Minimal reaction sets for Escherichia coli metabolism under different growth requirements and uptake environments

A computational procedure for identifying the minimal set of metabolic reactions capable of supporting various growth rates on different substrates is introduced and applied to a flux balance model of the Escherichia coli metabolic network. This task is posed mathematically as a generalized network optimization problem. The minimal reaction sets capable of supporting specified growth rates are determined for two different uptake conditions: (i) limiting the uptake of organic material to a single organic component (e.g., glucose or acetate) and (ii) allowing the importation of any metabolite with available cellular transport reactions. We find that minimal reaction network sets are highly dependent on the uptake environment and the growth requirements imposed on the network. Specifically, we predict that the E. coli network, as described by the flux balance model, requires 224 metabolic reactions to support growth on a glucose-only medium and 229 for an acetate-only medium, while only 122 reactions enable growth on a specially engineered growth medium.     

Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of Escherichia coli.

The very high concentration of macromolecules within cells can potentially have an overwhelming effect on the thermodynamic activity of cellular components because of excluded volume effects. To estimate the magnitudes of such effects, we have made an experimental study of the cytoplasm of Escherichia coli. Parameters from cells and cell extracts are used to calculate approximate activity coefficients for cytoplasmic conditions. These calculations require a representation of the sizes, concentrations and effective specific volumes of the macromolecules in the extracts. Macromolecule size representations are obtained either by applying a two-phase distribution assay to define a related homogeneous solution or by using the molecular mass distribution of macromolecules from gel filtration. Macromolecule concentrations in cytoplasm are obtained from analyses of extracts by applying a correction for the dilution that occurs during extraction. That factor is determined from experiments based upon the known impermeability of the cytoplasmic volume to sucrose in intact E. coli. Macromolecule concentrations in the cytoplasm of E. coli in either exponential or stationary growth phase are estimated to be approximately 0.3 to 0.4 g/ml. Macromolecule specific volumes are inferred from the composition of close-packed precipitates induced by polyethylene glycol. Several well-characterized proteins which bind to DNA (lac repressor, RNA polymerase) are extremely sensitive to changes in salt concentration in studies in vitro, but are insensitive in studies in vivo. Application of the activity coefficients from the present work indicates that at least part of this discrepancy arises from the difference in excluded volumes in these studies. Applications of the activity coefficients to solubility or to association reactions are also discussed, as are changes associated with cell growth phase and osmotic or other effects. The use of solutions of purified macromolecules that emulate the crowding conditions inferred for cytoplasm is discussed.     

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data

Modern 3D electron microscopy approaches have recently allowed unprecedented insight into the 3D ultrastructural organization of cells and tissues, enabling the visualization of large macromolecular machines, such as adhesion complexes, as well as higher-order structures, such as the cytoskeleton and cellular organelles in their respective cell and tissue context. Given the inherent complexity of cellular volumes, it is essential to first extract the features of interest in order to allow visualization, quantification, and therefore comprehension of their 3D organization. Each data set is defined by distinct characteristics, e.g., signal-to-noise ratio, crispness (sharpness) of the data, heterogeneity of its features, crowdedness of features, presence or absence of characteristic shapes that allow for easy identification, and the percentage of the entire volume that a specific region of interest occupies. All these characteristics need to be considered when deciding on which approach to take for segmentation.The six different 3D ultrastructural data sets presented were obtained by three different imaging approaches: resin embedded stained electron tomography, focused ion beam- and serial block face- scanning electron microscopy (FIB-SEM, SBF-SEM) of mildly stained and heavily stained samples, respectively. For these data sets, four different segmentation approaches have been applied: (1) fully manual model building followed solely by visualization of the model, (2) manual tracing segmentation of the data followed by surface rendering, (3) semi-automated approaches followed by surface rendering, or (4) automated custom-designed segmentation algorithms followed by surface rendering and quantitative analysis. Depending on the combination of data set characteristics, it was found that typically one of these four categorical approaches outperforms the others, but depending on the exact sequence of criteria, more than one approach may be successful. Based on these data, we propose a triage scheme that categorizes both objective data set characteristics and subjective personal criteria for the analysis of the different data sets.     

Predicting Calendar Aging in Lithium Metal Secondary Batteries: The Impacts of Solid Electrolyte Interphase Composition and Stability

Calendar aging of lithium metal batteries, in which cells' components degrade internally due to chemical reactions while no current is being applied, is a relatively unstudied field. In this work, a model to predict calendar aging of lithium metal cells is developed using two sets of readily obtainable data: solid electrolyte interphase (SEI) layer composition (measured via X‐ray photoelectron spectroscopy) and SEI stability (measured as a degradation rate using a simple constant current–constant voltage charging protocol). Electrolyte properties such as volume and salt concentration are varied in order to determine their effect on SEI stability and composition, with subsequent impacts to calendar aging. Lower salt concentrations produce a solvent‐based, more soluble SEI, while the highest concentration produces a salt‐based, less soluble SEI. Higher electrolyte volumes promote dissolution of the SEI and thus decrease its stability. The model predicts that lithium metal would be the limiting factor in calendar aging, depleting long before the electrolyte does. Additionally, the relative composition of the electrolyte during aging is modeled and found to eventually converge to the same value independent of initial salt concentration.     

Condition-dependent cell volume and concentration of Escherichia coli to facilitate data conversion for systems biology modeling

Systems biology modeling typically requires quantitative experimental data such as intracellular concentrations or copy numbers per cell. In order to convert population-averaging omics measurement data to intracellular concentrations or cellular copy numbers, the total cell volume and number of cells in a sample need to be known. Unfortunately, even for the often studied model bacterium Escherichia coli this information is hardly available and furthermore, certain measures (e.g. cell volume) are also dependent on the growth condition. In this work, we have determined these basic data for E. coli cells when grown in 22 different conditions so that respective data conversions can be done correctly. First, we determine growth-rate dependent cell volumes. Second, we show that in a 1 ml E. coli sample at an optical density (600 nm) of 1 the total cell volume is around 3.6 μl for all conditions tested. Third, we demonstrate that the cell number in a sample can be determined on the basis of the sample's optical density and the cells' growth rate. The data presented will allow for conversion of E. coli measurement data normalized to optical density into volumetric cellular concentrations and copy numbers per cell--two important parameters for systems biology model development.     

Graph identification of proteins in tomograms (GRIP-Tomo)

In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases for refinement. We hypothesized that the topological connectivity of protein structures is invariant, and they are distinctive for the purpose of protein identification from distorted data presented in volume densities. Three-dimensional densities of a protein or a complex from simulated tomographic volumes were transformed into mathematical graphs as observables. We systematically introduced data distortion or defects such as missing fullness of data, the tumbling effect, and the missing wedge effect into the simulated volumes, and varied the distance cutoffs in pixels to capture the varying connectivity between the density cluster centroids in the presence of defects. A similarity score between the graphs from the simulated volumes and the graphs transformed from the physical protein structures in point data was calculated by comparing their network theory order parameters including node degrees, betweenness centrality, and graph densities. By capturing the essential topological features defining the heterogeneous morphologies of a network, we were able to accurately identify proteins and homo-multimeric complexes from 10 topologically distinctive samples without realistic noise added. Our approach empowers future developments of tomogram processing by providing pattern mining with interpretability, to enable the classification of single-domain protein native topologies as well as distinct single-domain proteins from multimeric complexes within noisy volumes.     

A framework for whole-cell mathematical modeling

The default framework for modeling biochemical processes is that of a constant-volume reactor operating under steady-state conditions. This is satisfactory for many applications, but not for modeling growth and division of cells. In this study, a whole-cell modeling framework is developed that assumes expanding volumes and a cell-division cycle. A spherical newborn cell is designed to grow in volume during the growth phase of the cycle. After 80% of the cycle period, the cell begins to divide by constricting about its equator, ultimately affording two spherical cells with total volume equal to twice that of the original. The cell is partitioned into two regions or volumes, namely the cytoplasm (Vcyt) and membrane (Vmem), with molecular components present in each. Both volumes change during the cell cycle; Vcyt changes in response to osmotic pressure changes as nutrients enter the cell from the environment, while Vmem changes in response to this osmotic pressure effect such that membrane thickness remains invariant. The two volumes change at different rates; in most cases, this imposes periodic or oscillatory behavior on all components within the cell. Since the framework itself rather than a particular set of reactions and components is responsible for this behavior, it should be possible to model various biochemical processes within it, affording stable periodic solutions without requiring that the biochemical process itself generates oscillations as an inherent feature. Given that these processes naturally occur in growing and dividing cells, it is reasonable to conclude that the dynamics of component concentrations will be more realistic than when modeled within constant-volume and/or steady-state frameworks. This approach is illustrated using a symbolic whole cell model.     

Calculation of standard atomic volumes for RNA and comparison with proteins: RNA is packed more tightly

Traditionally, for biomolecular packing calculations research has focused on proteins. Besides proteins, RNA is the other large biomolecule that has tertiary structure interactions and complex packing. No one has yet quantitatively investigated RNA packing or compared its packing to that of proteins because, until recently, there were no large RNA structures. Here we address this question in detail, using Voronoi volume calculations on a set of high-resolution RNA crystal structures. We do a careful parameterization, taking into account many factors such as atomic radii, crystal packing, structural complexity, solvent, and associated protein to obtain a self-consistent, universal set of volumes that can be applied to both RNA and protein. We report this set of volumes, which we call the NucProt parameter set. Our measured values are consistent across the many different RNA structures and packing environments. When common atom types are compared between proteins and RNA, nine of 12 types show that RNA has a smaller volume and packs more tightly than protein, suggesting that close-packing may be as important for the folding of RNAs as it is for proteins. Moreover, calculated partial specific volumes show that RNA bases pack more densely than corresponding aromatic residues from proteins. Finally, we find that RNA bases have similar packing volumes to DNA bases, despite the absence of tertiary contacts in DNA. Programs, parameter sets and raw data are available online at.     

Preliminary research on body composition measurement using X-ray phase contrast imaging

Body composition measurement is of cardinal significance for medical and clinical applications. Currently, the dual-energy X-ray absorptiometry (DEXA) technique is widely applied for this measurement. In this study, we present a novel measurement method using the absorption and phase information obtained simultaneously from the X-ray grating-based interferometer (XGI). Rather than requiring two projection data sets with different X-ray energy spectra, with the proposed method, both the areal densities of the bone and the surrounding soft tissue can be acquired utilizing one projection data set. By using a human body phantom constructed to validate the proposed method, experimental results have shown that the compositions can be calculated with an improved accuracy comparing to the dual energy method, especially for the soft tissue measurement. Since the proposed method can be easily implemented on current XGI setup, it will greatly extend the applications of the XGI, and meanwhile has the potential to be an alternative to DEXA for human body composition measurement.     

A spatial genomic approach identifies time lags and historical barriers to gene flow in a rapidly fragmenting Appalachian landscape

The resolution offered by genomic data sets coupled with recently developed spatially informed analyses are allowing researchers to quantify population structure at increasingly fine temporal and spatial scales. However, both empirical research and conservation measures have been limited by questions regarding the impacts of data set size, data quality thresholds and the timescale at which barriers to gene flow become detectable. Here, we used restriction site associated DNA sequencing to generate a 2,140 single nucleotide polymorphism (SNP) data set for the copperhead snake (Agkistrodon contortrix) and address the population genomic impacts of recent and widespread landscape modification across an ~1,000‐km² region of eastern Kentucky, USA. Nonspatial population‐based assignment and clustering methods supported little to no population structure. However, using individual‐based spatial autocorrelation approaches we found evidence for genetic structuring which closely follows the path of a historically important highway which experienced high traffic volumes from c. 1920 to 1970 before losing most traffic to a newly constructed alternative route. We found no similar spatial genomic signatures associated with more recently constructed highways or surface mining activity, although a time lag effect may be responsible for the lack of any emergent spatial genetic patterns. Subsampling of our SNP data set suggested that similar results could be obtained with as few as 250 SNPs, and a range of thresholds for missing data exhibited limited impacts on the spatial patterns we detected. While we were not able to estimate relative effects of land uses or precise time lags, our findings highlight the importance of temporal factors in landscape genetics approaches, and suggest the potential advantages of genomic data sets and fine‐scale, spatially informed approaches for quantifying subtle genetic patterns in temporally complex landscapes.     

Calculations of protein volumes: sensitivity analysis and parameter database

MOTIVATION: The precise sizes of protein atoms in terms of occupied packing volume are of great importance. We have previously presented standard volumes for protein residues based on calculations with Voronoi-like polyhedra. To understand the applicability and limitations of our set, we investigated, in detail, the sensitivity of the volume calculations to a number of factors: (i) the van der Waals radii set, (ii) the criteria for including buried atoms in the calculations or atom selection, (iii) the method of positioning the dividing plane in polyhedra construction, and (iv) the set of structures used in the averaging. RESULTS: We find that different radii sets have only moderate affects to the distribution and mean of volumes. Atom selection and dividing plane methods cause larger changes in protein atoms volumes. More significantly, we show how the variation in volumes appears to be clearly related to the quality of the structures analyzed, with higher quality structures giving consistently smaller average volumes with less variance.     

Structural characteristics of immature rat Sertoli cells in vivo and in vitro.

The structural properties of pelleted prepubertal Sertoli cells (pre-culture pelleted cells) from 19-day-old rats and of similar cells cultured for 7 days were compared with Sertoli cells from the intact animal (testis tissue from 19- and 26-day-old rats, the in vivo groups). Sertoli cells from freshly isolated pellets and those cultured for 7 days were similar in cell and nuclear volumes to their in vivo counterparts. Cell volumes, organelle volumes, and organelle volume densities of newly isolated Sertoli cells were similar to those of sectioned cells taken from the 19-day-old in vivo group, indicating that the procedure for isolation does not grossly alter Sertoli cells. Mean height of cells cultured for 7 days was significantly lower than that of cells from intact animals at 19 and 26 days of age. In vivo, Sertoli cells of 26-day-old animals displayed increased organelle volumes and organelle surface areas compared with those from 19-day-old animals; volume densities and surface densities remained relatively constant, indicating that in vivo, organelle growth is in proportion to growth of the cell. Most organelle volume and surface densities were not significantly different when 19-day-old in vivo cells and pre-culture pelleted cells were compared. Many organelle volume and surface density values were significantly less in cells grown in culture for 7 days as compared to freshly isolated pelleted cells. After 7 days of culture, most Sertoli cell organelles were significantly less in both volume density and surface density, as compared to the in vivo cell groups (19 or 26 day). This indicates that in vitro the organelles do not develop in proportion to the growth of the cell. After 7 days in culture, the absolute volumes and surface areas of the organelles remained generally unchanged as compared to cells from 19-day-old animals. The data show that Sertoli cells grow in volume in vitro like their in vivo counterparts; however, their subcellular features, although well maintained, do not develop in proportion to the cell. This suggests that short-term cultures are a more ideal system in which to study biochemical responses. Also, cultured prepubertal Sertoli cells are most appropriately used to study prepubertal Sertoli cell function. This is the first study to quantify developmental changes in Sertoli cell structure in vivo as well as to compare them with cellular changes occurring in vitro.     

The effect of different rest intervals between sets on volume components and strength gains

The purpose of this study was to compare squat strength gains and volume components when resting 2 minutes vs. 4 minutes between sets over multiple mesocycles. After the first squat 1 repetition maximum, 15 trained men were matched and randomly assigned to either a 2-minute (n = 7) or a 4-minute (n = 8) rest interval group. Each group performed the same training program, with the only difference being the length of the rest interval between sets. Subjects performed two squat workouts per week; one was labeled as Heavy and the other was labeled as Light. The squat workouts varied in the intensity, number of sets, and repetitions performed per set in a nonlinear periodized manner throughout each mesocycle. Differences in strength gains and volume components (the load utilized per set, the repetitions performed per set, the intensity per set, and the volume performed per workout) were compared between groups. Both groups demonstrated large strength gains; however, these differences were not significant between groups (P = 0.47). During all mesocycles, the 4-minute group demonstrated significantly higher total volumes for the Heavy workouts (P < 0.05). The findings of the present study indicate that large squat strength gains can be achieved with a minimum of 2 minutes' rest between sets, and little additional gains are derived from resting 4 minutes between sets. Therefore, athletes attempting to achieve specific volume goals may need longer rest intervals initially but may later adapt so that shorter rest intervals can be utilized without excessive fatigue, leaving additional time to focus on other conditioning priorities.     

Volumetric behaviour of maltose-water, maltose-glycerol and starch-sorbitol-water systems mixtures in relation to structural relaxation

The densities of amorphous maltose-water, maltose-glycerol and starch-sorbitol-water mixtures were measured using a vibrating-tube density meter and pycnometry. The volumetric change on mixing was investigated through the calculation of the quantity DeltaV/V, the difference between (experimental) volume of the mixture and the linear composition weighted pure constituent volumes (ideal mixing). For all of the systems studied the quantity DeltaV/V was negative and approached a minimum of -0.03 and -0.015 at mass fractions of maltose in the region of 0.75 and 0.85 for the maltose-water and maltose-glycerol mixtures, respectively. Results are discussed in the context of volume change due to structural relaxation of vitreous materials and related to the phenomenon of antiplasticisation.     

Fluorescence correlation spectroscopy and its potential for intracellular applications

Fluorescence correlation spectroscopy (FCS) is a time-averaging fluctuation analysis of small molecular ensembles, combining maximum sensitivity with high statistical confidence. Among a multitude of physical parameters that are, in principle, accessible by FCS, it most conveniently allows to determine local concentrations, mobility coefficients, and characteristic rate constants of fast-reversible and slow-irreversible reactions of fluorescently labeled biomolecules at very low (nanomolar) concentrations, under equilibrium conditions and without physical separation. Its presently most popular instrumentation by confocal-microscope setups allows for a spatial resolution of fractions of femtoliters for the measurement volumes, containing sparse or even single molecules at any time, and encourages the adaptation of the solution-based technique for cellular applications. The scope of this review is thus, to introduce the FCS technique in particular to the reader with biological background, searching for new methods for a precise quantification of physical parameters governing cellular mechanisms and dynamics, especially if high sensitivity and fast dynamic resolution are required. After a short theoretical introduction, examples are given for the so far most important experimental applications, with respect to their implementation in cellular systems. As an interesting alternative to the confocal instrumentation, two-photon excitation will be introduced, offering a number of important advantages especially in cellular systems with high-noise and low-signal levels.     

Effects of volume history and vagotomy on pulmonary and chest wall mechanics in cats

Using the technique of rapid airway occlusion during constant-flow inflation, we studied the effects of inflation volume, different baseline tidal volumes (10, 20, and 30 ml/kg), and vagotomy on the resistive and elastic properties of the lungs and chest wall in six anesthetized tracheotomized paralyzed mechanically ventilated cats. Before vagotomy, airway resistance decreased significantly with increasing inflation volume at all baseline tidal volumes. At any given inflation volume, airway resistance decreased with increasing baseline tidal volume. After vagotomy, airway resistance decreased markedly and was no longer affected by baseline tidal volume. Prevagotomy, pulmonary tissue resistance increased progressively with increasing lung volume and was not affected by baseline tidal volume. Pulmonary tissue resistance decreased postvagotomy. Chest wall tissue resistance increased during lung inflation but was not affected by either baseline tidal volume or vagotomy. The static volume-pressure relationships of the lungs and chest wall were not affected by either baseline tidal volume or vagotomy. The data were interpreted in terms of a linear viscoelastic model of the respiratory system (J. Appl. Physiol. 67: 2276-2285, 1989).     

A single centrifugation method for isolating fat droplets from cells and tissues

Fat droplets (FDs) have important roles in cellular energy regulation. Isolating FDs from either cells or tissue continues to be important for studying these organelles. Here, we describe a procedure wherein whole homogenates of cultured cells or tissue are fractionated with a single centrifugation step in a standard microcentrifuge. This procedure reproducibly yields three fractions highly enriched in either FDs, soluble cellular components, or sedimentable organelles/membranes.     

Dual-energy micro-CT of the rodent lung

The purpose of this work is to investigate the use of dual-energy micro-computed tomography (CT) for the estimation of vascular, tissue, and air fractions in rodent lungs using a postreconstruction three material decomposition method. Using simulations, we have estimated the accuracy limits of the decomposition for realistic micro-CT noise levels. Next, we performed experiments involving ex vivo lung imaging in which intact rat lungs were carefully removed from the thorax, injected with an iodine-based contrast agent, and then inflated with different volumes of air (n = 2). Finally, we performed in vivo imaging studies in C57BL/6 mice (n = 5) using fast prospective respiratory gating in end inspiration and end expiration for three different levels of positive end expiratory pressure (PEEP). Before imaging, mice were injected with a liposomal blood pool contrast agent. The three-dimensional air, tissue, and blood fraction maps were computed and analyzed. The results indicate that separation and volume estimation of the three material components of the lungs are possible. The mean accuracy values for air, blood, and tissue were 93, 93, and 90%, respectively. The absolute accuracy in determining all fraction materials was 91.6%. The coefficient of variation was small (2.5%) indicating good repeatability. The minimum difference that we could detect in material fractions was 15%. As expected, an increase in PEEP levels for the living mouse resulted in statistically significant increases in air fractions at end expiration but no significant changes at end inspiration. Our method has applicability in preclinical pulmonary studies where changes in lung structure and gas volume as a result of lung injury, environmental exposures, or drug bioactivity would have important physiological implications.     

Refractive indices of the collagen fibrils and extrafibrillar material of the corneal stroma.

Ultrastructural data from x-ray diffraction studies of the cornea were used to estimate the refractive indices of the collagen fibrils and extrafibrillar material of human, ox, trout, and rabbit corneas. X-ray diffraction measurements of the size and spacing of the collagen fibrils and the separation between the constituent molecules of the fibrils were taken from a previous species study. The tissue volume fractions occupied by the stromal components were estimated and their refractive indices were calculated using the Gladstone-Dale law of mixtures. For the fibrils and extrafibrillar material, the refractive indices in the human cornea were 1.411 and 1.365; for the ox 1.413 and 1.357; for the rabbit 1.416 and 1.357; and for the trout 1.418 and 1.364, respectively. An alternative estimate based on the physical properties and chemical composition of bovine cornea, accounting for interfibrillar type VI collagen and cellular water, produced similar estimates of 1.416 and 1.356 for the fibrils and extrafibrillar material, respectively.