Directional reversals enable Myxococcus xanthus cells to produce collective one-dimensional streams during fruiting-body formation

The formation of a collectively moving group benefits individuals within a population in a variety of ways. The surface-dwelling bacterium Myxococcus xanthus forms dynamic collective groups both to feed on prey and to aggregate during times of starvation. The latter behaviour, termed fruiting-body formation, involves a complex, coordinated series of density changes that ultimately lead to three-dimensional aggregates comprising hundreds of thousands of cells and spores. How a loose, two-dimensional sheet of motile cells produces a fixed aggregate has remained a mystery as current models of aggregation are either inconsistent with experimental data or ultimately predict unstable structures that do not remain fixed in space. Here, we use high-resolution microscopy and computer vision software to spatio-temporally track the motion of thousands of individuals during the initial stages of fruiting-body formation. We find that cells undergo a phase transition from exploratory flocking, in which unstable cell groups move rapidly and coherently over long distances, to a reversal-mediated localization into one-dimensional growing streams that are inherently stable in space. These observations identify a new phase of active collective behaviour and answer a long-standing open question in Myxococcus development by describing how motile cell groups can remain statistically fixed in a spatial location.     

The Measurement of Little g: A Fertile Ground for Precision Measurement Science

The occasion of the 100th anniversary of Einstein’s “golden year” provides a wonderful opportunity to discuss some aspects of gravity—gravitation being an interest of Einstein’s that occurred a few years after 1905. I’ll do this by talking about the measurement of little g, the free-fall acceleration on the Earth’s surface that is mainly due to the Earth’s gravity but whose value is also affected by centrifugal forces that are a result of the Earth’s rotation. I will also describe two equivalence experiments and a test of the inverse-square law of gravitation. Finally, I will make some observations on the science of precision measurement—a subject that underpins much of scientific progress.     

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.     

Lag,lock, sync,slip: the many ‘phases’ of coupled flagella

In a multitude of life''s processes, cilia and flagella are found indispensable. Recently, the biflagellated chlorophyte alga Chlamydomonas has become a model organism for the study of ciliary motility and synchronization. Here, we use high-speed, high-resolution imaging of single pipette-held cells to quantify the rich dynamics exhibited by their flagella. Underlying this variability in behaviour are biological dissimilarities between the two flagella—termed cis and trans, with respect to a unique eyespot. With emphasis on the wild-type, we derive limit cycles and phase parametrizations for self-sustained flagellar oscillations from digitally tracked flagellar waveforms. Characterizing interflagellar phase synchrony via a simple model of coupled oscillators with noise, we find that during the canonical swimming breaststroke the cis flagellum is consistently phase-lagged relative to, while remaining robustly phase-locked with, the trans flagellum. Transient loss of synchrony, or phase slippage, may be triggered stochastically, in which the trans flagellum transitions to a second mode of beating with attenuated beat envelope and increased frequency. Further, exploiting this alga''s ability for flagellar regeneration, we mechanically induced removal of one or the other flagellum of the same cell to reveal a striking disparity between the beatings of the cis and trans flagella, in isolation. These results are evaluated in the context of the dynamic coordination of Chlamydomonas flagella.     

Ambiguities in Powder Indexing: the Impact of a Quaternary Lattice Metric Singularity on the Characterization of Mawsonite and Chatkalite

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The minerals Mawsonite and Chatkalite are of especial interest as both are characterized by tetragonal unit cells that correspond to the second member of a quaternary lattice metric singularity. This singularity includes lattices that are Cubic I, Tetragonal P, Orthorhombic F, and Orthorhombic P. The Mawsonite and Chatkalite lattices are unique in that they are highly specialized. In each case: (1) the determinative c/a ratio is very near 1/√2, (2) the symmetrical scalars of the reduced form [a · a : b · b : c · c = 1:2:2] have greater specialization than required for the given reduced form type, (3) the tetragonal lattice has derivative lattices of higher symmetry, and (4) the powder pattern is highly compressed. Mawsonite and Chatkalite serve as exemplar-type compounds. Their tetragonal structure has important implications in structure determination using powder diffraction data. First, any cubic I lattice — established solely on the basis of indexing procedures — may actually be tetragonal or orthorhombic. Second, in establishing the lattice of an unknown, results from powder data indexing require routine confirmation by other techniques (e.g., single crystal, optical, etc.).     

Conventional Cells—The Last Step Toward General Acceptance of Standard Conventional Cells for the Reporting of Crystallographic Data

In 1969, a seminal section on reduced forms and conventional cells was published in the International Tables for X-Ray Crystallography. The section contains a table that gives a metric classification of the 44 reduced forms. In 2001, this table with appropriate revisions was republished in the Journal of Research of the National Institute of Standards and Technology. An especially valuable feature of the table is that it defines and allows the user to determine a standard conventional cell. Since 1969, there has been an evolution toward acceptance and widespread use of such conventional cells. An inspection of the articles in key crystallographic journals reveals that most cells follow the conventions. However, one major exception remains—the centered monoclinic lattices. In approximately one-third of these cases, non-conventional C-centered cells are used, apparently to avoid the use of I-centered cells. It is recommended that the crystallographic community routinely use the I-centered conventional cell in such cases.     

Optical parameters of the tunable Bragg reflectors in squid

Cephalopods (e.g. octopus, squid and cuttlefish) dynamically tune the colour and brightness of their skin for camouflage and communication using specialized skin cells called iridocytes. We use high-resolution microspectrophotometry to investigate individual tunable Bragg structures (consisting of alternating reflectin protein-containing, high-refractive index lamellae and low-refractive index inter-lamellar spaces) in live and chemically fixed iridocytes of the California market squid, Doryteuthis opalescens. This subcellular, single-stack microspectrophotometry allows for spectral normalization, permitting use of a transfer-matrix model of Bragg reflectance to calculate all the parameters of the Bragg stack—the refractive indices, dimensions and numbers of the lamellae and inter-lamellar spaces. Results of the fitting analyses show that eight or nine pairs of low- and high-index layers typically contribute to the observed reflectivity in live cells, whereas six or seven pairs of low- and high-index layers typically contribute to the reflectivity in chemically fixed cells. The reflectin-containing, high-index lamellae of live cells have a refractive index proportional to the peak reflectivity, with an average of 1.405 ± 0.012 and a maximum around 1.44, while the reflectin-containing lamellae in fixed tissue have a refractive index of 1.413 ± 0.015 suggesting a slight increase of refractive index in the process of fixation. As expected, incremental changes in refractive index contribute to the greatest incremental changes in reflectivity for those Bragg stacks with the most layers. The excursions in dimensions required to tune the measured reflected wavelength from 675 (red) to 425 nm (blue) are a decrease from ca 150 to 80 nm for the high-index lamellae and from ca 120 to 50 nm for the low-index inter-lamellar spaces. Fixation-induced dimensional changes also are quantified, leading us to suggest that further microspectrophotometric analyses of this iridocyte system can be used as a model system to quantify the effects of various methods of tissue fixation. The microspectrophotometry technique described can be expected to provide deeper insights into the molecular and physical mechanisms governing other biophotonically active cells and structures.     

Effect of magnetic fields on cryptochrome-dependent responses in Arabidopsis thaliana

The scientific literature describing the effects of weak magnetic fields on living systems contains a plethora of contradictory reports, few successful independent replication studies and a dearth of plausible biophysical interaction mechanisms. Most such investigations have been unsystematic, devoid of testable theoretical predictions and, ultimately, unconvincing. A recent study, of magnetic responses in the model plant Arabidopsis thaliana, however, stands out; it has a clear hypothesis—that seedling growth is magnetically sensitive as a result of photoinduced radical-pair reactions in cryptochrome photoreceptors—tested by measuring several cryptochrome-dependent responses, all of which proved to be enhanced in a magnetic field of intensity 500 μT. The potential importance of this study in the debate on putative effects of extremely low-frequency electromagnetic fields on human health prompted us to subject it to the ‘gold standard’ of independent replication. With experimental conditions chosen to match those of the original study, we have measured hypocotyl lengths and anthocyanin accumulation for Arabidopsis seedlings grown in a 500 μT magnetic field, with simultaneous control experiments at 50 μT. Additionally, we have determined hypocotyl lengths of plants grown in 50 μT, 1 mT and approximately 100 mT magnetic fields (with zero-field controls), measured gene (CHS, HY5 and GST) expression levels, investigated blue-light intensity effects and explored the influence of sucrose in the growth medium. In no case were consistent, statistically significant magnetic field responses detected.     

Surface design with self-heating smart polymers for on–off switchable traps

We have developed a novel self-heating, temperature-responsive chromatography system for the effective separation of biomolecules. Temperature-responsive poly(N-isopropylacrylamide-co-N-hydroxymethylacrylamide), poly(NIPAAm-co-HMAAm), was covalently grafted onto the surface of magnetite/silica composites as ‘on-off’ switchable surface traps. The lower critical solution temperature (LCST) of the poly(NIPAAm-co-HMAAm)s was controlled from 35 to 55 °C by varying the HMAAm content. Using the heat generated by magnetic particles in an alternating magnetic field (AMF) we were able to induce the hydrophilic to hydrophobic phase separation of the grafted temperature-responsive polymers. To assess the feasibility of the poly(NIPAAm-co-HMAAm)-grafted magnetite/silica particles as the stationary phase for chromatography, we packed the particles into the glass column of a liquid chromatography system and analyzed the elusion profiles for steroids. The retention time for hydrophobic steroids markedly increased in the AMF, because the hydrophobic interaction was enhanced via self-heating of the grafted magnetite/silica particles, and this effect could be controlled by changing the AMF irradiation time. Turning off the AMF shortened the total analysis time for steroids. The proposed system is useful for separating bioactive compounds because their elution profiles can be easily controlled by an AMF.     

Crowdsourcing contest dilemma

Crowdsourcing offers unprecedented potential for solving tasks efficiently by tapping into the skills of large groups of people. A salient feature of crowdsourcing—its openness of entry—makes it vulnerable to malicious behaviour. Such behaviour took place in a number of recent popular crowdsourcing competitions. We provide game-theoretic analysis of a fundamental trade-off between the potential for increased productivity and the possibility of being set back by malicious behaviour. Our results show that in crowdsourcing competitions malicious behaviour is the norm, not the anomaly—a result contrary to the conventional wisdom in the area. Counterintuitively, making the attacks more costly does not deter them but leads to a less desirable outcome. These findings have cautionary implications for the design of crowdsourcing competitions.     

Complexity analysis of sleep and alterations with insomnia based on non-invasive techniques

For the first time, fractal analysis techniques are implemented to study the correlations present in sleep actigraphy for individuals suffering from acute insomnia with comparisons made against healthy subjects. Analysis was carried out for 21 healthy individuals with no diagnosed sleep disorders and 26 subjects diagnosed with acute insomnia during night-time hours. Detrended fluctuation analysis was applied in order to look for 1/f-fluctuations indicative of high complexity. The aim is to investigate whether complexity analysis can differentiate between people who sleep normally and people who suffer from acute insomnia. We hypothesize that the complexity will be higher in subjects who suffer from acute insomnia owing to increased night-time arousals. This hypothesis, although contrary to much of the literature surrounding complexity in physiology, was found to be correct—for our study. The complexity results for nearly all of the subjects fell within a 1/f-range, indicating the presence of underlying control mechanisms. The subjects with acute insomnia displayed significantly higher correlations, confirmed by significance testing—possibly a result of too much activity in the underlying regulatory systems. Moreover, we found a linear relationship between complexity and variability, both of which increased with the onset of insomnia. Complexity analysis is very promising and could prove to be a useful non-invasive identifier for people who suffer from sleep disorders such as insomnia.     

Transmission and dose�Cresponse experiments for social animals: a reappraisal of the colonization biology of Campylobacter jejuni in chickens

Dose–response experiments characterize the relationship between infectious agents and their hosts. These experiments are routinely used to estimate the minimum effective infectious dose for an infectious agent, which is most commonly characterized by the dose at which 50 per cent of challenged hosts become infected—the ID₅₀. In turn, the ID₅₀ is often used to compare between different agents and quantify the effect of treatment regimes. The statistical analysis of dose–response data typically makes the assumption that hosts within a given dose group are independent. For social animals, in particular avian species, hosts are routinely housed together in groups during experimental studies. For experiments with non-infectious agents, this poses no practical or theoretical problems. However, transmission of infectious agents between co-housed animals will modify the observed dose–response relationship with implications for the estimation of the ID₅₀ and the comparison between different agents and treatments. We derive a simple correction to the likelihood for standard dose–response models that allows us to estimate dose–response and transmission parameters simultaneously. We use this model to show that: transmission between co-housed animals reduces the apparent value of the ID₅₀ and increases the variability between replicates leading to a distinctive all-or-nothing response; in terms of the total number of animals used, individual housing is always the most efficient experimental design for ascertaining dose–response relationships; estimates of transmission from previously published experimental data for Campylobacter spp. in chickens suggest that considerable transmission occurred, greatly increasing the uncertainty in the estimates of dose–response parameters reported in the literature. Furthermore, we demonstrate that accounting for transmission in the analysis of dose–response data for Campylobacter spp. challenges our current understanding of the differing response of chickens with respect to host-age and in vivo passage of bacteria. Our findings suggest that the age-dependence of transmissibility between hosts—rather than their susceptibility to colonization—is the mechanism behind the ‘lag-phase’ reported in commercial flocks, which are typically found to be Campylobacter free for the first 14–21 days of life.     

Ambiguities in Powder Indexing: Conjunction of a Ternary and Binary Lattice Metric Singularity in the Cubic System

A lattice metric singularity occurs when unit cells defining two (or more) lattices yield the identical set of unique calculated d-spacings. The existence of such singularities, therefore, has a practical and theoretical impact on the indexing of powder patterns. For example, in experimental practice an indexing program may find only the lower symmetry member of a singularity. Obviously, it is important to recognize such cases and know how to proceed. Recently, we described:

1. a binary singularity involving a monoclinic and a rhombohedral lattice in a subcell-supercell relationship and
2. a second type of singularity—a ternary singularity–in which two of the three lattices are in a derivative composite relationship. In this work, we describe a ternary lattice metric singularity involving a cubic P, a tetragonal P, and an orthorhombic C lattice. Furthermore, there is a binary singularity, involving a hexagonal P and orthorhombic P lattice, which is characterized by a set of unique d-spacings very close to that of the ternary singularity. The existence of such singularities is more common than once thought and requires a paradigm shift in experimental practice. In addition singularities provide opportunities in material design as they point to highly specialized lattices that may be associated with unusual physical properties.

     

Osteogenic differentiation and mineralization in fibre-reinforced tubular scaffolds: theoretical study and experimental evidences

The development of composite scaffolds with well-organized architecture and multi-scale properties (i.e. porosity, degradation) represents a valid approach for achieving a tissue-engineered construct capable of reproducing the medium- and long-term in vitro behaviour of hierarchically complex tissues such as spongy bone. To date, the implementation of scaffold design strategies able to summarize optimal scaffold architecture as well as intrinsic mechanical, chemical and fluid transport properties still remains a challenging issue. In this study, poly ɛ-caprolactone/polylactid acid (PCL/PLA) tubular devices (fibres of PLA in a PCL matrix) obtained by phase inversion/salt leaching and filament winding techniques were proposed as cell instructive scaffold for bone osteogenesis. Continuous fibres embedded in the polymeric matrix drastically improved the mechanical response as confirmed by compression elastic moduli, which vary from 0.214 ± 0.065 to 1.174 ± 0.143 MPa depending on the relative fibre/matrix and polymer/solvent ratios. Moreover, computational fluid dynamic simulations demonstrated the ability of composite structure to transfer hydrodynamic forces during in vitro culture, thus indicating the optimal flow rate conditions that, case by case, enables specific cellular events—i.e. osteoblast differentiation from human mesenchymal stem cells (hMSCs), mineralization, etc. Hence, we demonstrate that the hMSC differentiation preferentially occurs in the case of higher perfusion rates—over 0.05 ml min^–1—as confirmed by the expression of alkaline phosphate and osteocalcin markers. In particular, the highest osteopontin values and a massive mineral phase precipitation of bone-like phases detected in the case of intermediate flow rates (i.e. 0.05 ml min^–1) allows us to identify the best condition to stimulate the bone extracellular matrix in-growth, in agreement with the hydrodynamic model prediction. All these results concur to prove the succesful use of tubular composite as temporary device for long bone treatment.     

The effect of remodelling and contractility of the actin cytoskeleton on the shear resistance of single cells: a computational and experimental investigation

The biomechanisms that govern the response of chondrocytes to mechanical stimuli are poorly understood. In this study, a series of in vitro tests are performed, in which single chondrocytes are subjected to shear deformation by a horizontally moving probe. Dramatically different probe force–indentation curves are obtained for untreated cells and for cells in which the actin cytoskeleton has been disrupted. Untreated cells exhibit a rapid increase in force upon probe contact followed by yielding behaviour. Cells in which the contractile actin cytoskeleton was removed exhibit a linear force–indentation response. In order to investigate the mechanisms underlying this behaviour, a three-dimensional active modelling framework incorporating stress fibre (SF) remodelling and contractility is used to simulate the in vitro tests. Simulations reveal that the characteristic force–indentation curve observed for untreated chondrocytes occurs as a result of two factors: (i) yielding of SFs due to stretching of the cytoplasm near the probe and (ii) dissociation of SFs due to reduced cytoplasm tension at the front of the cell. In contrast, a passive hyperelastic model predicts a linear force–indentation curve similar to that observed for cells in which the actin cytoskeleton has been disrupted. This combined modelling–experimental study offers a novel insight into the role of the active contractility and remodelling of the actin cytoskeleton in the response of chondrocytes to mechanical loading.     

In situ study of aggregate sizes formed in chalcopyrite-quartz mixture using temperature-responsive polymers

An interesting property of temperature-responsive polymers, such as poly(N-isopropylacrylamide) (PNIPAM), is the ability to behave as flocculants above a lower critical solution temperature (LCST). This study examines the aggregation of a chalcopyrite-quartz mixture using a sulfide-selective temperature-responsive polymer, P(NIPAM-co-ethyl xanthate methacrylate (EXMA)) in a continuously-sheared suspension, relative to polyacrylamide (PAM). The investigation was carried out in situ using imaging and Focused Beam Reflectance Measurement techniques to obtain real-time chord length distributions. While particle aggregates were observed in the presence of PNIPAM only upon heating above the LCST, P(NIPAM-co-EXMA) induced particle aggregation below the LCST, due to the attraction between the xanthate moiety and the sulfide surfaces. The largest aggregates were observed with P(NIPAM-co-EXMA) (1.5 MDa), followed by PNIPAM, PAM, and P(NIPAM-co-EXMA) (115?kDa). Particle aggregates formed with PAM did not exhibit further breakage under increasing shear to 1100?s^?1, while large-scale fragmentation was observed with the PNIPAM-based flocculants. Unlike PNIPAM, addition of P(NIPAM-co-EXMA) to suspension above the LCST was able to yield particle aggregation, attributed to the formation of charge-stabilised micelles. The influence of the shear rate on the size of the aggregates formed with P(NIPAM-co-EXMA) is unaffected by the polymer addition and measurement temperature below or above the LCST.     

Dynamics and pattern formation in thermally induced phase separation of polymer–solvent system

In this paper, the characteristic dynamics and pattern formation of polymer–solvent system, undergoing thermal induced phase separation (spinodal decomposition), have been studied using non-linear simulations. The modified Cahn–Hilliard equation with the incorporation of the Flory–Huggins free energy model is used. The development of a wide variety of initial and intermediate stage morphology is feasible either by introducing sharp/continuous spatial temperature variation or by altering the initial mean solvent concentration (C_o) in the vicinity of the minima (C_m) of the spinodal parameter (second derivative of excess Gibbs free energy w.r.t concentration). For C_o < C_m initial stage of phase separation proceeds by the formation of columns/island of the solvent rich phase dispersed in polymer rich continuous phase. On the contrary, C_o > C_m, phase separation leads to formation of holes of polymer rich phase dispersed in the continuous solvent rich phase. For an intermediate mean concentration very close to C_m inter-connecting structures are evolved. A continuous variation of spatial temperature leads to the directional (rather than random) evolution of phase separated pattern. The initial stage of evolution always propagates from the lowest to the highest temperature regime. A spatial step variation of temperature leads to formation of localized novel phase separated patterns. For a flow system, the dynamics and pattern formation can be controlled by tuning the different timescales: timescale of convection, de-mixing and coalescence.     

Immobilisation of bacteria onto magnetic nanoparticles for the decolorisation and degradation of azo dyes

Azo dyes are widely used in industries and their release in the environment contributes to the pollution of effluents. The authors aim to develop a new eco‐friendly water treatment method for the degradation of azo dyes based on in situ magnetic separation and immobilisation of bacterial cells. The immobilisation was achieved using superparamagnetic Fe₃ O₄ nanoparticles and offers the possibility of reusing bacteria by magnetic separation for several degradation cycles. The iron– oxide nanoparticles were synthesised by reverse co‐precipitation. The Gram‐positive bacteria Bacillus subtilis were immobilised using iron–oxide nanoparticles by adsorption and then separated with an external magnetic field. Transmission electron microscopy observation showed that the particles'' diameter was ∼20 nm with a narrow size distribution. Moreover, the iron–oxide nanoparticles were adsorbed onto the surface in order to coat the cells. B. subtilis has proved its ability to decolorise and degrade several azo dyes at different values of pH, with the highest decolorisation rate for Congo red. Furthermore, immobilised cells have a degradation activity similar to that of free cells. The system provided a degradation rate up to 80% and could be reused for seven batch cycles.Inspec keywords: biotechnology, microorganisms, pH, adsorption, iron compounds, superparamagnetism, transmission electron microscopy, ultraviolet spectra, chemical technology, wastewater treatment, effluents, dyes, magnetic separation, iron, magnetic particles, decontaminationOther keywords: degradation rate, immobilisation, magnetic nanoparticles, azo dyes, eco‐friendly water treatment method, degradation cycles, Gram‐positive bacteria, iron–oxide nanoparticles, external magnetic field, immobilised cells, degradation activity, magnetic separation, effluents, bacterial cells, Fe₃ O₄      

The role of mechanical forces in the planar-to-bulk transition in growing Escherichia coli microcolonies

Mechanical forces are obviously important in the assembly of three-dimensional multicellular structures, but their detailed role is often unclear. We have used growing microcolonies of the bacterium Escherichia coli to investigate the role of mechanical forces in the transition from two-dimensional growth (on the interface between a hard surface and a soft agarose pad) to three-dimensional growth (invasion of the agarose). We measure the position within the colony where the invasion transition happens, the cell density within the colony and the colony size at the transition as functions of the concentration of the agarose. We use a phenomenological theory, combined with individual-based computer simulations, to show how mechanical forces acting between the bacterial cells, and between the bacteria and the surrounding matrix, lead to the complex phenomena observed in our experiments—in particular the observation that agarose concentration non-trivially affects the colony size at transition. Matching these approaches leads to a prediction for how the friction between the bacteria and the agarose should vary with agarose concentration. Our experimental conditions mimic numerous clinical and environmental scenarios in which bacteria invade soft matrices, as well as shedding more general light on the transition between two- and three-dimensional growth in multicellular assemblies.     

A dose and time response Markov model for the in-host dynamics of infection with intracellular bacteria following inhalation: with application to Francisella tularensis

In a novel approach, the standard birth–death process is extended to incorporate a fundamental mechanism undergone by intracellular bacteria, phagocytosis. The model accounts for stochastic interaction between bacteria and cells of the immune system and heterogeneity in susceptibility to infection of individual hosts within a population. Model output is the dose–response relation and the dose-dependent distribution of time until response, where response is the onset of symptoms. The model is thereafter parametrized with respect to the highly virulent Schu S4 strain of Francisella tularensis, in the first such study to consider a biologically plausible mathematical model for early human infection with this bacterium. Results indicate a median infectious dose of about 23 organisms, which is higher than previously thought, and an average incubation period of between 3 and 7 days depending on dose. The distribution of incubation periods is right-skewed up to about 100 organisms and symmetric for larger doses. Moreover, there are some interesting parallels to the hypotheses of some of the classical dose–response models, such as independent action (single-hit model) and individual effective dose (probit model). The findings of this study support experimental evidence and postulations from other investigations that response is, in fact, influenced by both in-host and between-host variability.