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Decoding how tissue properties emerge across multiple spatial and temporal scales from the integration of local signals is a grand challenge in quantitative biology. For example, the collective behavior of epithelial cells is critical for shaping developing embryos. Understanding how epithelial cells interpret a diverse range of local signals to coordinate tissue-level processes requires a systems-level understanding of development. Integration of multiple signaling pathways that specify cell signaling information requires second messengers such as calcium ions. Increasingly, specific roles have been uncovered for calcium signaling throughout development. Calcium signaling regulates many processes including division, migration, death, and differentiation. However, the pleiotropic and ubiquitous nature of calcium signaling implies that many additional functions remain to be discovered. Here we review a selection of recent studies to highlight important insights into how multiple signals are transduced by calcium transients in developing epithelial tissues. Quantitative imaging and computational modeling have provided important insights into how calcium signaling integration occurs. Reverse-engineering the conserved features of signal integration mediated by calcium signaling will enable novel approaches in regenerative medicine and synthetic control of morphogenesis.

Complex biological systems offer a variety of interesting phenomena at the different physical scales. With increasing abstraction, details of the microscopic scales can often be extrapolated to average or typical macroscopic properties. However, emergent properties and cross-scale interactions can impede naïve abstractions and necessitate comprehensive investigations of these complex systems.

In this review paper, we focus on microbial communities, and first, summarize a general hierarchy of relevant scales and description levels to understand these complex systems: (1) genetic networks, (2) single cells, (3) populations, and (4) emergent multi-cellular properties. Second, we employ two illustrating examples, microbial competition and biofilm formation, to elucidate how cross-scale interactions and emergent properties enrich the observed multi-cellular behavior in these systems.

Finally, we conclude with pointing out the necessity of multi-scale investigations to understand complex biological systems and discuss recent investigations.

In quantitative analyses of biological processes, one may use many different scales of models (e.g. spatial or non-spatial, deterministic or stochastic, time-varying or at steady-state) or many different approaches to match models to experimental data (e.g. model fitting or parameter uncertainty/sloppiness quantification with different experiment designs). These different analyses can lead to surprisingly different results, even when applied to the same data and the same model. We use a simplified gene regulation model to illustrate many of these concerns, especially for ODE analyses of deterministic processes, chemical master equation and finite state projection analyses of heterogeneous processes, and stochastic simulations. For each analysis, we employ Matlab and Python software to consider a time-dependent input signal (e.g. a kinase nuclear translocation) and several model hypotheses, along with simulated single-cell data. We illustrate different approaches (e.g. deterministic and stochastic) to identify the mechanisms and parameters of the same model from the same simulated data. For each approach, we explore how uncertainty in parameter space varies with respect to the chosen analysis approach or specific experiment design. We conclude with a discussion of how our simulated results relate to the integration of experimental and computational investigations to explore signal-activated gene expression models in yeast (Neuert et al 2013 Science339 584–7) and human cells (Senecal et al 2014 Cell Rep. 8 75–83)⁵.

Cells of the immune system are confronted with opposing pro- and anti-inflammatory signals. Dendritic cells (DC) integrate these cues to make informed decisions whether to initiate an immune response. Confronted with exogenous microbial stimuli, DC endogenously produce both anti- (IL-10) and pro-inflammatory (TNFα) cues whose joint integration controls the cell's final decision. Backed by experimental measurements we present a theoretical model to quantitatively describe the integration mode of these opposing signals. We propose a two step integration model that modulates the effect of the two types of signals: an initial bottleneck integrates both signals (IL-10 and TNFα), the output of which is later modulated by the anti-inflammatory signal. We show that the anti-inflammatory IL-10 signaling is long ranged, as opposed to the short-ranged pro-inflammatory TNFα signaling. The model suggests that the population averaging and modulation of the pro-inflammatory response by the anti-inflammatory signal is a safety guard against excessive immune responses.

Cell division in Escherichia coli is morphologically symmetric due to, among other things, the ability of these cells to place the Z-ring at midcell. Studies have reported that, at sub-optimal temperatures, this symmetry decreases at the single-cell level, but the causes remain unclear. Using fluorescence microscopy, we observe FtsZ-GFP and DAPI-stained nucleoids to assess the robustness of the symmetry of Z-ring formation and positioning in individual cells under sub-optimal and critical temperatures. We find the Z-ring formation and positioning to be robust at sub-optimal temperatures, as the Z-ring's mean width, density and displacement from midcell maintain similar levels of correlation to one another as at optimal temperatures. However, at critical temperatures, the Z-ring displacement from midcell is greatly increased. We present evidence showing that this is due to enhanced distance between the replicated nucleoids and, thus, reduced Z-ring density, which explains the weaker precision in setting a morphologically symmetric division site. This also occurs in rich media and is cumulative, i.e. combining richer media and critically high temperatures enhances the asymmetries in division, which is evidence that the causes are biophysical. To further support this, we show that the effects are reversible, i.e. shifting cells from optimal to critical, and then to optimal again, reduces and then enhances the symmetry in Z-ring positioning, respectively, as the width and density of the Z-ring return to normal values. Overall, our findings show that the Z-ring positioning in E. coli is a robust biophysical process under sub-optimal temperatures, and that critical temperatures cause significant asymmetries in division.

Spatial relocalization of proteins is crucial for the correct functioning of living cells. An interesting example of spatial ordering is the light-induced clustering of plant photoreceptor proteins. Upon irradiation by white or red light, the red light-active phytochrome, phytochrome B, enters the nucleus and accumulates in large nuclear bodies (NBs). The underlying physical process of nuclear body formation remains unclear, but phytochrome B is thought to coagulate via a simple protein–protein binding process. We measure, for the first time, the distribution of the number of phytochrome B-containing NBs as well as their volume distribution. We show that the experimental data cannot be explained by a stochastic model of nuclear body formation via simple protein–protein binding processes using physically meaningful parameter values. Rather modelling suggests that the data is consistent with a two step process: a fast nucleation step leading to macroparticles followed by a subsequent slow step in which the macroparticles bind to form the nuclear body. An alternative explanation for the observed nuclear body distribution is that the phytochromes bind to a so far unknown molecular structure. We believe it is likely this result holds more generally for other nuclear body-forming plant photoreceptors and proteins.

Directed movement of eukaryotic cells toward spatiotemporally varied chemotactic stimuli enables rapid intracellular signaling responses. While macroscopic cellular manifestation is shaped by balancing external stimuli strength with finite internal delays, the organizing principles of the underlying molecular mechanisms remain to be clarified. Here, we developed a novel modeling framework based on a simple seesaw mechanism to elucidate how cells repeatedly reverse polarity. As a key feature of the modeling, the bottom module of bidirectional molecular transport is successively controlled by three upstream modules of signal reception, initial signal processing, and Rho GTPase regulation. Our simulations indicated that an isotropic cell is polarized in response to a graded input signal. By applying a reversal gradient to a chemoattractant signal, lamellipod-specific molecules (i.e. PIP₃ and PI3K) disappear, first from the cell front, and then they redistribute at the opposite side, whereas functional molecules at the rear of the cell (i.e. PIP₂ and PTEN) act oppositely. In particular, the model cell exhibits a seesaw-like spatiotemporal pattern for the establishment of front and rear and interconversion, consistent with those related experimental observations. Increasing the switching frequency of the chemotactic gradient causes the cell to stay in a trapped state, further supporting the proposed dynamics of eukaryotic chemotaxis with the underlying cytoskeletal remodeling.

Virus capsids are polymeric protein shells that protect the viral cargo. About half of known virus families have icosahedral capsids that self-assemble from tens to thousands of subunits. Capsid disassembly is critical to the lifecycles of many viruses yet is poorly understood. Here, we apply a graph and percolation theory to examine the effect of removing capsid subunits on capsid stability and fragmentation. Based on the structure of the icosahedral capsid of hepatitis B virus (HBV), we constructed a graph of rhombic subunits arranged with icosahedral symmetry. Though our approach neglects dependence on energetics, time, and molecular detail, it quantitatively predicts a percolation phase transition consistent with recent in vitro studies of HBV capsid dissociation. While the stability of the capsid graph followed a gradual quadratic decay, the rhombic tiling abruptly fragmented when we removed more than 25% of the 120 subunits, near the percolation threshold observed experimentally. This threshold may also affect results of capsid assembly, which also experimentally produces a preponderance of 90 mer intermediates, as the intermediate steps in these reactions are reversible and can thus resemble dissociation. Application of percolation theory to understanding capsid association and dissociation may prove a general approach to relating virus biology to the underlying biophysics of the virus particle.

We perform a detailed analysis of the migratory motion of human embryonic stem cells in two-dimensions, both when isolated and in close proximity to another cell, recorded with time-lapse microscopic imaging. We show that isolated cells tend to perform an unusual locally anisotropic walk, moving backwards and forwards along a preferred local direction correlated over a timescale of around 50 min and aligned with the axis of the cell elongation. Increasing elongation of the cell shape is associated with increased instantaneous migration speed. We also show that two cells in close proximity tend to move in the same direction, with the average separation of m or less and the correlation length of around 25 μm, a typical cell diameter. These results can be used as a basis for the mathematical modelling of the formation of clonal hESC colonies.