Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens

Novel design of fractional cholesterol dynamics and drug concentrations model with analysis on machine predictive networks

Within the intricate fabric of human physiology, cholesterol, a lipid present in cell membranes exerts a discernible effect on the concentration of the drug in human body that influence the aspects of drug pharmacokinetics. The objective of this work is to design a case study based fractional order cholesterol drug interaction model that encapsulates the nuanced dynamics inherent in the multifaceted human physiology with identification of essential variables including drug concentration Ksb and cholesterol level γ. The strength of nonlinear autoregressive with exogenous inputs (NARX) neural networks are exploited to predict the temporal dynamics that reveal the hidden intricacies and subtle patterns within the fractional model. Grünwald-Letnikov (GL) based fractional solver is used to generate the synthetic data, serving as a robust foundation for training, testing and validation of the NARX neural networks for different use cases of cholesterol drug interaction control strategies. A thorough comparative analysis based on exhaustive simulation unveiled a marginal distinction between the results obtained from NARX and the outcomes of fractal technique showing remarkably low MSE in the range of 10-12. The strength of the designed methodology is further verified by using other performance metrics such as MSE, regression index, autocorrelation and cross correlation. The integration of genetic and genomic information tailor the model to address the unique characteristics of individual patient facilitating advancement in precision medicines.

Multifractal spectral features enhance classification of anomalous diffusion

Anomalous diffusion processes, characterized by their nonstandard scaling of the mean-squared displacement, pose a unique challenge in classification and characterization. In a previous study [Mangalam et al., Phys. Rev. Res. 5, 023144 (2023)2643-156410.1103/PhysRevResearch.5.023144], we established a comprehensive framework for understanding anomalous diffusion using multifractal formalism. The present study delves into the potential of multifractal spectral features for effectively distinguishing anomalous diffusion trajectories from five widely used models: fractional Brownian motion, scaled Brownian motion, continuous-time random walk, annealed transient time motion, and Lévy walk. We generate extensive datasets comprising 10^{6} trajectories from these five anomalous diffusion models and extract multiple multifractal spectra from each trajectory to accomplish this. Our investigation entails a thorough analysis of neural network performance, encompassing features derived from varying numbers of spectra. We also explore the integration of multifractal spectra into traditional feature datasets, enabling us to assess their impact comprehensively. To ensure a statistically meaningful comparison, we categorize features into concept groups and train neural networks using features from each designated group. Notably, several feature groups demonstrate similar levels of accuracy, with the highest performance observed in groups utilizing moving-window characteristics and p varation features. Multifractal spectral features, particularly those derived from three spectra involving different timescales and cutoffs, closely follow, highlighting their robust discriminatory potential. Remarkably, a neural network exclusively trained on features from a single multifractal spectrum exhibits commendable performance, surpassing other feature groups. In summary, our findings underscore the diverse and potent efficacy of multifractal spectral features in enhancing the predictive capacity of machine learning to classify anomalous diffusion processes.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Inferring characteristics of bacterial swimming in biofilm matrix from time-lapse confocal laser scanning microscopy

Biofilms are spatially organized communities of microorganisms embedded in a self-produced organic matrix, conferring to the population emerging properties such as an increased tolerance to the action of antimicrobials. It was shown that some bacilli were able to swim in the exogenous matrix of pathogenic biofilms and to counterbalance these properties. Swimming bacteria can deliver antimicrobial agents in situ, or potentiate the activity of antimicrobial by creating a transient vascularization network in the matrix. Hence, characterizing swimmer trajectories in the biofilm matrix is of particular interest to understand and optimize this new biocontrol strategy in particular, but also more generally to decipher ecological drivers of population spatial structure in natural biofilms ecosystems. In this study, a new methodology is developed to analyze time-lapse confocal laser scanning images to describe and compare the swimming trajectories of bacilli swimmers populations and their adaptations to the biofilm structure. The method is based on the inference of a kinetic model of swimmer populations including mechanistic interactions with the host biofilm. After validation on synthetic data, the methodology is implemented on images of three different species of motile bacillus species swimming in a Staphylococcus aureus biofilm. The fitted model allows to stratify the swimmer populations by their swimming behavior and provides insights into the mechanisms deployed by the micro-swimmers to adapt their swimming traits to the biofilm matrix.

Anyone who has ever cleaned a bathroom probably faced biofilms, the dark, slimy deposits that lurk around taps and pipes. These structures are created by bacteria which abandon their solitary lifestyle to work together as a community, secreting various substances that allow the cells to organise themselves in 3D and to better resist external aggression.

Unwanted biofilms can impair industrial operations or endanger health, for example when they form inside medical equipment or water supplies. Removing these structures usually involves massive application of substances which can cause long-term damage to the environment.

Recently, researchers have observed that a range of small rod-shaped bacteria – or ‘bacilli’ – can penetrate a harmful biofilm and dig transient tunnels in its 3D structure. These ‘swimmers’ can enhance the penetration of anti-microbial agents, or could even be modified to deliver these molecules right inside the biofilm. However, little is known about how the various types of bacilli, which have very different shapes and propelling systems, can navigate the complex environment that is a biofilm. This knowledge would be essential for scientists to select which swimmers could be the best to harness for industrial and medical applications.

To investigate this question, Ravel et al. established a way to track how three species of bacilli swim inside a biofilm compared to in a simple fluid. A mathematical model was created which integrated several swimming behaviors such as speed adaptation and direction changes in response to the structure and density of the biofilm. This modelling was then fitted on microscopy images of the different species navigating the two types of environments.

Different motion patterns for the three bacilli emerged, each showing different degrees of adapting to moving inside a biofilm. One species, in particular, was able to run straight in and out of this environment because it could adapt its speed to the biofilm density as well as randomly change direction.

The new method developed by Ravel et al. can be redeployed to systematically study swimmer candidates in different types of biofilms. This would allow scientists to examine how various swimming characteristics impact how bacteria-killing chemicals can penetrate the altered biofilms. In addition, as the mathematical model can predict trajectories, it could be used in computational studies to examine which species of bacilli would be best suited in industrial settings.

What Is the Trait d’Union between Retroactivity and Molecular Communication Performance Limits?

Information exchange is a critical process in all communication systems, including biological ones. Retroactivity describes the load that downstream modules apply to their upstream systems in biological circuits. The motivation behind this work is that of integrating retroactivity, a concept proper of biochemical circuits, with the metrics defined in Information Theory and Digital Communications. This paper focuses on studying the impact of retroactivity on different biological signaling system models, which present analogies with well-known telecommunication systems. The mathematical analysis is performed both in the high and low molecular counts regime, by mean of the Chemical Master Equation and the Linear Noise Approximation, respectively. The main goal of this work is to provide analytical tools to maximize the reliable information exchange across different biomolecular circuit models. Results highlight how, in general, retroactivity harms communication performance. This negative effect can be mitigated by adding to the signaling circuit an independent upstream system that connects with the same pool of downstream circuits.

Roles of Remote and Contact Forces in Epithelial Cell Structure Formation

Cancer cells collectively form a large-scale structure for their growth. In this article, we report that HeLa cells, epithelial-like human cervical cancer cells, aggressively migrate on Matrigel and form a large-scale structure in a cell-density-dependent manner. To explain the experimental results, we develop a simple model in which cells interact and migrate using the two fundamentally different types of force, remote and contact forces, and show how cells form a large-scale structure. We demonstrate that the simple model reproduces experimental observations, suggesting that the remote and contact forces considered in this work play a major role in large-scale structure formation of HeLa cells. This article provides important evidence that cancer cells form a large-scale structure and develops an understanding into the poorly understood mechanisms of their structure formation.

Quantifying emergence and self-organisation of Enterobacter cloacae microbial communities

From microbial communities to cancer cells, many such complex collectives embody emergent and self-organising behaviour. Such behaviour drives cells to develop composite features such as formation of aggregates or expression of specific genes as a result of cell-cell interactions within a cell population. Currently, we lack universal mathematical tools for analysing the collective behaviour of biological swarms. To address this, we propose a multifractal inspired framework to measure the degree of emergence and self-organisation from scarce spatial (geometric) data and apply it to investigate the evolution of the spatial arrangement of Enterobacter cloacae aggregates. In a plate of semi-solid media, Enterobacter cloacae form a spatially extended pattern of high cell density aggregates. These aggregates nucleate from the site of inoculation and radiate outward to fill the entire plate. Multifractal analysis was used to characterise these patterns and calculate dynamics changes in emergence and self-organisation within the bacterial population. In particular, experimental results suggest that the new aggregates align their location with respect to the old ones leading to a decrease in emergence and increase in self-organisation.

Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?