Table of contents

This paper concerns the identification of gene co-expression modules in transcriptomics data, i.e. collections of genes which are highly co-expressed and potentially linked to a biological mechanism. Weighted gene co-expression network analysis (WGCNA) is a widely used method for module detection based on the computation of eigengenes, the weights of the first principal component for the module gene expression matrix. This eigengene has been used as a centroid in a k-means algorithm to improve module memberships. In this paper, we present four new module representatives: the eigengene subspace, flag mean, flag median and module expression vector. The eigengene subspace, flag mean and flag median are subspace module representatives which capture more variance of the gene expression within a module. The module expression vector is a weighted centroid of the module which leverages the structure of the module gene co-expression network. We use these module representatives in Linde–Buzo–Gray clustering algorithms to refine WGCNA module membership. We evaluate these methodologies on two transcriptomics data sets. We find that most of our module refinement techniques improve upon the WGCNA modules by two statistics: (1) module classification between phenotype and (2) module biological significance according to Gene Ontology terms.

While moving, animals must frequently make decisions about their future travel direction, whether they are alone or in a group. Here we investigate this process for zebrafish (Danio rerio), which naturally move in cohesive groups. Employing state-of-the-art virtual reality, we study how real fish (RF) follow one or several moving, virtual conspecifics (leaders). These data are used to inform, and test, a model of social response that includes a process of explicit decision-making, whereby the fish can decide which of the virtual conspecifics to follow, or to follow in some average direction. This approach is in contrast with previous models where the direction of motion was based on a continuous computation, such as directional averaging. Building upon a simplified version of this model (Sridhar et al 2021 Proc. Natl Acad. Sci.118 e2102157118), which was limited to a one-dimensional projection of the fish motion, we present here a model that describes the motion of the RF as it swims freely in two-dimensions. Motivated by experimental observations, the swim speed of the fish in this model uses a burst-and-coast swimming pattern, with the burst frequency being dependent on the distance of the fish from the followed conspecific(s). We demonstrate that this model is able to explain the observed spatial distribution of the RF behind the virtual conspecifics in the experiments, as a function of their average speed and number. In particular, the model naturally explains the observed critical bifurcations for a freely swimming fish, which appear in the spatial distributions whenever the fish makes a decision to follow only one of the virtual conspecifics, instead of following them as an averaged group. This model can provide the foundation for modeling a cohesive shoal of swimming fish, while explicitly describing their directional decision-making process at the individual level.

Social animals can use the choices made by other members of their groups as cues in decision making. Individuals must balance the private information they receive from their own sensory cues with the social information provided by observing what others have chosen. These two cues can be integrated using decision making rules, which specify the probability to select one or other options based on the quality and quantity of social and non-social information. Previous empirical work has investigated which decision making rules can replicate the observable features of collective decision making, while other theoretical research has derived forms for decision making rules based on normative assumptions about how rational agents should respond to the available information. Here we explore the performance of one commonly used decision making rule in terms of the expected decision accuracy of individuals employing it. We show that parameters of this model which have typically been treated as independent variables in empirical model-fitting studies obey necessary relationships under the assumption that animals are evolutionarily optimised to their environment. We further investigate whether this decision making model is appropriate to all animal groups by testing its evolutionary stability to invasion by alternative strategies that use social information differently, and show that the likely evolutionary equilibrium of these strategies depends sensitively on the precise nature of group identity among the wider population of animals it is embedded within.

Spatial patterning of different cell types is crucial for tissue engineering and is characterized by the formation of sharp boundary between segregated groups of cells of different lineages. The cell−cell boundary layers, depending on the relative adhesion forces, can result in kinks in the border, similar to fingering patterns between two viscous partially miscible fluids which can be characterized by its fractal dimension. This suggests that mathematical models used to analyze the fingering patterns can be applied to cell migration data as a metric for intercellular adhesion forces. In this study, we develop a novel computational analysis method to characterize the interactions between blood endothelial cells (BECs) and lymphatic endothelial cells (LECs), which form segregated vasculature by recognizing each other through podoplanin. We observed indiscriminate mixing with LEC−LEC and BEC−BEC pairs and a sharp boundary between LEC−BEC pair, and fingering-like patterns with pseudo-LEC−BEC pairs. We found that the box counting method yields fractal dimension between 1 for sharp boundaries and 1.3 for indiscriminate mixing, and intermediate values for fingering-like boundaries. We further verify that these results are due to differential affinity by performing random walk simulations with differential attraction to nearby cells and generate similar migration pattern, confirming that higher differential attraction between different cell types result in lower fractal dimensions. We estimate the characteristic velocity and interfacial tension for our simulated and experimental data to show that the fractal dimension negatively correlates with capillary number (Ca), further indicating that the mathematical models used to study viscous fingering pattern can be used to characterize cell−cell mixing. Taken together, these results indicate that the fractal analysis of segregation boundaries can be used as a simple metric to estimate relative cell−cell adhesion forces between different cell types.

In this paper, we reconsider the spin model suggested recently to understand some features of collective decision making among higher organisms (Hartnett et al 2016 Phys. Rev. Lett.116 038701). Within the model, the state of an agent i is described by the pair of variables corresponding to its opinion $S_i = \pm 1$ and a bias ω_i toward any of the opposing values of S_i. Collective decision making is interpreted as an approach to the equilibrium state within the nonlinear voter model subject to a social pressure and a probabilistic algorithm. Here, we push such a physical analogy further and give the statistical physics interpretation of the model, describing it in terms of the Hamiltonian of interaction and looking for the equilibrium state via explicit calculation of its partition function. We show that, depending on the assumptions about the nature of social interactions, two different Hamiltonians can be formulated, which can be solved using different methods. In such an interpretation the temperature serves as a measure of fluctuations, not considered before in the original model. We find exact solutions for the thermodynamics of the model on the complete graph. The general analytical predictions are confirmed using individual-based simulations. The simulations also allow us to study the impact of system size and initial conditions on the collective decision making in finite-sized systems, in particular, with respect to convergence to metastable states.

Recently, there has been an increasing need for tools to simulate cell size regulation due to important applications in cell proliferation and gene expression. However, implementing the simulation usually presents some difficulties, as the division has a cycle-dependent occurrence rate. In this article, we gather a recent theoretical framework in PyEcoLib, a python-based library to simulate the stochastic dynamics of the size of bacterial cells. This library can simulate cell size trajectories with an arbitrarily small sampling period. In addition, this simulator can include stochastic variables, such as the cell size at the beginning of the experiment, the cycle duration timing, the growth rate, and the splitting position. Furthermore, from a population perspective, the user can choose between tracking a single lineage or all cells in a colony. They can also simulate the most common division strategies (adder, timer, and sizer) using the division rate formalism and numerical methods. As an example of PyecoLib applications, we explain how to couple size dynamics with gene expression predicting, from simulations, how the noise in protein levels increases by increasing the noise in division timing, the noise in growth rate and the noise in cell splitting position. The simplicity of this library and its transparency about the underlying theoretical framework yield the inclusion of cell size stochasticity in complex models of gene expression.

Conventionally, only the normal cell membrane fluctuations have been studied and used to ascertain membrane properties like the bending rigidity. A new concept, the membrane local slope fluctuations was introduced recently (Vaippully et al 2020 Soft Matter16 7606), which can be modelled as a gradient of the normal fluctuations. It has been found that the power spectral density (PSD) of slope fluctuations behave as (frequency)⁻¹ while the normal fluctuations yields (frequency)$^{-5/3}$ even on the apical cell membrane in the high frequency region. In this manuscript, we explore a different situation where the cell is applied with the drug Latrunculin-B which inhibits actin polymerization and find the effect on membrane fluctuations. We find that even as the normal fluctuations show a power law (frequency)$^{-5/3}$ as is the case for a free membrane, the slope fluctuations PSD remains (frequency)⁻¹, with exactly the same coefficient as the case when the drug was not applied. Moreover, while sometimes, when the normal fluctuations at high frequency yield a power law of (frequency)$^{-4/3}$, the pitch PSD still yields (frequency)⁻¹. Thus, this presents a convenient opportunity to study membrane parameters like bending rigidity as a function of time after application of the drug, while the membrane softens. We also investigate the active athermal fluctuations of the membrane appearing in the PSD at low frequencies and find active timescales of slower than 1 s.

The output of the bacterial chemotaxis signaling pathway, the level of the intracellular regulator CheY-P, modulates the rotation direction of the flagellar motor, thereby regulating bacterial run-and-tumble behavior. The multiple flagellar motors on an E. coli cell are controlled by a common cytoplasmic pool of CheY-P. Fluctuation of the CheY-P level was thought to be able to coordinate the switching of multiple motors. Here, we measured the correlation of rotation directions between two motors on a cell, finding that it surprisingly exhibits two well separated timescales. We found that the slow timescale (∼6 s) can be explained by the slow fluctuation of the CheY-P level due to stochastic activity of the chemotactic adaptation enzymes, whereas the fast timescale (∼0.3 s) can be explained by the random pulse-like fluctuation of the CheY-P level, due probably to the activity of the chemoreceptor clusters. We extracted information on the properties of the fast CheY-P pulses based on the correlation measurements. The two well-separated timescales in the fluctuation of CheY-P level help to coordinate multiple motors on a cell and to enhance bacterial chemotactic performance.

The network-shaped body plan distinguishes the unicellular slime mould Physarum polycephalum in body architecture from other unicellular organisms. Yet, network-shaped body plans dominate branches of multi-cellular life such as in fungi. What survival advantage does a network structure provide when facing a dynamic environment with adverse conditions? Here, we probe how network topology impacts P. polycephalum's avoidance response to an adverse blue light. We stimulate either an elongated, I-shaped amoeboid or a Y-shaped networked specimen and subsequently quantify the evacuation process of the light-exposed body part. The result shows that Y-shaped specimen complete the avoidance retraction in a comparable time frame, even slightly faster than I-shaped organisms, yet, at a lower almost negligible increase in migration velocity. Contraction amplitude driving mass motion is further only locally increased in Y-shaped specimen compared to I-shaped—providing further evidence that Y-shaped's avoidance reaction is energetically more efficient than in I-shaped amoeboid organisms. The difference in the retraction behaviour suggests that the complexity of network topology provides a key advantage when encountering adverse environments. Our findings could lead to a better understanding of the transition from unicellular to multicellularity.

The mechanisms by which a protein's 3D structure can be determined based on its amino acid sequence have long been one of the key mysteries of biophysics. Often simplistic models, such as those derived from geometric constraints, capture bulk real-world 3D protein-protein properties well. One approach is using protein contact maps (PCMs) to better understand proteins' properties. In this study, we explore the emergent behaviour of contact maps for different geometrically constrained models and compare them to real-world protein systems. Specifically, we derive an analytical approximation for the distribution of amino acid distances, denoted as P(s), using a mean-field approach based on a geometric constraint model. This approximation is then validated for amino acid distance distributions generated from a 2D and 3D version of the geometrically constrained random interaction model. For real protein data, we show how the analytical approximation can be used to fit amino acid distance distributions of protein chain lengths of L ≈ 100, L ≈ 200, and L ≈ 300 generated from two different methods of evaluating a PCM, a simple cutoff based method and a shadow map based method. We present evidence that geometric constraints are sufficient to model the amino acid distance distributions of protein chains in bulk and amino acid sequences only play a secondary role, regardless of the definition of the PCM.

Classical normal mode analysis (cNMA) is a standard method for studying the equilibrium vibrations of macromolecules. A major limitation of cNMA is that it requires a cumbersome step of energy minimization that also alters the input structure significantly. Variants of normal mode analysis (NMA) exist that perform NMA directly on PDB structures without energy minimization, while maintaining most of the accuracy of cNMA. Spring-based NMA (sbNMA) is such a model. sbNMA uses an all-atom force field as cNMA does, which includes bonded terms such as bond stretching, bond angle bending, torsional, improper, and non-bonded terms such as van der Waals interactions. Electrostatics was not included in sbNMA because it introduced negative spring constants. In this work, we present a way to incorporate most of the electrostatic contributions in normal mode computations, which marks another significant step toward a free-energy-based elastic network model (ENM) for NMA. The vast majority of ENMs are entropy models. One significance of having a free energy-based model for NMA is that it allows one to study the contributions of both entropy and enthalpy. As an application, we apply this model to study the binding stability between SARS-COV2 and angiotensin converting enzyme 2 (or ACE2). Our results show that the stability at the binding interface is contributed nearly equally by hydrophobic interactions and hydrogen bonds.

Modelling evolution of foodborne pathogens is crucial for mitigation and prevention of outbreaks. We apply network-theoretic and information-theoretic methods to trace evolutionary pathways of Salmonella Typhimurium in New South Wales, Australia, by studying whole genome sequencing surveillance data over a five-year period which included several outbreaks. The study derives both undirected and directed genotype networks based on genetic proximity, and relates the network's structural property (centrality) to its functional property (prevalence). The centrality-prevalence space derived for the undirected network reveals a salient exploration-exploitation distinction across the pathogens, further quantified by the normalised Shannon entropy and the Fisher information of the corresponding shell genome. This distinction is also analysed by tracing the probability density along evolutionary paths in the centrality-prevalence space. We quantify the evolutionary pathways, and show that pathogens exploring the evolutionary search-space during the considered period begin to exploit their environment (their prevalence increases resulting in outbreaks), but eventually encounter a bottleneck formed by epidemic containment measures.

The cell surface area (SA) increase with volume (V) is determined by growth and regulation of size and shape. Most studies of the rod-shaped model bacterium Escherichia coli have focussed on the phenomenology or molecular mechanisms governing such scaling. Here, we proceed to examine the role of population statistics and cell division dynamics in such scaling by a combination of microscopy, image analysis and statistical simulations. We find that while the SA of cells sampled from mid-log cultures scales with V by a scaling exponent 2/3, i.e. the geometric law SA ∼V$^{2/3}$, filamentous cells have higher exponent values. We modulate the growth rate to change the proportion of filamentous cells, and find SA-V scales with an exponent ${\gt}2/3$, exceeding that predicted by the geometric scaling law. However, since increasing growth rates alter the mean and spread of population cell size distributions, we use statistical modeling to disambiguate between the effect of the mean size and variability. Simulating (i) increasing mean cell length with a constant standard deviation (s.d.), (ii) a constant mean length with increasing s.d. and (iii) varying both simultaneously, results in scaling exponents that exceed the 2/3 geometric law, when population variability is included, with the s.d. having a stronger effect. In order to overcome possible effects of statistical sampling of unsynchronized cell populations, we 'virtually synchronized' time-series of cells by using the frames between birth and division identified by the image-analysis pipeline and divided them into four equally spaced phases—B, C1, C2 and D. Phase-specific scaling exponents estimated from these time series and the cell length variability were both found to decrease with the successive stages of birth (B), C1, C2 and division (D). These results point to a need to consider population statistics and a role for cell growth and division when estimating SA-V scaling of bacterial cells.