of turning angles on the success of non-oriented animal searches

Animal searches cover a full range of possibilities from highly deterministic to apparently completely random behaviors. However, even those stochastic components of animal movement can be adaptive, since not all random distributions lead to similar success in finding targets. Here we address the general problem of optimizing encounter rates in non-deterministic, non-oriented searches, both in homogeneous and patchy target landscapes. Specifically, we investigate how two different features related to turning angle distributions influence encounter success: (i) the shape (relative kurtosis) of the angular distribution and (ii) the correlations between successive relative orientations (directional memory). Such influence is analyzed in correlated random walk models using a proper choice of representative turning angle distributions of the recently proposed Jones and Pewsey class. We consider the cases of distributions with nearly the same shape but considerably distinct correlation lengths, and distributions with same correlation but with contrasting relative kurtosis. In homogeneous landscapes, we find that the correlation length has a large influence in the search efficiency. Moreover, similar search efficiencies can be reached by means of distinctly shaped turning angle distributions, provided that the resulting correlation length is the same. In contrast, in patchy landscapes the particular shape of the distribution also becomes relevant for the search efficiency, specially at high target densities. Excessively sharp distributions generate very inefficient searches in landscapes where local target density fluctuations are large. These results are of evolutionary interest. On the one hand, it is shown that equally successful directional memory can arise from contrasting turning behaviors, therefore increasing the likelihood of robust adaptive stochastic behavior. On the other hand, when target landscape is patchy, adequate tumbling may help to explore better local scale heterogeneities, being some details of the shape of the distribution also potentially adaptive.     

Platelet-Derived Growth Factors-BB and Fibroblast Growth Factors-Base Induced Proliferation of Schwann Cells in a 3D Environment

The proliferation of neonatal Schwann cells (SCs) in response to mitogenic agents has been well analyzed in vitro (mono-layer-culture method, 2D environment), but not in vivo (3D environment). To assess the mitogenic effect of platelet-derived growth factors-BB (PDGF-BB), Fibroblast Growth Factors-base (bFGF), and their combinations for SCs in collagen gel (three-dimensional, 3D environment), we have developed an integrated microfluidic device on which can reproducibly measure the proliferation from small number of cells (1–100). The rat SCs were cultured for 4 week at the different concentrations of growth factors generated by concentration gradient generator. In the collagen gel culture, almost all of the cells in colonies presented a round cell morphology and maintained their round morphology by the 4th week. The results showed that PDGF-BB and bFGF are all capable of moderately stimulating SCs growth and every group reached the peak in the growth curve at 3 weeks. Moreover, the proliferation test using the conventional method was performed simultaneously and revealed similar results. The biggest difference between 2D and 3D was that cells decrease more remarkable in 3D than that in 2D at 4 weeks. And at 2 and 3 weeks, the growth rate in the collagen gel with 7.14/2.86 and 8.57/1.43 ng/mL groups was higher than that in the mono-layer culture. Our results showed that PDGF-BB and bFGF are capable of moderately stimulating neonatal SCs growth, respectively and synergistically, and the microfluidic technique is highly controllable, contamination free, fully automatic, and inexpensive.     

Extracting the Stepping Dynamics of Molecular Motors in Living Cells from Trajectories of Single Particles

Molecular motors are responsible of transporting a wide variety of cargos in the cytoplasm. Current efforts are oriented to characterize the biophysical properties of motors in cells with the aim of elucidating the mechanisms of these nanomachines in the complex cellular environment. In this study, we present an algorithm designed to extract motor step sizes and dwell times between steps from trajectories of motors or cargoes driven by motors in cells. The algorithm is based on finding patterns in the trajectory compatible with the behavior expected for a motor step, i.e., a region of confined motion followed by a jump in the position to another region of confined motion with similar characteristics to the previous one. We show that this algorithm allows the analysis of 2D trajectories even if they present complex motion patterns such as active transport interspersed with diffusion and does not require the assumption of a given step size or dwell period. The confidence on the step detection can be easily obtained and allows the evaluation of the confidence of the dwell and step size distributions. To illustrate the possible applications of this algorithm, we analyzed trajectories of myosin-V driven organelles in living cells.     

System for measuring oxygen consumption rates of mammalian cells in static culture under hypoxic conditions

Estimating the oxygen consumption rates (OCRs) of mammalian cells in hypoxic environments is essential for designing and developing a three‐dimensional (3‐D) cell culture system. However, OCR measurements under hypoxic conditions are infrequently reported in the literature. Here, we developed a system for measuring OCRs at low oxygen levels. The system injects nitrogen gas into the environment and measures the oxygen concentration by an optical oxygen microsensor that consumes no oxygen. The developed system was applied to HepG2 cells in static culture. Specifically, we measured the spatial profiles of the local dissolved oxygen concentration in the medium, then estimated the OCRs of the cells. The OCRs, and also the pericellular oxygen concentrations, decreased nonlinearly as the oxygen partial pressure in the environment decreased from 19% to 1%. The OCRs also depended on the culture period and the matrix used for coating the dish surface. Using this system, we can precisely estimate the OCRs of various cell types under environments that mimic 3‐D culture conditions, contributing crucial data for an efficient 3‐D culture system design. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 32:189–197, 2016     

A multiphysics 3D model of tissue growth under interstitial perfusion in a tissue-engineering bioreactor

The main challenge in engineered cartilage consists in understanding and controlling the growth process towards a functional tissue. Mathematical and computational modelling can help in the optimal design of the bioreactor configuration and in a quantitative understanding of important culture parameters. In this work, we present a multiphysics computational model for the prediction of cartilage tissue growth in an interstitial perfusion bioreactor. The model consists of two separate sub-models, one two-dimensional (2D) sub-model and one three-dimensional (3D) sub-model, which are coupled between each other. These sub-models account both for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Navier–Stokes equation, the mass transport equation and the biomass growth. The biomass, assumed as a phase comprising cells and the synthesised extracellular matrix, has been modelled by using a moving boundary approach. In particular, the boundary at the fluid–biomass interface is moving with a velocity depending from the local oxygen concentration and viscous stress. In this work, we show that all parameters predicted, such as oxygen concentration and wall shear stress, by the 2D sub-model with respect to the ones predicted by the 3D sub-model are systematically overestimated and thus the tissue growth, which directly depends on these parameters. This implies that further predictive models for tissue growth should take into account of the three dimensionality of the problem for any scaffold microarchitecture.     

Nucleation causes an actin network to fragment into multiple high-density domains

Actin networks rely on nucleation mechanisms to generate new filaments because spontaneous nucleation is kinetically disfavored. Branching nucleation of actin filaments by actin-related protein (Arp2/3), in particular, is critical for actin self-organization. In this study, we use the simulation platform for active matter MEDYAN to generate 2000 s long stochastic trajectories of actin networks, under varying Arp2/3 concentrations, in reaction volumes of biologically meaningful size (>20 μm³). We find that the dynamics of Arp2/3 increase the abundance of short filaments and increases network treadmilling rate. By analyzing the density fields of F-actin, we find that at low Arp2/3 concentrations, F-actin is organized into a single connected and contractile domain, while at elevated Arp2/3 levels (10 nM and above), such high-density actin domains fragment into smaller domains spanning a wide range of volumes. These fragmented domains are extremely dynamic, continuously merging and splitting, owing to the high treadmilling rate of the underlying actin network. Treating the domain dynamics as a drift-diffusion process, we find that the fragmented state is stochastically favored, and the network state slowly drifts toward the fragmented state with considerable diffusion (variability) in the number of domains. We suggest that tuning the Arp2/3 concentration enables cells to transition from a globally coherent cytoskeleton, whose response involves the entire cytoplasmic network, to a fragmented cytoskeleton, where domains can respond independently to locally varying signals.     

Evolution of robustness to damage in artificial 3-dimensional development

GReaNs is an Artificial Life platform we have built to investigate the general principles that guide evolution of multicellular development and evolution of artificial gene regulatory networks. The embryos develop in GReaNs in a continuous 3-dimensional (3D) space with simple physics. The developmental trajectories are indirectly encoded in linear genomes. The genomes are not limited in size and determine the topology of gene regulatory networks that are not limited in the number of nodes. The expression of the genes is continuous and can be modified by adding environmental noise. In this paper we evolved development of structures with a specific shape (an ellipsoid) and asymmetrical pattering (a 3D pattern inspired by the French flag problem), and investigated emergence of the robustness to damage in development and the emergence of the robustness to noise. Our results indicate that both types of robustness are related, and that including noise during evolution promotes higher robustness to damage. Interestingly, we have observed that some evolved gene regulatory networks rely on noise for proper behaviour.