Logic programming to predict cell fate patterns and retrodict genotypes in organogenesis

Caenorhabditis elegans vulval development is a paradigm system for understanding cell differentiation in the process of organogenesis. Through temporal and spatial controls, the fate pattern of six cells is determined by the competition of the LET-23 and the Notch signalling pathways. Modelling cell fate determination in vulval development using state-based models, coupled with formal analysis techniques, has been established as a powerful approach in predicting the outcome of combinations of mutations. However, computing the outcomes of complex and highly concurrent models can become prohibitive. Here, we show how logic programs derived from state machines describing the differentiation of C. elegans vulval precursor cells can increase the speed of prediction by four orders of magnitude relative to previous approaches. Moreover, this increase in speed allows us to infer, or ‘retrodict’, compatible genomes from cell fate patterns. We exploit this technique to predict highly variable cell fate patterns resulting from dig-1 reduced-function mutations and let-23 mosaics. In addition to the new insights offered, we propose our technique as a platform for aiding the design and analysis of experimental data.     

Signatures of active and passive optimized Lévy searching in jellyfish

Some of the strongest empirical support for Lévy search theory has come from telemetry data for the dive patterns of marine predators (sharks, bony fishes, sea turtles and penguins). The dive patterns of the unusually large jellyfish Rhizostoma octopus do, however, sit outside of current Lévy search theory which predicts that a single search strategy is optimal. When searching the water column, the movement patterns of these jellyfish change over time. Movement bouts can be approximated by a variety of Lévy and Brownian (exponential) walks. The adaptive value of this variation is not known. On some occasions movement pattern data are consistent with the jellyfish prospecting away from a preferred depth, not finding an improvement in conditions elsewhere and so returning to their original depth. This ‘bounce’ behaviour also sits outside of current Lévy walk search theory. Here, it is shown that the jellyfish movement patterns are consistent with their using optimized ‘fast simulated annealing’—a novel kind of Lévy walk search pattern—to locate the maximum prey concentration in the water column and/or to locate the strongest of many olfactory trails emanating from more distant prey. Fast simulated annealing is a powerful stochastic search algorithm for locating a global maximum that is hidden among many poorer local maxima in a large search space. This new finding shows that the notion of active optimized Lévy walk searching is not limited to the search for randomly and sparsely distributed resources, as previously thought, but can be extended to embrace other scenarios, including that of the jellyfish R. octopus. In the presence of convective currents, it could become energetically favourable to search the water column by riding the convective currents. Here, it is shown that these passive movements can be represented accurately by Lévy walks of the type occasionally seen in R. octopus. This result vividly illustrates that Lévy walks are not necessarily the result of selection pressures for advantageous searching behaviour but can instead arise freely and naturally from simple processes. It also shows that the family of Lévy walkers is vastly larger than previously thought and includes spores, pollens, seeds and minute wingless arthropods that on warm days disperse passively within the atmospheric boundary layer.     

A search game model of the scatter hoarder's problem

Scatter hoarders are animals (e.g. squirrels) who cache food (nuts) over a number of sites for later collection. A certain minimum amount of food must be recovered, possibly after pilfering by another animal, in order to survive the winter. An optimal caching strategy is one that maximizes the survival probability, given worst case behaviour of the pilferer. We modify certain ‘accumulation games’ studied by Kikuta & Ruckle (2000 J. Optim. Theory Appl.) and Kikuta & Ruckle (2001 Naval Res. Logist.), which modelled the problem of optimal diversification of resources against catastrophic loss, to include the depth at which the food is hidden at each caching site. Optimal caching strategies can then be determined as equilibria in a new ‘caching game’. We show how the distribution of food over sites and the site-depths of the optimal caching varies with the animal''s survival requirements and the amount of pilfering. We show that in some cases, ‘decoy nuts’ are required to be placed above other nuts that are buried further down at the same site. Methods from the field of search games are used. Some empirically observed behaviour can be shown to be optimal in our model.     

Three-dimensional tracking and behaviour monitoring of multiple fruit flies

The increasing interest in the investigation of social behaviours of a group of animals has heightened the need for developing tools that provide robust quantitative data. Drosophila melanogaster has emerged as an attractive model for behavioural analysis; however, there are still limited ways to monitor fly behaviour in a quantitative manner. To study social behaviour of a group of flies, acquiring the position of each individual over time is crucial. There are several studies that have tried to solve this problem and make this data acquisition automated. However, none of these studies has addressed the problem of keeping track of flies for a long period of time in three-dimensional space. Recently, we have developed an approach that enables us to detect and keep track of multiple flies in a three-dimensional arena for a long period of time, using multiple synchronized and calibrated cameras. After detecting flies in each view, correspondence between views is established using a novel approach we call the ‘sequential Hungarian algorithm’. Subsequently, the three-dimensional positions of flies in space are reconstructed. We use the Hungarian algorithm and Kalman filter together for data association and tracking. We evaluated rigorously the system''s performance for tracking and behaviour detection in multiple experiments, using from one to seven flies. Overall, this system presents a powerful new method for studying complex social interactions in a three-dimensional environment.     

Ambush frequency should increase over time during optimal predator search for prey

We advance and apply the mathematical theory of search games to model the problem faced by a predator searching for prey. Two search modes are available: ambush and cruising search. Some species can adopt either mode, with their choice at a given time traditionally explained in terms of varying habitat and physiological conditions. We present an additional explanation of the observed predator alternation between these search modes, which is based on the dynamical nature of the search game they are playing: the possibility of ambush decreases the propensity of the prey to frequently change locations and thereby renders it more susceptible to the systematic cruising search portion of the strategy. This heuristic explanation is supported by showing that in a new idealized search game where the predator is allowed to ambush or search at any time, and the prey can change locations at intermittent times, optimal predator play requires an alternation (or mixture) over time of ambush and cruise search. Thus, our game is an extension of the well-studied ‘Princess and Monster’ search game. Search games are zero sum games, where the pay-off is the capture time and neither the Searcher nor the Hider knows the location of the other. We are able to determine the optimal mixture of the search modes when the predator uses a mixture which is constant over time, and also to determine how the mode mixture changes over time when dynamic strategies are allowed (the ambush probability increases over time). In particular, we establish the ‘square root law of search predation’: the optimal proportion of active search equals the square root of the fraction of the region that has not yet been explored.     

Fractal analysis of behaviour in a wild primate: behavioural complexity in health and disease

Parasitism and other stressors are ubiquitous in nature but their effects on animal behaviour can be difficult to identify. We investigated the effects of nematode parasitism and other indicators of physiological impairment on the sequential complexity of foraging and locomotion behaviour among wild Japanese macaques (Macaca fuscata yakui). We observed all sexually mature individuals (n = 28) in one macaque study group between October 2007 and August 2008, and collected two faecal samples/month/individual (n = 362) for parasitological examination. We used detrended fluctuation analysis (DFA) to investigate long-range autocorrelation in separate, binary sequences of foraging (n = 459) and locomotion (n = 446) behaviour collected via focal sampling. All behavioural sequences exhibited long-range autocorrelation, and linear mixed-effects models suggest that increasing infection with the nodular worm Oesophagostomum aculeatum, clinically impaired health, reproductive activity, ageing and low dominance status were associated with reductions in the complexity of locomotion, and to a lesser extent foraging, behaviour. Furthermore, the sequential complexity of behaviour increased with environmental complexity. We argue that a reduction in complexity in animal behaviour characterizes individuals in impaired or ‘stressed’ states, and may have consequences if animals cannot cope with heterogeneity in their natural habitats.     

A dynamic broadband reflector built from microscopic silica spheres in the ‘disco’ clam Ctenoides ales

The ‘disco’ or ‘electric’ clam Ctenoides ales (Limidae) is the only species of bivalve known to have a behaviourally mediated photic display. This display is so vivid that it has been repeatedly confused for bioluminescence, but it is actually the result of scattered light. The flashing occurs on the mantle lip, where electron microscopy revealed two distinct tissue sides: one highly scattering side that contains dense aggregations of spheres composed of silica, and one highly absorbing side that does not. High-speed video confirmed that the two sides act in concert to alternate between vivid broadband reflectance and strong absorption in the blue region of the spectrum. Optical modelling suggests that the diameter of the spheres is nearly optimal for scattering visible light, especially at shorter wavelengths which predominate in their environment. This simple mechanism produces a striking optical effect that may function as a signal.     

Anatomy of a negative feedback loop: the case of IκBα

The magnitude, duration and oscillation of cellular signalling pathway responses are often limited by negative feedback loops, defined as an ‘activator-induced inhibitor’ regulatory motif. Within the NFκB signalling pathway, a key negative feedback regulator is IκBα. We show here that, contrary to current understanding, NFκB-inducible expression is not sufficient for providing effective negative feedback. We then employ computational simulations of NFκB signalling to identify IκBα molecular properties that are critical for proper negative feedback control and test the resulting predictions in biochemical and single-cell live-imaging studies. We identified nuclear import and nuclear export of IκBα and the IκBα–NFκB complex, as well as the free IκBα half-life, as key determinants of post-induction repression of NFκB and the potential for subsequent reactivation. Our work emphasizes that negative feedback is an emergent systems property determined by multiple molecular and biophysical properties in addition to the required ‘activator-induced inhibitor’ relationship.     

Aggregation by depletion attraction in cultures of bacteria producing exopolysaccharide

In bacteria, the production of exopolysaccharides—polysaccharides secreted by the cells into their growth medium—is integral to the formation of aggregates and biofilms. These exopolysaccharides often form part of a matrix that holds the cells together. Investigating the bacterium Sinorhizobium meliloti, we found that a mutant that overproduces the exopolysaccharide succinoglycan showed enhanced aggregation, resulting in phase separation of the cultures. However, the aggregates did not appear to be covered in polysaccharides. Succinoglycan purified from cultures was applied to different concentrations of cells, and observation of the phase behaviour showed that the limiting polymer concentration for aggregation and phase separation to occur decreased with increasing cell concentration, suggesting a ‘crowding mechanism’ was occurring. We suggest that, as found in colloidal dispersions, the presence of a non-adsorbing polymer in the form of the exopolysaccharide succinoglycan drives aggregation of S. meliloti by depletion attraction. This force leads to self-organization of the bacteria into small clusters of laterally aligned cells, and, furthermore, leads to aggregates clustering into biofilm-like structures on a surface.     

Modelling and analysis of bacterial tracks suggest an active reorientation mechanism in Rhodobacter sphaeroides

Most free-swimming bacteria move in approximately straight lines, interspersed with random reorientation phases. A key open question concerns varying mechanisms by which reorientation occurs. We combine mathematical modelling with analysis of a large tracking dataset to study the poorly understood reorientation mechanism in the monoflagellate species Rhodobacter sphaeroides. The flagellum on this species rotates counterclockwise to propel the bacterium, periodically ceasing rotation to enable reorientation. When rotation restarts the cell body usually points in a new direction. It has been assumed that the new direction is simply the result of Brownian rotation. We consider three variants of a self-propelled particle model of bacterial motility. The first considers rotational diffusion only, corresponding to a non-chemotactic mutant strain. Two further models incorporate stochastic reorientations, describing ‘run-and-tumble’ motility. We derive expressions for key summary statistics and simulate each model using a stochastic computational algorithm. We also discuss the effect of cell geometry on rotational diffusion. Working with a previously published tracking dataset, we compare predictions of the models with data on individual stopping events in R. sphaeroides. This provides strong evidence that this species undergoes some form of active reorientation rather than simple reorientation by Brownian rotation.     

The entropic basis of collective behaviour

We identify a unique viewpoint on the collective behaviour of intelligent agents. We first develop a highly general abstract model for the possible future lives these agents may encounter as a result of their decisions. In the context of these possibilities, we show that the causal entropic principle, whereby agents follow behavioural rules that maximize their entropy over all paths through the future, predicts many of the observed features of social interactions among both human and animal groups. Our results indicate that agents are often able to maximize their future path entropy by remaining cohesive as a group and that this cohesion leads to collectively intelligent outcomes that depend strongly on the distribution of the number of possible future paths. We derive social interaction rules that are consistent with maximum entropy group behaviour for both discrete and continuous decision spaces. Our analysis further predicts that social interactions are likely to be fundamentally based on Weber''s law of response to proportional stimuli, supporting many studies that find a neurological basis for this stimulus–response mechanism and providing a novel basis for the common assumption of linearly additive ‘social forces’ in simulation studies of collective behaviour.     

The principles of pedestrian route choice

Pedestrian route choice, the process by which individuals decide on their walking path between two locations, is a fundamental problem across disciplines. Because this behaviour is investigated from different conceptual and methodological angles, and because it strongly depends on the environmental context, it is challenging to establish a systematic framework for research. Here, by reviewing previous work, we identify four principles for pedestrian route choice that are relevant across disciplines. First, ‘information perception’ deals with how pedestrians can perceive information selectively and purposely, given the limited available information. Second, ‘information integration’ considers how pedestrians subjectively integrate environmental spatial information into mental representations. Third, ‘responding to information’ is concerned with how pedestrians tend to be attracted and repelled by specific attributes individually and how this can lead to positive or negative feedback loops across many individuals. Fourth ‘decision-making mechanisms'' describe how pedestrians trade off the evidence provided by different attributes. How pedestrians perceive, integrate, respond to, and act upon information is not fixed but varies with the context. We give examples for each principle and explain how these principles shape pedestrian choice behaviours. We hope this contribution provides a systematic overview of the field and helps to spark inspiration among specialists.     

Exploration–exploitation trade-off features a saltatory search behaviour

Searching experiments conducted in different virtual environments over a gender-balanced group of people revealed a gender irrelevant scale-free spread of searching activity on large spatio-temporal scales. We have suggested and solved analytically a simple statistical model of the coherent-noise type describing the exploration–exploitation trade-off in humans (‘should I stay’ or ‘should I go’). The model exhibits a variety of saltatory behaviours, ranging from Lévy flights occurring under uncertainty to Brownian walks performed by a treasure hunter confident of the eventual success.     

Fast,high-throughput measurement of collective behaviour in a bacterial population

Swimming bacteria explore their environment by performing a random walk, which is biased in response to, for example, chemical stimuli, resulting in a collective drift of bacterial populations towards ‘a better life’. This phenomenon, called chemotaxis, is one of the best known forms of collective behaviour in bacteria, crucial for bacterial survival and virulence. Both single-cell and macroscopic assays have investigated bacterial behaviours. However, theories that relate the two scales have previously been difficult to test directly. We present an image analysis method, inspired by light scattering, which measures the average collective motion of thousands of bacteria simultaneously. Using this method, a time-varying collective drift as small as 50 nm s⁻¹ can be measured. The method, validated using simulations, was applied to chemotactic Escherichia coli bacteria in linear gradients of the attractant α-methylaspartate. This enabled us to test a coarse-grained minimal model of chemotaxis. Our results clearly map the onset of receptor methylation, and the transition from linear to logarithmic sensing in the bacterial response to an external chemoeffector. Our method is broadly applicable to problems involving the measurement of collective drift with high time resolution, such as cell migration and fluid flows measurements, and enables fast screening of tactic behaviours.     

Structural performance of a climbing cactus: making the most of softness

Climbing plants must reach supports and navigate gaps to colonize trees. This requires a structural organization ensuring the rigidity of so-called ‘searcher’ stems. Cacti have succulent stems adapted for water storage in dry habitats. We investigate how a climbing cactus Selenicereus setaceus develops its stem structure and succulent tissues for climbing. We applied a ‘wide scale’ approach combining field-based bending, tensile and swellability tests with fine-scale rheological, compression and anatomical analyses in laboratory conditions. Gap-spanning ‘searcher’ stems rely significantly on the soft cortex and outer skin of the stem for rigidity in bending (60–94%). A woody core contributes significantly to axial and radial compressive strength (80%). Rheological tests indicated that storage moduli were consistently higher than loss moduli indicating that the mucilaginous cortical tissue behaved like a viscoelastic solid with properties similar to physical or chemical hydrogels. Rheological and compression properties of the soft tissue changed from young to old stages. The hydrogel–skin composite is a multi-functional structure contributing to rigidity in searcher stems but also imparting compliance and benign failure in environmental situations when stems must fail. Soft tissue composites changing in function via changes in development and turgescence have a great potential for exploring candidate materials for technical applications.     

Remote automated multi-generational growth and observation of an animal in low Earth orbit

The ultimate survival of humanity is dependent upon colonization of other planetary bodies. Key challenges to such habitation are (patho)physiologic changes induced by known, and unknown, factors associated with long-duration and distance space exploration. However, we currently lack biological models for detecting and studying these changes. Here, we use a remote automated culture system to successfully grow an animal in low Earth orbit for six months. Our observations, over 12 generations, demonstrate that the multi-cellular soil worm Caenorhabditis elegans develops from egg to adulthood and produces progeny with identical timings in space as on the Earth. Additionally, these animals display normal rates of movement when fully fed, comparable declines in movement when starved, and appropriate growth arrest upon starvation and recovery upon re-feeding. These observations establish C. elegans as a biological model that can be used to detect changes in animal growth, development, reproduction and behaviour in response to environmental conditions during long-duration spaceflight. This experimental system is ready to be incorporated on future, unmanned interplanetary missions and could be used to study cost-effectively the effects of such missions on these biological processes and the efficacy of new life support systems and radiation shielding technologies.     

Novel temperature-responsive polymer brushes with carbohydrate residues facilitate selective adhesion and collection of hepatocytes

Temperature-responsive glycopolymer brushes were designed to investigate the effects of grafting architectures of the copolymers on the selective adhesion and collection of hypatocytes. Homo, random and block sequences of N-isopropylacrylamide and 2-lactobionamidoethyl methacrylate were grafted on glass substrates via surface-initiated atom transfer radical polymerization. The galactose/lactose-specific lectin RCA₁₂₀ and HepG2 cells were used to test for specific recognition of the polymer brushes containing galactose residues over the lower critical solution temperatures (LCSTs). RCA₁₂₀ showed a specific binding to the brush surfaces at 37 °C. These brush surfaces also facilitated the adhesion of HepG2 cells at 37 °C under nonserum conditions, whereas no adhesion was observed for NIH-3T3 fibroblasts. When the temperature was decreased to 25 °C, almost all the HepG2 cells detached from the block copolymer brush, whereas the random copolymer brush did not release the cells. The difference in releasing kinetics of cells from the surfaces with different grafting architectures can be explained by the correlated effects of significant changes in LCST, mobility, hydrophilicity and mechanical properties of the grafted polymer chains. These findings are important for designing ‘on–off’ cell capture/release substrates for various biomedical applications such as selective cell separation.     

How signalling games explain mimicry at many levels: from viral epidemiology to human sociology

Mimicry is exhibited in multiple scales, ranging from molecular, to organismal, and then to human society. ‘Batesian’-type mimicry entails a conflict of interest between sender and receiver, reflected in a deceptive mimic signal. ‘Müllerian’-type mimicry occurs when there is perfect common interest between sender and receiver in a particular type of encounter, manifested by an honest co-mimic signal. Using a signalling games approach, simulations show that invasion by Batesian mimics will make Müllerian mimicry unstable, in a coevolutionary chase. We use these results to better understand the deceptive strategies of SARS-CoV-2 and their key role in the COVID-19 pandemic. At the biomolecular level, we explain how cellularization promotes Müllerian molecular mimicry, and discourages Batesian molecular mimicry. A wide range of processes analogous to cellularization are presented; these might represent a manner of reducing oscillatory instabilities. Lastly, we identify examples of mimicry in human society that might be addressed using a signalling game approach.     

Analysis of a complete DNA–protein affinity landscape

Properties of biological fitness landscapes are of interest to a wide sector of the life sciences, from ecology to genetics to synthetic biology. For biomolecular fitness landscapes, the information we currently possess comes primarily from two sources: sparse samples obtained from directed evolution experiments; and more fine-grained but less authentic information from ‘in silico’ models (such as NK-landscapes). Here we present the entire protein-binding profile of all variants of a nucleic acid oligomer 10 bases in length, which we have obtained experimentally by a series of highly parallel on-chip assays. The resulting complete landscape of sequence-binding pairs, comprising more than one million binding measurements in duplicate, has been analysed statistically using a number of metrics commonly applied to synthetic landscapes. These metrics show that the landscape is rugged, with many local optima, and that this arises from a combination of experimental variation and the natural structural properties of the oligonucleotides.     

Thermally reversible colloidal gels for three-dimensional chondrocyte culture

Healthy cells are required in large numbers to form a tissue-engineered construct and primary cells must therefore be increased in number in a process termed ‘expansion’. There are significant problems with existing procedures, including cell injury and an associated loss of phenotype, but three-dimensional culture has been reported to offer a solution. Reversible gels, which allow for the recovery of cells after expansion would therefore have great value in the expansion of chondrocytes for tissue engineering applications, but they have received relatively little attention to date. In this study, we examined the synthesis and use of thermoresponsive polymers that form reversible three-dimensional gels for chondrocyte cell culture. A series of polymers comprising N-isopropylacrylamide (NIPAM) and styrene was synthesized before studying their thermoresponsive solution behaviour and gelation. A poly(NIPAM-co-styrene-graft-N-vinylpyrrolidone) variant was also synthesized in order to provide increased water content. Both random- and graft-copolymers formed particulate gels above the lower critical solution temperature and, on cooling, re-dissolved to allow enzyme-free cell recovery. Chondrocytes remained viable in all of these materials for 24 days, increased in number and produced collagen type II and glycosaminoglycans.