We compare the results of two-dimensional, biased random walk models of individual swimming micro-organisms with advection-diffusion models for the whole population. In particular, we consider the influence of the local flow environment (gyrotaxis) on the resulting motion. In unidirectional flows, the results of the individual and population models are generally in good agreement, even in flows in which the cells can experience a range of shear environments, and both models successfully predict the phenomena of gravitactic focusing. Numerical results are also compared with asymptotic expressions for weak and strong shear. Discrepancies between the models arise in two cases: (i) when reflective boundary conditions change the orientation distribution in the random walk model from that predicted by the long-term asymptotics used to derive the advection-diffusion model; (ii) when the spatial and temporal scales are not large enough for the advection-diffusion model to apply. We also use a simple twodimensional flow containing a variety of flow regimes to explore what happens when there are localized regions in which the generalized Taylor dispersion theory used in the derivation of the population model does not apply. For spherical cells, we find good agreement between the models outside the 'break-down' regions, but comparison of the results within these regions is complicated by the presence of nearby boundaries and their influence on the random walk model. In contrast, for rod-shaped cells which are reorientated by both vorticity and strain, we see qualitatively different spatial patterns between individual and advection-diffusion models even in the absence of gyrotaxis, because cells are advected between regions of differing rates of strain.

Coordinated changes of DNA (de)methylation, nucleosome positioning, and chromatin binding of the architectural protein CTCF play an important role for establishing cell-type-specific chromatin states during differentiation. To elucidate molecular mechanisms that link these processes, we studied the perturbed DNA modification landscape in mouse embryonic stem cells (ESCs) carrying a double knockout (DKO) of the Tet1 and Tet2 dioxygenases. These enzymes are responsible for the conversion of 5-methylcytosine (5mC) into its hydroxymethylated (5hmC), formylated (5fC), or carboxylated (5caC) forms. We determined changes in nucleosome positioning, CTCF binding, DNA methylation, and gene expression in DKO ESCs and developed biophysical models to predict differential CTCF binding. Methylation-sensitive nucleosome repositioning accounted for a significant portion of CTCF binding loss in DKO ESCs, whereas unmethylated and nucleosome-depleted CpG islands were enriched for CTCF sites that remained occupied. A number of CTCF sites also displayed direct correlations with the CpG modification state: CTCF was preferentially lost from sites that were marked with 5hmC in wild-type (WT) cells but not from 5fC-enriched sites. In addition, we found that some CTCF sites can act as bifurcation points defining the differential methylation landscape. CTCF loss from such sites, for example, at promoters, boundaries of chromatin loops, and topologically associated domains (TADs), was correlated with DNA methylation/ demethylation spreading and can be linked to down-regulation of neighboring genes. Our results reveal a hierarchical interplay between cytosine modifications, nucleosome positions, and DNA sequence that determines differential CTCF binding and regulates gene expression.

In response to changing extracellular pH levels, phosphate-limited continuous cultures of Clostridium acetobutylicum reversibly switches its metabolism from the dominant formation of acids to the prevalent production of solvents. Previous experimental and theoretical studies have revealed that this pH-induced metabolic switch involves a rearrangement of the intracellular transcriptomic, proteomic and metabolomic composition of the clostridial cells. However, the influence of the population dynamics on the observations reported has so far been neglected. Here, we present a method for linking the pH shift, clostridial growth and the acetone-butanol-ethanol fermentation metabolic network systematically into a model which combines the dynamics of the external pH and optical density with a metabolic model. Furthermore, the recently found antagonistic expression pattern of the aldehyde/alcohol dehydrogenases AdhE1/2 and pH-dependent enzyme activities have been included into this combined model. Our model predictions reveal that the pH-induced metabolic shift under these experimental conditions is governed by a phenotypic switch of predominantly acidogenic subpopulation towards a predominantly solventogenic subpopulation. This model-driven explanation of the pH-induced shift from acidogenesis to solventogenesis by population dynamics casts an entirely new light on the clostridial response to changing pH levels. Moreover, the results presented here underline that pH-dependent growth and pH-dependent specific enzymatic activity play a crucial role in this adaptation. In particular, the behaviour of AdhE1 and AdhE2 seems to be the key factor for the product formation of the two phenotypes, their pH-dependent growth, and thus, the pH-induced metabolic switch in C. acetobutylicum.

Abstract. Random walks are used to model movement in a wide variety of contexts: from the movement of cells undergoing chemotaxis to the migration of animals. In a twodimensional biased random walk, the diffusion about the mean drift position is entirely dependent on the moments of the angular distribution used to determine the movement direction at each step. Here we consider biased random walks using several different angular distributions and derive expressions for the diffusion coefficients in each direction based on either a fixed or variable movement speed, and we use these to generate a probability density function for the long-time spatial distribution. We demonstrate how diffusion is typically anisotropic around the mean drift position and illustrate these theoretical results using computer simulations. We relate these results to earlier studies of swimming microorganisms and explain how the results can be generalized to other types of animal movement.

Clinically, osteoarthritis (OA) pain is significantly associated with synovial inflammation. Identification of the mechanisms driving inflammation could reveal new targets to relieve this prevalent pain state. Herein, a role of polyadenylation in OA synovial samples was investigated, and the potential of the polyadenylation inhibitor cordycepin (3’ deoxyadenosine) to inhibit inflammation as well as to reduce pain and structural OA progression were studied. Joint tissues from people with OA with high or low grade inflammation and non-arthritic post-mortem controls were analysed for the polyadenylation factor CPSF4 and inflammatory markers. Effects of cordycepin on pain behavior and joint pathology were studied in models of OA (intra-articular injection of monosodium iodoacetate in rats and surgical destabilisation of the medial meniscus in mice). Human monocyte-derived macrophages and a mouse macrophage cell line were used to determine effects of cordycepin on nuclear localisation of the inflammatory transcription factor NFĸB and polyadenylation factors (WDR33 and CPSF4). CPSF4 and NFκB expression were increased in synovia from OA patients with high grade inflammation. Cordycepin reduced pain behaviour, synovial inflammation and joint pathology in both OA models. Stimulation of macrophages induced nuclear localisation of NFĸB and polyadenylation factors, effects inhibited by cordycepin. Knockdown of polyadenylation factors also prevented nuclear localisation of NFĸB. The increased expression of polyadenylation factors in OA synovia indicates a new target for analgesia treatments. This is supported by the finding that polyadenylation factors are required for inflammation in macrophages and by the fact that the polyadenylation inhibitor cordycepin attenuates pain and pathology in models of OA.