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By analyzing 30 min, high-resolution recordings of single Escherichia coli flagellar motors in the physiological regime, we show that two main properties of motor switching—the mean clockwise and mean counter-clockwise interval durations—vary significantly. When we represent these quantities on a two-dimensional plot for several cells, the data do not fall on a one-dimensional curve, as expected with a single control parameter, but instead spread in two dimensions, pointing to motor individuality. The largest variations are in the mean counter-clockwise interval, and are attributable to variations in the concentration of the internal signaling molecule CheY-P. In contrast, variations in the mean clockwise interval are interpreted in terms of motor individuality. We argue that the sensitivity of the mean counter-clockwise interval to fluctuations in CheY-P is consistent with an optimal strategy of run and tumble. The concomittent variability in mean run length may allow populations of cells to better survive in rapidly changing environments by 'hedging their bets'.

Cells sense and respond to diverse environmental stimuli using a set of intracellular signaling components. Often, the signal transduction pathways contain shared components which lead to cross activation at different levels of the pathway. To discover the design principles that ensure signaling specificity is a challenging task, especially for pathways that contain numerous components. Here, we present an analysis of cross-activating pathways and show that a general inhibitory scheme, asymmetric hierarchical inhibition, is sufficient to ensure signaling specificity. Based on this inhibitory scheme, we are able to enumerate all possible network topologies containing two inhibitory links that guarantee specificity. Furthermore, we apply our methodology to the mating and filamentous growth pathways of the yeast model system Saccharomyces cerevisiae. We enumerate the possible ways to wire this model system and determine which topology is consistent with experimental data.

The state of collagen molecules in the fibres of tail tendon, skin and demineralized bone has been investigated in situ using differential scanning calorimetry (DSC). Hydroxyproline analysis and tissue digestion with bacterial collagenase and trypsin were used to confirm that the common cause of all the DSC endotherms was collagen denaturation. This occurred within a narrow temperature range in tendons, but over a wide temperature range in demineralized bone and old skin and demonstrated that in tendon and demineralized bone at least the same type I collagen molecule exists in different thermal states. Hypothesizing that this might be caused by different degrees of confinement within the fibre lattice, experiments were performed to measure the effect of changing the lattice dimensions by extracting the collagen into dilute solution with pepsin, swelling the lattice in acetic acid, and contracting the lattice by dehydration. A theoretical analysis was undertaken to predict the effect of dehydration. Results were consistent with the hypothesis, demonstrating that collagen molecules within the natural fibres of bone and old skin are located at different intermolecular spacings, revealing differences between molecules in the magnitude of either the attractive or repulsive forces controlling their separation. One potential cause of such variation is known differences in covalent cross-linking.

Asexual reproduction in multicellular organisms is a complex biophysical process that is not yet well understood quantitatively. Here, we report a detailed population study for the asexual freshwater planarian Schmidtea mediterranea, which can reproduce via transverse fission due to a large stem cell contingent. Our long-term observations of isolated non-interacting planarian populations reveal that the characteristic fission waiting time distributions for head and tail fragments differ significantly from each other. The stochastic fission dynamics of tail fragments exhibits non-negligible memory effects, implying that an accurate mathematical description of future data should be based on non-Markovian tree models. By comparing the effective growth of non-interacting planarian populations with those of self-interacting populations, we are able to quantify the influence of interactions between flatworms and physical conditions on the population growth. A surprising result is the non-monotonic relationship between effective population growth rate and nutrient supply: planarians exhibit a tendency to become 'obese' if the feeding frequency exceeds a critical level, resulting in a decreased reproduction activity. This suggests that these flatworms, which possess many genes homologous to those of humans, could become a new model system for studying dietary effects on reproduction and regeneration in multicellular organisms.

The role of flexibility in the selectivity of calcium channels is studied using a simple model with two parameters that accounts for the selectivity of calcium (and sodium) channels in many ionic solutions of different compositions and concentrations using two parameters with unchanging values. We compare the distribution of side chains (oxygens) and cations (Na⁺ and Ca²⁺) and integrated quantities. We compare the occupancies of cations Ca²⁺/Na⁺ and linearized conductance of Na⁺. The distributions show a strong dependence on the locations of fixed side chains and the flexibility of the side chains. Holding the side chains fixed at certain predetermined locations in the selectivity filter distorts the distribution of Ca²⁺ and Na⁺ in the selectivity filter. However, integrated quantities—occupancy and normalized conductance—are much less sensitive. Our results show that some flexibility of side chains is necessary to avoid obstruction of the ionic pathway by oxygen ions in 'unfortunate' fixed positions. When oxygen ions are mobile, they adjust 'automatically' and move 'out of the way', so they can accommodate the permeable cations in the selectivity filter. Structure is the computed consequence of the forces in this model. The structures are self-organized, at their free energy minimum. The relationship of ions and side chains varies with an ionic solution. Monte Carlo simulations are particularly well suited to compute induced-fit, self-organized structures because the simulations yield an ensemble of structures near their free energy minimum. The exact location and mobility of oxygen ions has little effect on the selectivity behavior of calcium channels. Seemingly, nature has chosen a robust mechanism to control selectivity in calcium channels: the first-order determinant of selectivity is the density of charge in the selectivity filter. The density is determined by filter volume along with the charge and excluded volume of structural ions confined within it. Flexibility seems a second-order determinant. These results justify our original assumption that the important factor in Ca²⁺ versus Na⁺ selectivity is the density of oxygen ions in the selectivity filter along with (charge) polarization (i.e. dielectric properties). The assumption of maximum mobility of oxygens seems to be an excellent approximate working hypothesis in the absence of exact structural information. These conclusions, of course, apply to what we study here. Flexibility and fine structural details may have an important role in other properties of calcium channels that are not studied in this paper. They surely have important roles in other channels, enzymes, and proteins.

Ribosome is a molecular machine that polymerizes a protein where the sequence of the amino acid residues, the monomers of the protein, is dictated by the sequence of codons (triplets of nucleotides) on a messenger RNA (mRNA) that serves as the template. The ribosome is a molecular motor that utilizes the template mRNA strand also as the track. Thus, in each step the ribosome moves forward by one codon and, simultaneously, elongates the protein by one amino acid. We present a theoretical model that captures most of the main steps in the mechanochemical cycle of a ribosome. The stochastic movement of the ribosome consists of an alternating sequence of pause and translocation; the sum of the durations of a pause and the following translocation is the time of dwell of the ribosome at the corresponding codon. We derive the analytical expression for the distribution of the dwell times of a ribosome in our model. Wherever experimental data are available, our theoretical predictions are consistent with those results. We suggest appropriate experiments to test the new predictions of our model, particularly the effects of the quality control mechanism of the ribosome and that of their crowding on the mRNA track.

We mapped promoter regions of double-stranded DNA with respect to the probabilities of appearance of relatively large bubble openings exclusively due to thermal fluctuations at physiological temperatures. We analyzed five well-studied promoter regions of procaryotic type and found a spatial correlation between the binding sites of transcription factors and the position of peaks in the probability pattern of large thermal openings. Other distinct peaks of the calculated patterns correlate with potential binding sites of DNA-binding proteins. These results suggest that a DNA molecule would more frequently expose the bases that participate in contacts with proteins, which would probably enhance the probability of the latter to reach their targets. It also stands for using this method as a means to analyze DNA sequences based on their intrinsic thermal properties.

The cytoskeletal protein FtsZ polymerizes to a ring structure (Z ring) at the inner cytoplasmic membrane that marks the future division site and scaffolds the division machinery in many bacterial species. FtsZ is known to polymerize in the presence of GTP into single-stranded protofilaments. In vivo, FtsZ polymers become associated with the cytoplasmic membrane via interaction with the membrane-binding proteins FtsA and ZipA. The FtsZ ring structure is highly dynamic and undergoes constantly polymerization and depolymerization processes and exchange with the cytoplasmic pool. In this theoretical study, we consider a scenario of Z ring self-organization via self-enhanced attachment of FtsZ polymers due to end-to-end interactions and lateral interactions of FtsZ polymers on the membrane. With the assumption of exclusively circumferential polymer orientations, we derive coarse-grained equations for the dynamics of the pool of cytoplasmic and membrane-bound FtsZ. To capture stochastic effects expected in the system due to low particle numbers, we simulate our computational model using a Gillespie-type algorithm. We obtain ring- and arc-shaped aggregations of FtsZ polymers on the membrane as a function of monomer numbers in the cell. In particular, our model predicts the number of FtsZ rings forming in the cell as a function of cell geometry and FtsZ concentration. We also calculate the time of FtsZ ring localization to the midplane in the presence of Min oscillations. Finally, we demonstrate that the assumptions and results of our model are confirmed by 3D reconstructions of fluorescently-labeled FtsZ structures in E. coli that we obtained.

Bacterial colonies often exhibit complex spatio-temporal organization. This collective behavior is affected by a multitude of factors ranging from the properties of individual cells (shape, motility, membrane structure) to chemotaxis and other means of cell–cell communication. One of the important but often overlooked mechanisms of spatio-temporal organization is direct mechanical contact among cells in dense colonies such as biofilms. While in natural habitats all these different mechanisms and factors act in concert, one can use laboratory cell cultures to study certain mechanisms in isolation. Recent work demonstrated that growth and ensuing expansion flow of rod-like bacteria Escherichia coli in confined environments leads to orientation of cells along the flow direction and thus to ordering of cells. However, the cell orientational ordering remained imperfect. In this paper we study one mechanism responsible for the persistence of disorder in growing cell populations. We demonstrate experimentally that a growing colony of nematically ordered cells is prone to the buckling instability. Our theoretical analysis and discrete-element simulations suggest that the nature of this instability is related to the anisotropy of the stress tensor in the ordered cell colony.

A two-dimensional model is proposed for intercellular calcium (Ca^{2 +}) waves with Ca^{2 +}-induced IP₃ regeneration and the diffusion of IP₃ through gap junctions. Many experimental observations in glial cells, i.e. responding to local mechanical stimulation, glutamate application, mechanical stimulation followed by ACh application, and glutamate followed by mechanical stimulation, are reproduced and classified by the model. We show that a glial cell model with bistable dynamics, i.e. a Ca^{2 +} oscillation state coexisting with a fixed point, can cause a prolonged plateau of Ca^{2 +} signals in the cells nearby the stimulated cell when the cell network responds to the local mechanical stimulation.

The degree to which diffusion contributes to positioning cellular structures is an open question. Here we investigate the question of whether diffusive motion of centrin granules would allow them to interact with the mother centriole. The role of centrin granules in centriole duplication remains unclear, but some proposed functions of these granules, for example, in providing pre-assembled centriole subunits, or by acting as unstable 'pre-centrioles' that need to be captured by the mother centriole (La Terra et al 2005 J. Cell Biol.168 713–22), require the centrin foci to reach the mother. To test whether diffusive motion could permit such interactions in the necessary time scale, we measured the motion of centrin-containing foci in living human U2OS cells. We found that these centrin foci display apparently diffusive undirected motion. Using the apparent diffusion constant obtained from these measurements, we calculated the time scale required for diffusion to capture by the mother centrioles and found that it would greatly exceed the time available in the cell cycle. We conclude that mechanisms invoking centrin foci capture by the mother, whether as a pre-centriole or as a source of components to support later assembly, would require a form of directed motility of centrin foci that has not yet been observed.

The integration of processes at different scales is a key problem in the modelling of cell populations. Owing to increased computational resources and the accumulation of data at the cellular and subcellular scales, the use of discrete, cell-level models, which are typically solved using numerical simulations, has become prominent. One of the merits of this approach is that important biological factors, such as cell heterogeneity and noise, can be easily incorporated. However, it can be difficult to efficiently draw generalizations from the simulation results, as, often, many simulation runs are required to investigate model behaviour in typically large parameter spaces. In some cases, discrete cell-level models can be coarse-grained, yielding continuum models whose analysis can lead to the development of insight into the underlying simulations. In this paper we apply such an approach to the case of a discrete model of cell dynamics in the intestinal crypt. An analysis of the resulting continuum model demonstrates that there is a limited region of parameter space within which steady-state (and hence biologically realistic) solutions exist. Continuum model predictions show good agreement with corresponding results from the underlying simulations and experimental data taken from murine intestinal crypts.

Most cancers are curable if they are diagnosed and treated at an early stage. Recent studies suggest that nanoarchitectural changes occur within cells during early carcinogenesis and that such changes precede microscopically evident tissue alterations. It follows that the ability to comprehensively interrogate cell nanoarchitecture (e.g., macromolecular complexes, DNA, RNA, proteins and lipid membranes) could be critical to the diagnosis of early carcinogenesis. We present a study of the nanoscale mass-density fluctuations of biological tissues by quantifying their degree of disorder at the nanoscale. Transmission electron microscopy images of human tissues are used to construct corresponding effective disordered optical lattices. The properties of nanoscale disorder are then studied by statistical analysis of the inverse participation ratio (IPR) of the spatially localized eigenfunctions of these optical lattices at the nanoscale. Our results show an increase in the disorder of human colonic epithelial cells in subjects harboring early stages of colon neoplasia. Furthermore, our findings strongly suggest that increased nanoscale disorder correlates with the degree of tumorigenicity. Therefore, the IPR technique provides a practicable tool for the detection of nanoarchitectural alterations in the earliest stages of carcinogenesis. Potential applications of the technique for early cancer screening and detection are also discussed.

The mechanical properties (e.g. stiffness) of the extracellular matrix (ECM) influence cell fate and tissue morphogenesis and contribute to disease progression. Nevertheless, our understanding of the mechanisms by which ECM rigidity modulates cell behavior and fate remains rudimentary. To address this issue, a number of two and three-dimensional (3D) hydrogel systems have been used to explore the effects of the mechanical properties of the ECM on cell behavior. Unfortunately, many of these systems have limited application because fiber architecture, adhesiveness and/or pore size often change in parallel when gel elasticity is varied. Here we describe the use of ECM-adsorbed, synthetic, self-assembling peptide (SAP) gels that are able to recapitulate normal epithelial acini morphogenesis and gene expression in a 3D context. By exploiting the range of viscoelasticity attainable with these SAP gels, and their ability to recreate native-like ECM fibril topology with minimal variability in ligand density and pore size, we were able to reconstitute normal and tumor-like phenotypes and gene expression patterns in nonmalignant mammary epithelial cells. Accordingly, this SAP hydrogel system presents the first tunable system capable of independently assessing the interplay between ECM stiffness and multi-cellular epithelial phenotype in a 3D context.

In this work, we model biological tissues using a simple, mechanistic simulation based on dissipative particle dynamics. We investigate the continuum behavior of the simulated tissue and determine its dependence on the properties of the individual cell. Cells in our simulation adhere to each other, expand in volume, divide after reaching a specific size checkpoint and undergo apoptosis at a constant rate, leading to a steady-state homeostatic pressure in the tissue. We measure the dependence of the homeostatic state on the microscopic parameters of our model and show that homeostatic pressure, rather than the unconfined rate of cell division, determines the outcome of tissue competitions. Simulated cell aggregates are cohesive and round up due to the effect of tissue surface tension, which we measure for different tissues. Furthermore, mixtures of different cells unmix according to their adhesive properties. Using a variety of shear and creep simulations, we study tissue rheology by measuring yield stresses, shear viscosities, complex viscosities as well as the loss tangents as a function of model parameters. We find that cell division and apoptosis lead to a vanishing yield stress and fluid-like tissues. The effects of different adhesion strengths and levels of noise on the rheology of the tissue are also measured. In addition, we find that the level of cell division and apoptosis drives the diffusion of cells in the tissue. Finally, we present a method for measuring the compressibility of the tissue and its response to external stress via cell division and apoptosis.

Models of calcium (Ca^{2 +}) release sites derived from continuous-time Markov chain (CTMC) models of intracellular Ca^{2 +} channels exhibit collective gating reminiscent of the experimentally observed phenomenon of Ca^{2 +} puffs and sparks. In order to overcome the state-space explosion that occurs in compositionally defined Ca^{2 +} release site models, we have implemented an automated procedure for model reduction that replaces aggregated states of the full release site model with much simpler CTMCs that have similar within-group phase-type sojourn times and inter-group transitions. Error analysis based on comparison of full and reduced models validates the method when applied to release site models composed of 20 three-state channels that are both activated and inactivated by Ca^{2 +}. Although inspired by existing techniques for fitting moments of phase-type distributions, the automated reduction method for compositional Ca^{2 +} release site models is unique in several respects and novel in this biophysical context.

In very low density situations where a single myxobacterial cell is isolated from direct contact with other cells, the slime capsule interaction with the substrate or slime tracks on the substrate produce a viscous drag that results in a smooth gliding motion. Viscoelastic interactions of myxobacteria cells in a low-density domain close to the edge of a swarm are studied using a combination of a cell-based three-dimensional computational model and cell-tracking experiments. The model takes into account the flexible nature of Myxococcus xanthus as well as the effects of adhesion between cells arising from the interaction of the capsular polysaccharide covering two cells in contact with each other. New image and dynamic cell curvature analysis algorithms are used to track and measure the change in cell shapes that occur as flexible cells undergo significant bending during collisions resulting in direct calibration of the model parameters. Like aspect-ratio and directional reversals, the flexibility of cells and the adhesive cell–cell and cell–substrate interactions of M. xanthus play an important role in smooth gliding and more efficient swarming.

Geometric targeting (GT) is a recently introduced method for rapidly generating all-atom pathways from one protein state to another, based on geometric rather than energetic considerations. To generate pathways, a bias is applied that gradually moves atoms toward a target structure, while a set of geometric constraints between atoms is enforced to keep the structure stereochemically acceptable. In this work, we compare conformational pathways generated from GT to pathways from the much more computationally intensive and commonly used targeted molecular dynamics (TMD) technique, for a complicated conformational change in the signaling protein nitrogen regulatory protein C. We show that the all-atom pathways from GT are similar to previously reported TMD pathways for this protein, by comparing motion along six progress variables that describe the various structural changes. The results suggest that for nitrogen regulatory protein C, finding an all-atom pathway is primarily a problem of geometry, and that a detailed force field in this case constitutes an unnecessary extra layer of detail. We also show that the pathway snapshots from GT have good structure quality, by measuring various structure quality metrics. Transient hydrogen bonds detected by the two methods show some similarities but also some differences. The results justify the usage of GT as a rapid, approximate alternative to TMD for generating stereochemically acceptable all-atom pathways in highly constrained protein systems.

The affiliations for Robert M Hoffman given for this paper were incomplete. The correct affiliations are below.

Robert M Hoffman^3,4

³AntiCancer Inc., 7917 Ostrow Street, San Diego, California 92111, USA ⁴Department of Surgery, University of California San Diego, 200 West Arbor Drive, San Diego, California 92103-8220, USA