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The myocardial ischemic border zone is associated with the initiation and sustenance of arrhythmias. The profile of ionic concentrations across the border zone play a significant role in determining cellular electrophysiology and conductivity, yet their spatial-temporal evolution and regulation are not well understood. To investigate the changes in ion concentrations that regulate cellular electrophysiology, a mathematical model of ion movement in the intra and extracellular space in the presence of ionic, potential and material property heterogeneities was developed. The model simulates the spatial and temporal evolution of concentrations of potassium, sodium, chloride, calcium, hydrogen and bicarbonate ions and carbon dioxide across an ischemic border zone. Ischemia was simulated by sodium-potassium pump inhibition, potassium channel activation and respiratory and metabolic acidosis. The model predicted significant disparities in the width of the border zone for each ionic species, with intracellular sodium and extracellular potassium having discordant gradients, facilitating multiple gradients in cellular properties across the border zone. Extracellular potassium was found to have the largest border zone and this was attributed to the voltage dependence of the potassium channels. The model also predicted the efflux of [Formula: see text] from the ischemic region due to electrogenic drift and diffusion within the intra and extracellular space, respectively, which contributed to [Formula: see text] depletion in the ischemic region.

The link between metals, Alzheimer's disease (AD) and its implicated protein, amyloid-β (Aβ), is complex and highly studied. AD is believed to occur as a result of the misfolding and aggregation of Aβ. The dyshomeostasis of metal ions and their propensity to interact with Aβ has also been implicated in AD. In this work, we use single molecule atomic force spectroscopy to measure the rupture force required to dissociate two Aβ (1-42) peptides in the presence of copper ions, Cu(2+). In addition, we use atomic force microscopy to resolve the aggregation of Aβ formed. Previous research has shown that metal ions decrease the lag time associated with Aβ aggregation. We show that with the addition of copper ions the unbinding force increases notably. This suggests that the reduction of lag time associated with Aβ aggregation occurs on a single molecule level as a result of an increase in binding forces during the very initial interactions between two Aβ peptides. We attribute these results to copper ions acting as a bridge between the two peptide molecules, increasing the stability of the peptide-peptide complex.

One of the most challenging problems in microbiology is to understand how a small fraction of microbes that resists killing by antibiotics can emerge in a population of genetically identical cells, the phenomenon known as persistence or drug tolerance. Its characteristic signature is the biphasic kill curve, whereby microbes exposed to a bactericidal agent are initially killed very rapidly but then much more slowly. Here we relate this problem to the more general problem of understanding the emergence of distinct growth phenotypes in clonal populations. We address the problem mathematically by adopting the framework of the phenomenon of so-called weak ergodicity breaking, well known in dynamical physical systems, which we extend to the biological context. We show analytically and by direct stochastic simulations that distinct growth phenotypes can emerge as a consequence of slow-down of stochastic fluctuations in the expression of a gene controlling growth rate. In the regime of fast gene transcription, the system is ergodic, the growth rate distribution is unimodal, and accounts for one phenotype only. In contrast, at slow transcription and fast translation, weakly non-ergodic components emerge, the population distribution of growth rates becomes bimodal, and two distinct growth phenotypes are identified. When coupled to the well-established growth rate dependence of antibiotic killing, this model describes the observed fast and slow killing phases, and reproduces much of the phenomenology of bacterial persistence. The model has major implications for efforts to develop control strategies for persistent infections., 26 pages, 7 figures

The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps.

We investigate the dynamics of a deterministic finite-sized network of synaptically coupled spiking neurons and present a formalism for computing the network statistics in a perturbative expansion. The small parameter for the expansion is the inverse number of neurons in the network. The network dynamics are fully characterized by a neuron population density that obeys a conservation law analogous to the Klimontovich equation in the kinetic theory of plasmas. The Klimontovich equation does not possess well-behaved solutions but can be recast in terms of a coupled system of well-behaved moment equations, known as a moment hierarchy. The moment hierarchy is impossible to solve but in the mean field limit of an infinite number of neurons, it reduces to a single well-behaved conservation law for the mean neuron density. For a large but finite system, the moment hierarchy can be truncated perturbatively with the inverse system size as a small parameter but the resulting set of reduced moment equations that are still very difficult to solve. However, the entire moment hierarchy can also be re-expressed in terms of a functional probability distribution of the neuron density. The moments can then be computed perturbatively using methods from statistical field theory. Here we derive the complete mean field theory and the lowest order second moment corrections for physiologically relevant quantities. Although we focus on finite-size corrections, our method can be used to compute perturbative expansions in any parameter., Author Summary One avenue towards understanding how the brain functions is to create computational and mathematical models. However, a human brain has on the order of a hundred billion neurons with a quadrillion synaptic connections. Each neuron is a complex cell comprised of multiple compartments hosting a myriad of ions, proteins and other molecules. Even if computing power continues to increase exponentially, directly simulating all the processes in the brain on a computer is not feasible in the foreseeable future and even if this could be achieved, the resulting simulation may be no simpler to understand than the brain itself. Hence, the need for more tractable models. Historically, systems with many interacting bodies are easier to understand in the two opposite limits of a small number or an infinite number of elements and most of the theoretical efforts in understanding neural networks have been devoted to these two limits. There has been relatively little effort directed to the very relevant but difficult regime of large but finite networks. In this paper, we introduce a new formalism that borrows from the methods of many-body statistical physics to analyze finite size effects in spiking neural networks.

The Drosophila blastoderm embryo undergoes rapid cycles of nuclear division. This poses a challenge to genes that need to reliably sense the concentrations of morphogen molecules to form desired expression patterns. Here we investigate whether the transcriptional state of hunchback (hb), a target gene directly activated by the morphogenetic protein Bicoid (Bcd), exhibits properties indicative of inheritance between mitotic cycles. To achieve this, we build a dataset of hb transcriptional states at the resolution of individual nuclei in embryos at early cycle 14. We perform a spatial point pattern (SPP) analysis to evaluate the spatial relationships among the nuclei that have distinct numbers of hb gene copies undergoing active transcription in snapshots of embryos. Our statistical tests and simulation studies reveal properties of dispersed clustering for nuclei with both or neither copies of hb undergoing active transcription. Modeling of nuclear lineages from cycle 11 to cycle 14 suggests that these two types of nuclei can achieve spatial clustering when, and only when, the transcriptional states are allowed to propagate between mitotic cycles. Our results are consistent with the possibility where the positional information encoded by the Bcd morphogen gradient may not need to be decoded de novo at all mitotic cycles in the Drosophila blastoderm embryo.

Fluorescent dyes are vital for studying static and dynamic patterns and pattern formation in cell biology. Emission properties of the dyes incorporated in a biological interface are known to be sensitive to their local environment. We report that the fluorescence intensity of dye molecules embedded in lipid interfaces is indeed a thermodynamic observable of the system. Opto-mechanical coupling of lipid-dye system was measured as a function of the thermodynamic state of the interface. The corresponding state diagrams quantify the thermodynamic coupling between intensity I and lateral pressure π. We further demonstrate that the coupling is conserved upon varying the temperature T. Notably, the observed opto-mechanical coupling is not limited to equilibrium conditions, but also holds for propagating pressure pulses. The non-equilibrium data show, that fluorescence is especially sensitive to dynamic changes in state such as the LE-LC phase transition. We conclude that variations in the thermodynamic state (here π and T, in general pH, membrane potential V, etc also) of lipid membranes are capable of controlling fluorescence intensity. Therefore, interfacial thermodynamic state diagrams of I should be obtained for a proper interpretation of intensity data.

To listen to the brain activities as a piece of music, we proposed the scale-free brainwave music (SFBM) technology, which translated scalp EEGs into music notes according to the power law of both EEG and music. In the present study, the methodology was extended for deriving a quartet from multi-channel EEGs with artistic beat and tonality filtering. EEG data from multiple electrodes were first translated into MIDI sequences by SFBM, respectively. Then, these sequences were processed by a beat filter which adjusted the duration of notes in terms of the characteristic frequency. And the sequences were further filtered from atonal to tonal according to a key defined by the analysis of the original music pieces. Resting EEGs with eyes closed and open of 40 subjects were utilized for music generation. The results revealed that the scale-free exponents of the music before and after filtering were different: the filtered music showed larger variety between the eyes-closed (EC) and eyes-open (EO) conditions, and the pitch scale exponents of the filtered music were closer to 1 and thus it was more approximate to the classical music. Furthermore, the tempo of the filtered music with eyes closed was significantly slower than that with eyes open. With the original materials obtained from multi-channel EEGs, and a little creative filtering following the composition process of a potential artist, the resulted brainwave quartet opened a new window to look into the brain in an audible musical way. In fact, as the artistic beat and tonal filters were derived from the brainwaves, the filtered music maintained the essential properties of the brain activities in a more musical style. It might harmonically distinguish the different states of the brain activities, and therefore it provided a method to analyze EEGs from a relaxed audio perspective.

We introduce a method for calculating the extent to which chain non-crossing is important in the most efficient, optimal trajectories or pathways for a protein to fold. This involves recording all unphysical crossing events of a ghost chain, and calculating the minimal uncrossing cost that would have been required to avoid such events. A depth-first tree search algorithm is applied to find minimal transformations to fold [Formula: see text], [Formula: see text], [Formula: see text], and knotted proteins. In all cases, the extra uncrossing/non-crossing distance is a small fraction of the total distance travelled by a ghost chain. Different structural classes may be distinguished by the amount of extra uncrossing distance, and the effectiveness of such discrimination is compared with other order parameters. It was seen that non-crossing distance over chain length provided the best discrimination between structural and kinetic classes. The scaling of non-crossing distance with chain length implies an inevitable crossover to entanglement-dominated folding mechanisms for sufficiently long chains. We further quantify the minimal folding pathways by collecting the sequence of uncrossing moves, which generally involve leg, loop, and elbow-like uncrossing moves, and rendering the collection of these moves over the unfolded ensemble as a multiple-transformation "alignment". The consensus minimal pathway is constructed and shown schematically for representative cases of an [Formula: see text], [Formula: see text], and knotted protein. An overlap parameter is defined between pathways; we find that [Formula: see text] proteins have minimal overlap indicating diverse folding pathways, knotted proteins are highly constrained to follow a dominant pathway, and [Formula: see text] proteins are somewhere in between. Thus we have shown how topological chain constraints can induce dominant pathway mechanisms in protein folding.

International audience; Using complex roots of unity and the Fast Fourier Transform, we design a new thermodynamics-based algorithm, FFTbor, that computes the Boltzmann probability that secondary structures differ by k base pairs from an arbitrary initial structure of a given RNA sequence. The algorithm, which runs in quartic time O(n^4) and quadratic space O(n^2), is used to determine the correlation between kinetic folding speed and the ruggedness of the energy landscape, and to predict the location of riboswitch expression platform candidates. A web server is available at http://bioinformatics.bc.edu/clotelab/FFTbor/

Important biological processes like cell signalling and gene expression have noisy components and are very complex at the same time. Mathematical analysis of such systems has often been limited to the study of isolated subsystems, or approximations are used that are difficult to justify. Here we extend a recently published method (Thurley and Falcke, PNAS 2011) which is formulated in observable system configurations instead of molecular transitions. This reduces the number of system states by several orders of magnitude and avoids fitting of kinetic parameters. The method is applied to [Formula: see text] signalling. [Formula: see text] is a ubiquitous second messenger transmitting information by stochastic sequences of concentration spikes, which arise by coupling of subcellular [Formula: see text] release events (puffs). We derive analytical expressions for a mechanistic [Formula: see text] model, based on recent data from live cell imaging, and calculate [Formula: see text] spike statistics in dependence on cellular parameters like stimulus strength or number of [Formula: see text] channels. The new approach substantiates a generic [Formula: see text] model, which is a very convenient way to simulate [Formula: see text] spike sequences with correct spiking statistics.

A general method for facilitating the interpretation of computer simulations of protein folding with minimally frustrated energy landscapes is detailed and applied to a designed ankyrin repeat protein (4ANK). In the method, groups of residues are assigned to foldons and these foldons are used to map the conformational space of the protein onto a set of discrete macrobasins. The free energies of the individual macrobasins are then calculated, informing practical kinetic analysis. Two simple assumptions about the universality of the rate for downhill transitions between macrobasins and the natural local connectivity between macrobasins lead to a scheme for predicting overall folding and unfolding rates, generating chevron plots under varying thermodynamic conditions, and inferring dominant kinetic folding pathways. To illustrate the approach, free energies of macrobasins were calculated from biased simulations of a non-additive structure-based model using two structurally motivated foldon definitions at the full and half ankyrin repeat resolutions. The calculated chevrons have features consistent with those measured in stopped flow chemical denaturation experiments. The dominant inferred folding pathway has an "inside-out", nucleation-propagation like character. Fil: Schafer, Nicholas P.. Rice University; Estados Unidos. University of California at San Diego; Estados Unidos Fil: Hoffman, Ryan M. B.. University of California at San Diego; Estados Unidos. Rice University; Estados Unidos Fil: Burger, Anat. University of California at San Diego; Estados Unidos. Rice University; Estados Unidos Fil: Craig, Patricio Oliver. University of California at San Diego; Estados Unidos. Rice University; Estados Unidos. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Komives, Elizabeth A.. University of California at San Diego; Estados Unidos Fil: Wolynes, Peter G.. Rice University; Estados Unidos. University of California at San Diego; Estados Unidos

Continuum elastic models that account for membrane thickness variations are especially useful in the description of nanoscale deformations due to the presence of membrane proteins with hydrophobic mismatch. We show that terms involving the gradient and the Laplacian of the area per lipid are significant and must be retained in the effective Hamiltonian of the membrane. We reanalyze recent numerical data, as well as experimental data on gramicidin channels, in light of our model. This analysis yields consistent results for the term stemming from the gradient of the area per molecule. The order of magnitude we find for the associated amplitude, namely 13-60 mN/m, is in good agreement with the 25 mN/m contribution of the interfacial tension between water and the hydrophobic part of the membrane. The presence of this term explains a systematic variation in previously published numerical data., Comment: 34 pages, 9 figures

Different codons encoding the same amino acid are not used equally in protein-coding sequences. In bacteria, there is a bias towards codons with high translation rates. This bias is most pronounced in highly expressed proteins, but a recent study of synthetic GFP-coding sequences did not find a correlation between codon usage and GFP expression, suggesting that such correlation in natural sequences is not a simple property of translational mechanisms. Here, we investigate the effect of evolutionary forces on codon usage. The relation between codon bias and protein abundance is quantitatively analyzed based on the hypothesis that codon bias evolved to ensure the efficient usage of ribosomes, a precious commodity for fast growing cells. An explicit fitness landscape is formulated based on bacterial growth laws to relate protein abundance and ribosomal load. The model leads to a quantitative relation between codon bias and protein abundance, which accounts for a substantial part of the observed bias for E. coli. Moreover, by providing an evolutionary link, the ribosome load model resolves the apparent conflict between the observed relation of protein abundance and codon bias in natural sequences and the lack of such dependence in a synthetic gfp library. Finally, we show that the relation between codon usage and protein abundance can be used to predict protein abundance from genomic sequence data alone without adjustable parameters.

One of the key issues in the theoretical prediction of RNA folding is the prediction of loop structure from the sequence. RNA loop free energies are dependent on the loop sequence content. However, most current models account only for the loop length-dependence. The previously developed “Vfold” model (a coarse-grained RNA folding model) provides an effective method to generate the complete ensemble of coarse-grained RNA loop and junction conformations. However, due to the lack of sequence-dependent scoring parameters, the method is unable to identify the native and near-native structures from the sequence. In this study, using a previously developed iterative method for extracting the knowledge-based potential parameters from the known structures, we derive a set of dinucleotide-based statistical potentials for RNA loops and junctions. A unique advantage of the approach is its ability to go beyond the the (known) native structures by accounting for the full free energy landscape, including all the nonnative folds. The benchmark tests indicate that for given loop/junction sequences, the statistical potentials enable successful predictions for the coarse-grained 3D structures from the complete conformational ensemble generated by the Vfold model. The predicted coarse-grained structures can provide useful initial folds for further detailed structural refinement.

Identification of discrete states is a common task when studying biological systems on microscopic scales. Here, we present a novel step detection algorithm that is ideally suited to locate steplike features separating adjacent plateaus, even if they are smooth and hidden by noise. It can be adjusted to detect very low or narrow steps that cannot be recognized by conventional methods. We demonstrate the applicability of the technique on various experimental data and show strong evidence of sub-10-pN steps in atomic force spectroscopy measurements performed with living lymphocytes.

The association of hemagglutinin (HA) with lipid rafts in the plasma membrane is an important feature of the assembly process of influenza virus A. Lipid rafts are thought to be small, fluctuating patches of membrane enriched in saturated phospholipids, sphingolipids, cholesterol and certain types of protein. However, raft-associating transmembrane (TM) proteins generally partition into Ld domains in model membranes, which are enriched in unsaturated lipids and depleted in saturated lipids and cholesterol. The reason for this apparent disparity in behavior is unclear, but model membranes differ from the plasma membrane in a number of ways. In particular, the higher protein concentration in the plasma membrane may influence the partitioning of membrane proteins for rafts. To investigate the effect of high local protein concentration, we have conducted coarse-grained molecular dynamics (CG MD) simulations of HA clusters in domain-forming bilayers. During the simulations, we observed a continuous increase in the proportion of raft-type lipids (saturated phospholipids and cholesterol) within the area of membrane spanned by the protein cluster. Lateral diffusion of unsaturated lipids was significantly attenuated within the cluster, while saturated lipids were relatively unaffected. On this basis, we suggest a possible explanation for the change in lipid distribution, namely that steric crowding by the slow-diffusing proteins increases the chemical potential for unsaturated lipids within the cluster region. We therefore suggest that a local aggregation of HA can be sufficient to drive association of the protein with raft-type lipids. This may also represent a general mechanism for the targeting of TM proteins to rafts in the plasma membrane, which is of functional importance in a wide range of cellular processes., Author Summary The cell membrane is composed of a wide variety of lipids and proteins. Until recently, these were thought to be mixed evenly, but we now have evidence of the existence of “lipid rafts” — small, slow-moving areas of membrane in which certain types of lipid and protein accumulate. Rafts have many important biological functions in healthy cells, but also play a role in the assembly of influenza virus. For example, after the viral protein hemagglutinin is made inside the host cell, it accumulates in rafts. Exiting virus particles then take these portions of cell membrane with them as they leave the host cell. However, the mechanism by which proteins associate with lipid rafts is unclear. Here, we have used computers to simulate lipid membranes containing hemagglutinin. The simulations allow us to look in detail at the motions and interactions of individual proteins and lipids. We found that clusters of proteins altered the properties of nearby lipids, leading to accumulation of raft-type lipids. It therefore appears that aggregation of hemagglutinin may be enough to drive its association with rafts. This helps us to better understand both the influenza assembly process and the properties of lipid rafts.

Recently, we demonstrated that yeast protein evolutionary rate at the level of individual amino acid residues scales linearly with degree of solvent accessibility. This residue-level structure-evolution relationship is sensitive to protein core size: surface residues from large-core proteins evolve much faster than those from small-core proteins, while buried residues are equally constrained independent of protein core size. In this work, we investigate the joint effects of protein core size and expression on the residue-level structure-evolution relationship. At the whole-protein level, protein expression is a much more dominant determinant of protein evolutionary rate than protein core size. In contrast, at the residue level, protein core size and expression both have major impacts on protein structure-evolution relationships. In addition, protein core size and expression influence residue-level structure-evolution relationships in qualitatively different ways. Protein core size preferentially affects the non-synonymous substitution rates of surface residues compared to buried residues, and has little influence on synonymous substitution rates. In comparison, protein expression uniformly affects all residues independent of degree of solvent accessibility, and affects both non-synonymous and synonymous substitution rates. Protein core size and expression exert largely independent effects on protein evolution at the residue level, and can combine to produce dramatic changes in the slope of the linear relationship between residue evolutionary rate and solvent accessibility. Our residue-level findings demonstrate that protein core size and expression are both important, yet qualitatively different, determinants of protein evolution. These results underscore the complementary nature of residue-level and whole-protein analysis of protein evolution.

Systematic numerical investigations of conformational motions in single actin molecules were performed by employing a simple elastic-network (EN) model of this protein. Similar to previous investigations for myosin, we found that G-actin essentially behaves as a strain sensor, responding by well-defined domain motions to mechanical perturbations. Several sensitive residues within the nucleotide-binding pocket (NBP) could be identified, such that the perturbation of any of them can induce characteristic flattening of actin molecules and closing of the cleft between their two mobile domains. Extending the EN model by introduction of a set of breakable links which become effective only when two domains approach one another, it was observed that G-actin can possess a metastable state corresponding to a closed conformation and that a transition to this state can be induced by appropriate perturbations in the NBP region. The ligands were roughly modeled as a single particle (ADP) or a dimer (ATP), which were placed inside the NBP and connected by elastic links to the neighbors. Our approximate analysis suggests that, when ATP is present, it stabilizes the closed conformation of actin. This may play an important role in the explanation why, in the presence of ATP, the polymerization process is highly accelerated.

In injured neurons, “leaky” voltage-gated sodium channels (Nav) underlie dysfunctional excitability that ranges from spontaneous subthreshold oscillations (STO), to ectopic (sometimes paroxysmal) excitation, to depolarizing block. In recombinant systems, mechanical injury to Nav1.6-rich membranes causes cytoplasmic Na+-loading and “Nav-CLS”, i.e., coupled left-(hyperpolarizing)-shift of Nav activation and availability. Metabolic injury of hippocampal neurons (epileptic discharge) results in comparable impairment: left-shifted activation and availability and hence left-shifted INa-window. A recent computation study revealed that CLS-based INa-window left-shift dissipates ion gradients and impairs excitability. Here, via dynamical analyses, we focus on sustained excitability patterns in mildly damaged nodes, in particular with more realistic Gaussian-distributed Nav-CLS to mimic “smeared” injury intensity. Since our interest is axons that might survive injury, pumps (sine qua non for live axons) are included. In some simulations, pump efficacy and system volumes are varied. Impacts of current noise inputs are also characterized. The diverse modes of spontaneous rhythmic activity evident in these scenarios are studied using bifurcation analysis. For “mild CLS injury”, a prominent feature is slow pump/leak-mediated EIon oscillations. These slow oscillations yield dynamic firing thresholds that underlie complex voltage STO and bursting behaviors. Thus, Nav-CLS, a biophysically justified mode of injury, in parallel with functioning pumps, robustly engenders an emergent slow process that triggers a plethora of pathological excitability patterns. This minimalist “device” could have physiological analogs. At first nodes of Ranvier and at nociceptors, e.g., localized lipid-tuning that modulated Nav midpoints could produce Nav-CLS, as could co-expression of appropriately differing Nav isoforms., Author Summary Nerve cells damaged by trauma, stroke, epilepsy, inflammatory conditions etc, have chronically leaky sodium channels that eventually kill. The usual job of sodium channels is to make brief voltage signals –action potentials– for long distance propagation. After sodium channels open to generate action potentials, sodium pumps work harder to re-establish the intracellular/extracellular sodium imbalance that is, literally, the neuron's battery for firing action potentials. Wherever tissue damage renders membranes overly fluid, we hypothesize, sodium channels become chronically leaky. Our experimental findings justify this. In fluidized membranes, sodium channel voltage sensors respond too easily, letting channels spend too much time open. Channels leak, pumps respond. By mathematical modeling, we show that in damaged channel-rich membranes the continual pump/leak counterplay would trigger the kinds of bizarre intermittent action potential bursts typical of injured neurons. Arising ectopically from injury regions, such neuropathic firing is unrelated to events in the external world. Drugs that can silence these deleterious electrical barrages without blocking healthy action potentials are needed. If fluidized membranes house the problematic leaky sodium channels, then drug side effects could be diminished by using drugs that accumulate most avidly into fluidized membranes, and that bind their targets with highest affinity there.

The comparison of volumes of cells and subcellular structures with the pH values reported for them leads to a conflict with the definition of the pH scale. The pH scale is based on the ionic product of water, K(w) = [H(+)]×[OH(-)].We used K(w) [in a reversed way] to calculate the number of undissociated H(2)O molecules required by this equilibrium constant to yield at least one of its daughter ions, H(+) or OH(-) at a given pH. In this way we obtained a formula that relates pH to the minimal volume V(pH) required to provide a physical meaning to K(w), V(pH)=10(pH-pK(w/2) x 10(pK(w/2)/N(A) (where N(A) is Avogadro's number). For example, at pH 7 (neutral at 25°C) V(pH) =16.6 aL. Any deviation from neutral pH results in a larger V(pH) value. Our results indicate that many subcellular structures, including coated vesicles and lysosomes, are too small to contain free H(+) ions at equilibrium, thus the definition of pH based on K(w) is no longer valid. Larger subcellular structures, such as mitochondria, apparently contain only a few free H(+) ions. These results indicate that pH fails to describe intracellular conditions, and that water appears to be dissociated too weakly to provide free H(+) ions as a general source for biochemical reactions. Consequences of this finding are discussed.

Networks are often used to understand a whole system by modeling the interactions among its pieces. Examples include biomolecules in a cell interacting to provide some primary function, or species in an environment forming a stable community. However, these interactions are often unknown; instead, the pieces' dynamic states are known, and network structure must be inferred. Because observed function may be explained by many different networks (e.g., ≈ 10(30) for the yeast cell cycle process), considering dynamics beyond this primary function means picking a single network or suitable sample: measuring over all networks exhibiting the primary function is computationally infeasible. We circumvent that obstacle by calculating the network class ensemble. We represent the ensemble by a stochastic matrix T, which is a transition-by-transition superposition of the system dynamics for each member of the class. We present concrete results for T derived from boolean time series dynamics on networks obeying the Strong Inhibition rule, by applying T to several traditional questions about network dynamics. We show that the distribution of the number of point attractors can be accurately estimated with T. We show how to generate Derrida plots based on T. We show that T-based Shannon entropy outperforms other methods at selecting experiments to further narrow the network structure. We also outline an experimental test of predictions based on T. We motivate all of these results in terms of a popular molecular biology boolean network model for the yeast cell cycle, but the methods and analyses we introduce are general. We conclude with open questions for T, for example, application to other models, computational considerations when scaling up to larger systems, and other potential analyses.

Feedforward loops (FFLs) consist of three genes which code for three different transcription factors A, B and C where B regulates C and A regulates both B and C. We develop a detailed model to describe the dynamical behavior of various types of coherent and incoherent FFLs in the transcription factor networks. We consider the deterministic and stochastic dynamics of both promoter-states and synthesis and degradation of mRNAs of various genes associated with FFL motifs. Detailed analysis shows that the response times of FFLs strongly dependent on the ratios (wh = ?pc/?ph where h = a, b, c corresponding to genes A, B and C) between the lifetimes of mRNAs (1/?mh) of genes A, B and C and the protein of C (1/?pc). Under strong binding conditions we can categorize all the possible types of FFLs into groups I, II and III based on the dependence of the response times of FFLs on wh. Group I that includes C1 and I1 type FFLs seem to be less sensitive to the changes in wh. The coherent C1 type seems to be more robust against changes in other system parameters. We argue that this could be one of the reasons for the abundant nature of C1 type coherent FFLs. � 2012 Rajamanickam Murugan.

Oxime drugs translocate through the 20 A active-site gorge of acetylcholinesterase in order to liberate the enzyme from organophosphorus compounds’ (such as tabun) conjugation. Here we report bidirectional steered molecular dynamics simulations of oxime drug (Ortho-7) translocation through the gorge of tabun intoxicated enzyme, in which time dependent external forces accelerate the translocation event. The simulations reveal the participation of drug-enzyme hydrogen bonding, hydrophobic interactions and water bridges between them. Employing nonequilibrium theorems that recovers the free energy from irreversible work done, we reconstruct potential of mean force along the translocation pathway such that the desired quantity represents an unperturbed system. The potential locates the binding sites and barriers for the drug to translocate inside the gorge. Configurational entropic contribution of the protein-drug binding entity and the role of solvent translational mobility in the binding energetics is further assessed.

Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a Brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.

Nucleosome structure and stability affect genetic accessibility by altering the local chromatin morphology. Recent FRET experiments on nucleosomes have given valuable insight into the structural transformations they can adopt. Yet, even if performed under seemingly identical conditions, experiments performed in bulk and at the single molecule level have given mixed answers due to the limitations of each technique. To compare such experiments, however, they must be performed under identical conditions. Here we develop an experimental framework that overcomes the conventional limitations of each method: single molecule FRET experiments are carried out at bulk concentrations by adding unlabeled nucleosomes, while bulk FRET experiments are performed in microplates at concentrations near those used for single molecule detection. Additionally, the microplate can probe many conditions simultaneously before expending valuable instrument time for single molecule experiments. We highlight this experimental strategy by exploring the role of selective acetylation of histone H3 on nucleosome structure and stability; in bulk, H3-acetylated nucleosomes were significantly less stable than non-acetylated nucleosomes. Single molecule FRET analysis further revealed that acetylation of histone H3 promoted the formation of an additional conformational state, which is suppressed at higher nucleosome concentrations and which could be an important structural intermediate in nucleosome regulation.

A main question for the study of collective motion in living organisms is the origin of orientational polar order, i.e., how organisms align and what are the benefits of such collective behaviour. In the case of micro-organisms swimming at a low Reynolds number, steric repulsion and long-range hydrodynamic interactions are not sufficient to explain a homogeneous polar order state in which the direction of motion is aligned. An external symmetry-breaking guiding field such as a mechanism of taxis appears necessary to understand this phonemonon. We have investigated the onset of polar order in the velocity field induced by phototaxis in a suspension of a motile micro-organism, the algae Chlamydomonas reinhardtii, for density values above the limit provided by the hydrodynamic approximation of a force dipole model. We show that polar order originates from a combination of both the external guiding field intensity and the population density. In particular, we show evidence for a linear dependence of a phototactic guiding field on cell density to determine the polar order for dense suspensions and demonstrate the existence of a density threshold for the origin of polar order. This threshold represents the density value below which cells undergoing phototaxis are not able to maintain a homogeneous polar order state and marks the transition to ordered collective motion. Such a transition is driven by a noise dominated phototactic reorientation where the noise is modelled as a normal distribution with a variance that is inversely proportional to the guiding field strength. Finally, we discuss the role of density in dense suspensions of phototactic micro-swimmers.

The brain keeps its overall dynamics in a corridor of intermediate activity and it has been a long standing question what possible mechanism could achieve this task. Mechanisms from the field of statistical physics have long been suggesting that this homeostasis of brain activity could occur even without a central regulator, via self-organization on the level of neurons and their interactions, alone. Such physical mechanisms from the class of self-organized criticality exhibit characteristic dynamical signatures, similar to seismic activity related to earthquakes. Measurements of cortex rest activity showed first signs of dynamical signatures potentially pointing to self-organized critical dynamics in the brain. Indeed, recent more accurate measurements allowed for a detailed comparison with scaling theory of non-equilibrium critical phenomena, proving the existence of criticality in cortex dynamics. We here compare this new evaluation of cortex activity data to the predictions of the earliest physics spin model of self-organized critical neural networks. We find that the model matches with the recent experimental data and its interpretation in terms of dynamical signatures for criticality in the brain. The combination of signatures for criticality, power law distributions of avalanche sizes and durations, as well as a specific scaling relationship between anomalous exponents, defines a universality class characteristic of the particular critical phenomenon observed in the neural experiments. The spin model is a candidate for a minimal model of a self-organized critical adaptive network for the universality class of neural criticality. As a prototype model, it provides the background for models that include more biological details, yet share the same universality class characteristic of the homeostasis of activity in the brain., 17 pages, 5 figures

Recent progress in stem cell biology, notably cell fate conversion, calls for novel theoretical understanding for cell differentiation. The existing qualitative concept of Waddington’s “epigenetic landscape” has attracted particular attention because it captures subsequent fate decision points, thus manifesting the hierarchical (“tree-like”) nature of cell fate diversification. Here, we generalized a recent work and explored such a developmental landscape for a two-gene fate decision circuit by integrating the underlying probability landscapes with different parameters (corresponding to distinct developmental stages). The change of entropy production rate along the parameter changes indicates which parameter changes can represent a normal developmental process while other parameters’ change can not. The transdifferentiation paths over the landscape under certain conditions reveal the possibility of a direct and reversible phenotypic conversion. As the intensity of noise increases, we found that the landscape becomes flatter and the dominant paths more straight, implying the importance of biological noise processing mechanism in development and reprogramming. We further extended the landscape of the one-step fate decision to that for two-step decisions in central nervous system (CNS) differentiation. A minimal network and dynamic model for CNS differentiation was firstly constructed where two three-gene motifs are coupled. We then implemented the SDEs (Stochastic Differentiation Equations) simulation for the validity of the network and model. By integrating the two landscapes for the two switch gene pairs, we constructed the two-step development landscape for CNS differentiation. Our work provides new insights into cellular differentiation and important clues for better reprogramming strategies.

Neural populations encode information about their stimulus in a collective fashion, by joint activity patterns of spiking and silence. A full account of this mapping from stimulus to neural activity is given by the conditional probability distribution over neural codewords given the sensory input. To be able to infer a model for this distribution from large-scale neural recordings, we introduce a stimulus-dependent maximum entropy (SDME) model---a minimal extension of the canonical linear-nonlinear model of a single neuron, to a pairwise-coupled neural population. The model is able to capture the single-cell response properties as well as the correlations in neural spiking due to shared stimulus and due to effective neuron-to-neuron connections. Here we show that in a population of 100 retinal ganglion cells in the salamander retina responding to temporal white-noise stimuli, dependencies between cells play an important encoding role. As a result, the SDME model gives a more accurate account of single cell responses and in particular outperforms uncoupled models in reproducing the distributions of codewords emitted in response to a stimulus. We show how the SDME model, in conjunction with static maximum entropy models of population vocabulary, can be used to estimate information-theoretic quantities like surprise and information transmission in a neural population., 11 pages, 7 figures

Cells respond to external cues by precisely coordinating multiple molecular events. Co-regulation may be established by the so-called single-input module (SIM), where a common regulator controls multiple targets. Using mathematical modeling, we compared the ability of SIM architectures to precisely coordinate protein levels despite environmental fluctuations and uncertainties in parameter values. We find that post-transcriptional co-regulation as exemplified by bacterial small RNAs (sRNAs) is particularly robust: sRNA-mediated regulation establishes highly synchronous gene expression thresholds for all mRNA targets without a need for fine-tuning of kinetic parameters. Our analyses reveal that the non-catalytic nature of sRNA action is essential for robust gene expression synchronization, and that sRNA sequestration effects underlie coupling of multiple mRNA pools. This principle also operates in the temporal regime, implying that sRNAs could robustly coordinate the kinetics of mRNA induction as well. Moreover, we observe that multi-target regulation by a small RNA can strongly enhance ultrasensitivity in mRNA expression when compared to the single-target case. Our findings may explain why bacterial small RNAs frequently coordinate all-or-none responses to cellular stress.

Background Despite their notorious diversity, biological cells are mechanically well characterized by only a few robust and universal laws. Intriguingly, the law characterizing the nonlinear response to stretch appears self-contradictory. Various cell types have been reported to both stiffen and soften, or “fluidize” upon stretch. Within the classical paradigm of cells as viscoelastic bodies, this constitutes a paradox. Principal Findings Our measurements reveal that minimalistic reconstituted cytoskeletal networks (F-actin/HMM) exhibit a similarly peculiar response. A mathematical model of transiently crosslinked polymer networks, the so-called inelastic glassy wormlike chain (iGwlc) model, can simulate the data and resolve the apparent contradiction. It explains the observations in terms of two antagonistic physical mechanisms, the nonlinear viscoelastic resistance of biopolymers to stretch, and the breaking of weak transient bonds between them. Conclusions Our results imply that the classical paradigm of cells as viscoelastic bodies has to be replaced by such an inelastic mechanical model.

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.

We employ 4Pi-microscopy to study SC organization in mouse spermatocyte nuclei allowing for the three-dimensional reconstruction of the SC's backbone arrangement. Additionally, we model the SCs in the cell nucleus by confined, self-avoiding polymers, whose chain ends are attached to the envelope of the confining cavity and diffuse along it. This work helps to elucidate the role of entropy in shaping pachytene SC organization. The framework provided by the complex interplay between SC polymer rigidity, tethering and confinement is able to qualitatively explain features of SC organization, such as mean squared end-to-end distances, mean squared center-of-mass distances, or SC density distributions. However, it fails in correctly assessing SC entanglement within the nucleus. In fact, our analysis of the 4Pi-microscopy images reveals a higher ordering of SCs within the nuclear volume than what is expected by our numerical model. This suggests that while effects of entropy impact SC organization, the dedicated action of proteins or actin cables is required to fine-tune the spatial ordering of SCs within the cell nucleus.

Pollen tube growth is central to the sexual reproduction of plants and is a longstanding model for cellular tip growth. For rapid tip growth, cell wall deposition and hardening must balance the rate of osmotic water uptake, and this involves the control of turgor pressure. Pressure contributes directly to both the driving force for water entry and tip expansion causing thinning of wall material. Understanding tip growth requires an analysis of the coordination of these processes and their regulation. Here we develop a quantitative physiological model which includes water entry by osmosis, the incorporation of cell wall material and the spreading of that material as a film at the tip. Parameters of the model have been determined from the literature and from measurements, by light, confocal and electron microscopy, together with results from experiments made on dye entry and plasmolysis in Lilium longiflorum. The model yields values of variables such as osmotic and turgor pressure, growth rates and wall thickness. The model and its predictive capacity were tested by comparing programmed simulations with experimental observations following perturbations of the growth medium. The model explains the role of turgor pressure and its observed constancy during oscillations; the stability of wall thickness under different conditions, without which the cell would burst; and some surprising properties such as the need for restricting osmotic permeability to a constant area near the tip, which was experimentally confirmed. To achieve both constancy of pressure and wall thickness under the range of conditions observed in steady-state growth the model reveals the need for a sensor that detects the driving potential for water entry and controls the deposition rate of wall material at the tip.

We propose a model for the self-propulsion of the marine bacterium Synechococcus utilizing a continuous looped helical track analogous to that found in Myxobacteria [1]. In our model cargo-carrying protein motors, driven by proton-motive force, move along a continuous looped helical track. The movement of the cargo creates surface distortions in the form of small amplitude traveling ridges along the S-layer above the helical track. The resulting fluid motion adjacent to the helical ribbon provides the propulsive thrust. A variation on the helical rotor model of [1] allows the motors to be anchored to the peptidoglycan layer, where they drive rotation of the track creating traveling helical waves along the S-layer. We derive expressions relating the swimming speed to the amplitude, wavelength, and velocity of the surface waves induced by the helical rotor, and show that they fall in reasonable ranges to explain the velocity and rotation rate of swimming Synechococcus.

This study investigated how substrate geometry influences in-vitro tissue formation at length scales much larger than a single cell. Two-millimetre thick hydroxyapatite plates containing circular pores and semi-circular channels of 0.5 mm radius, mimicking osteons and hemi-osteons respectively, were incubated with MC3T3-E1 cells for 4 weeks. The amount and shape of the tissue formed in the pores, as measured using phase contrast microscopy, depended on the substrate geometry. It was further demonstrated, using a simple geometric model, that the observed curvature-controlled growth can be derived from the assembly of tensile elements on a curved substrate. These tensile elements are cells anchored on distant points of the curved surface, thus creating an actin "chord" by generating tension between the adhesion sites. Such a chord model was used to link the shape of the substrate to cell organisation and tissue patterning. In a pore with a circular cross-section, tissue growth increases the average curvature of the surface, whereas a semi-circular channel tends to be flattened out. Thereby, a single mechanism could describe new tissue growth in both cortical and trabecular bone after resorption due to remodelling. These similarities between in-vitro and in-vivo patterns suggest geometry as an important signal for bone remodelling.

Positioning of the mitotic spindle through the interaction of astral microtubules with the cell boundary often determines whether the cell division will be symmetric or asymmetric. This process plays a crucial role in development. In this paper, a numerical model is presented that deals with the force exerted on the spindle by astral microtubules that are bent by virtue of their confinement within the cell boundary. It is found that depending on parameters, the symmetric position of the spindle can be stable or unstable. Asymmetric stable equilibria also exist, and two or more stable positions can exist simultaneously. The theory poses new types of questions for experimental research. Regarding the cases of symmetric spindle positioning, it is necessary to ask whether the microtubule parameters are controlled by the cell so that the bending mechanics favors symmetry. If they are not, then it is necessary to ask what forces external to the microtubule cytoskeleton counteract the bending effects sufficiently to actively establish symmetry. Conversely, regarding the cases with asymmetry, it is now necessary to investigate whether the cell controls the microtubule parameters so that the bending favors asymmetry apart from any forces that are external to the microtubule cytoskeleton.

The orderly packing and precise arrangement of epithelial cells is essential to the functioning of many tissues, and refinement of this packing during development is a central theme in animal morphogenesis. The mechanisms that determine epithelial cell shape and position, however, remain incompletely understood. Here, we investigate these mechanisms in a striking example of planar order in a vertebrate epithelium: The periodic, almost crystalline distribution of cone photoreceptors in the adult teleost fish retina. Based on observations of the emergence of photoreceptor packing near the retinal margin, we propose a mathematical model in which ordered columns of cells form as a result of coupling between planar cell polarity (PCP) and anisotropic tissue-scale mechanical stresses. This model recapitulates many observed features of cone photoreceptor organization during retinal growth and regeneration. Consistent with the model's predictions, we report a planar-polarized distribution of Crumbs2a protein in cone photoreceptors in both unperturbed and regenerated tissue. We further show that the pattern perturbations predicted by the model to occur if the imposed stresses become isotropic closely resemble defects in the cone pattern in zebrafish lrp2 mutants, in which intraocular pressure is increased, resulting in altered mechanical stress and ocular enlargement. Evidence of interactions linking PCP, cell shape, and mechanical stresses has recently emerged in a number of systems, several of which show signs of columnar cell packing akin to that described here. Our results may hence have broader relevance for the organization of cells in epithelia. Whereas earlier models have allowed only for unidirectional influences between PCP and cell mechanics, the simple, phenomenological framework that we introduce here can encompass a broad range of bidirectional feedback interactions among planar polarity, shape, and stresses; our model thus represents a conceptual framework that can address many questions of importance to morphogenesis., Author Summary Many tissues and organs, including sensory organs like the vertebrate retina and inner ear, are built from sheets of connected cells called epithelia. The precise arrangement of different types of cells within these epithelia can be essential to their function. (For example, photoreceptor cells in eyes must be properly spaced to collect an optimal, undistorted signal.) We combine experimental observations with computational modeling to understand how a particular example of such epithelial organization—the planar crystalline packing of cone photoreceptor cells in the fish retina—is created. Specifically, we introduce a model where the strength of cell-cell adhesion along an interface depends on the orientation of that interface. When a global mechanical compression is applied along one direction, this model can recapitulate observed features of the cone packing and gives qualitatively correct predictions of the cone photoreceptor pattern observed in regenerated and mutant retinas. Our analysis shows that simple local interactions can direct the creation of regular, long-ranged order among epithelial cells, and it also clarifies the mechanical interactions needed to establish and maintain the integrity of the retinal epithelium. Our model may thus ultimately provide a foundation for insights into diseases in which epithelial integrity is lost.

Throughout the life of animals and human beings, blood vessel systems are continuously adapting their structures - the diameter of vessel lumina, the thickness of vessel walls, and the number of micro-vessels - to meet the changing metabolic demand of the tissue. The competition between an ever decreasing tendency of luminal diameters and an increasing stimulus from the wall shear stress plays a key role in the adaptation of luminal diameters. However, it has been shown in previous studies that the adaptation dynamics based only on these two effects is unstable. In this work, we propose a minimal adaptation model of vessel luminal diameters, in which we take into account the effects of metabolic flow regulation in addition to wall shear stresses and the decreasing tendency of luminal diameters. In particular, we study the role, in the adaptation process, of fluctuations in capillary flow distribution which is an important means of metabolic flow regulation. The fluctuation in the flow of a capillary group is idealized as a switch between two states, i.e., an open-state and a close-state. Using this model, we show that the adaptation of blood vessel system driven by wall shear stress can be efficiently stabilized when the open time ratio responds sensitively to capillary flows. As micro-vessel rarefaction is observed in our simulations with a uniformly decreased open time ratio of capillary flows, our results point to a possible origin of micro-vessel rarefaction, which is believed to induce hypertension.

Considering the recent experimental discovery of Green et al that present-day non-Africans have 1 to [Formula: see text] of their nuclear DNA of Neanderthal origin, we propose here a model which is able to quantify the genetic interbreeding between two subpopulations with equal fitness, living in the same geographic region. The model consists of a solvable system of deterministic ordinary differential equations containing as a stochastic ingredient a realization of the neutral Wright-Fisher process. By simulating the stochastic part of the model we are able to apply it to the interbreeding of the African ancestors of Eurasians and Middle Eastern Neanderthal subpopulations and estimate the only parameter of the model, which is the number of individuals per generation exchanged between subpopulations. Our results indicate that the amount of Neanderthal DNA in living non-Africans can be explained with maximum probability by the exchange of a single pair of individuals between the subpopulations at each 77 generations, but larger exchange frequencies are also allowed with sizeable probability. The results are compatible with a long coexistence time of 130,000 years, a total interbreeding population of order [Formula: see text] individuals, and with all living humans being descendants of Africans both for mitochondrial DNA and Y chromosome.

Contractile function of striated muscle cells depends crucially on the almost crystalline order of actin and myosin filaments in myofibrils, but the physical mechanisms that lead to myofibril assembly remains ill-defined. Passive diffusive sorting of actin filaments into sarcomeric order is kinetically impossible, suggesting a pivotal role of active processes in sarcomeric pattern formation. Using a one-dimensional computational model of an initially unstriated actin bundle, we show that actin filament treadmilling in the presence of processive plus-end crosslinking provides a simple and robust mechanism for the polarity sorting of actin filaments as well as for the correct localization of myosin filaments. We propose that the coalescence of crosslinked actin clusters could be key for sarcomeric pattern formation. In our simulations, sarcomere spacing is set by filament length prompting tight length control already at early stages of pattern formation. The proposed mechanism could be generic and apply both to premyofibrils and nascent myofibrils in developing muscle cells as well as possibly to striated stress-fibers in non-muscle cells., Author Summary Muscle contraction driving voluntary movements and the beating of the heart relies on the contraction of highly regular bundles of actin and myosin filaments, which share a periodic, sarcomeric pattern. We know little about the mechanisms by which these ‘biological crystals’ are assembled and it is a general question how order on a scale of 100 micrometers can emerge from the interactions of micrometer-sized building blocks, such as actin and myosin filaments. In our paper, we consider a computational model for a bundle of actin filaments and discuss physical mechanisms by which periodic order emerges spontaneously. Mutual crosslinking of actin filaments results in the formation and coalescence of growing actin clusters. Active elongation and shrinkage dynamics of actin filaments generates polymerization forces and causes local actin flow that can act like a conveyor belt to sort myosin filaments in place.

Made available in DSpace on 2013-08-28T14:10:43Z (GMT). No. of bitstreams: 1 WOS000305339900001.pdf: 824062 bytes, checksum: fdf00aba0b220ad77f5bb64fcc2c30b6 (MD5) Made available in DSpace on 2013-09-30T19:01:52Z (GMT). No. of bitstreams: 2 WOS000305339900001.pdf: 824062 bytes, checksum: fdf00aba0b220ad77f5bb64fcc2c30b6 (MD5) WOS000305339900001.pdf.txt: 57949 bytes, checksum: 0f6449f60fbddaf052d06bd806528d50 (MD5) Previous issue date: 2012-06-01 Submitted by Vitor Silverio Rodrigues (vitorsrodrigues@reitoria.unesp.br) on 2014-05-20T14:13:34Z No. of bitstreams: 2 WOS000305339900001.pdf: 824062 bytes, checksum: fdf00aba0b220ad77f5bb64fcc2c30b6 (MD5) WOS000305339900001.pdf.txt: 57949 bytes, checksum: 0f6449f60fbddaf052d06bd806528d50 (MD5) Made available in DSpace on 2014-05-20T14:13:34Z (GMT). No. of bitstreams: 2 WOS000305339900001.pdf: 824062 bytes, checksum: fdf00aba0b220ad77f5bb64fcc2c30b6 (MD5) WOS000305339900001.pdf.txt: 57949 bytes, checksum: 0f6449f60fbddaf052d06bd806528d50 (MD5) Previous issue date: 2012-06-01 Air Force Office of Scientific Research NIH National Center for Research Resources Center for Exploitation of Nanostructures in Sensor and Energy Systems (CENSES) under NSF In an attempt to optimize a high yield, high efficiency artificial photosynthetic protein we have discovered unique energy and spatial architecture limits which apply to all light-activated photosynthetic systems. We have generated an analytical solution for the time behavior of the core three cofactor charge separation element in photosynthesis, the photosynthetic cofactor triad, and explored the functional consequences of its makeup including its architecture, the reduction potentials of its components, and the absorption energy of the light absorbing primary-donor cofactor. Our primary findings are two: First, that a high efficiency, high yield triad will have an absorption frequency more than twice the reorganization energy of the first electron transfer, and second, that the relative distance of the acceptor and the donor from the primary-donor plays an important role in determining the yields, with the highest efficiency, highest yield architecture having the light absorbing cofactor closest to the acceptor. Surprisingly, despite the increased complexity found in natural solar energy conversion proteins, we find that the construction of this central triad in natural systems matches these predictions. Our analysis thus not only suggests explanations for some aspects of the makeup of natural photosynthetic systems, it also provides specific design criteria necessary to create high efficiency, high yield artificial protein-based triads. Univ Estadual Paulista, Inst Fis Teor, BR-01405 São Paulo, Brazil CUNY City Coll, Dept Phys, New York, NY 10031 USA Univ Estadual Paulista, Inst Fis Teor, BR-01405 São Paulo, Brazil Air Force Office of Scientific Research: FA9550-10-1-0350 NIH: 5G12 RR03060 CENSES under NSF: 0833180

The formation of vesicles is essential for many biological processes, in particular for the trafficking of membrane proteins within cells. The Endosomal Sorting Complex Required for Transport (ESCRT) directs membrane budding away from the cytosol. Unlike other vesicle formation pathways, the ESCRT-mediated budding occurs without a protein coat. Here, we propose a minimal model of ESCRT-induced vesicle budding. Our model is based on recent experimental observations from direct fluorescence microscopy imaging that show ESCRT proteins colocalized only in the neck region of membrane buds. The model, cast in the framework of membrane elasticity theory, reproduces the experimentally observed vesicle morphologies with physically meaningful parameters. In this parameter range, the minimum energy configurations of the membrane are coatless buds with ESCRTs localized in the bud neck, consistent with experiment. The minimum energy configurations agree with those seen in the fluorescence images, with respect to both bud shapes and ESCRT protein localization. On the basis of our model, we identify distinct mechanistic pathways for the ESCRT-mediated budding process. The bud size is determined by membrane material parameters, explaining the narrow yet different bud size distributions in vitro and in vivo. Our membrane elasticity model thus sheds light on the energetics and possible mechanisms of ESCRT-induced membrane budding., Author Summary Lipid membranes enclose the cytosol of biological cells and compartmentalize their interior. Vesicles are used to transport membrane proteins between cellular compartments. The ESCRT protein machinery induces the creation of such vesicles away from the cytosol. The resulting vesicles are uncoated by protein. Upon vesicle scission and release into the endosome, the ESCRT proteins are recycled into the cytosol. We develop a membrane-elasticity model that captures this budding process. The model reproduces the vesicle morphologies observed in fluorescence microscopy images, and identifies the energetic driving force of vesiculation. We also characterize possible mechanisms of ESCRT-induced membrane budding. The size of the resulting vesicles is determined by membrane material parameters, explaining the narrow yet different bud size distributions in vitro and in vivo. Our membrane elasticity model thus provides insight into the energetics and mechanisms of uncoated vesicle formation.

International audience; The arborescent architecture of mammalian conductive airways results from the repeated branching of lung endoderm into surrounding mesoderm. Subsequent lung's striking geometrical features have long raised the question of developmental mechanisms involved in morphogenesis. Many molecular actors have been identified, and several studies demonstrated the central role of Fgf10 and Shh in growth and branching. However, the actual branching mechanism and the way branching events are organized at the organ scale to achieve a self-avoiding tree remain to be understood through a model compatible with evidenced signaling. In this paper we show that the mere diffusion of FGF10 from distal mesenchyme involves differential epithelial proliferation that spontaneously leads to branching. Modeling FGF10 diffusion from sub-mesothelial mesenchyme where Fgf10 is known to be expressed and computing epithelial and mesenchymal growth in a coupled manner, we found that the resulting laplacian dynamics precisely accounts for the patterning of FGF10-induced genes, and that it spontaneously involves differential proliferation leading to a self-avoiding and space-filling tree, through mechanisms that we detail. The tree's fine morphological features depend on the epithelial growth response to FGF10, underlain by the lung's complex regulatory network. Notably, our results suggest that no branching information has to be encoded and that no master routine is required to organize branching events at the organ scale. Despite its simplicity, this model identifies key mechanisms of lung development, from branching to organ-scale organization, and could prove relevant to the development of other branched organs relying on similar pathways.

Cellular Potts models (CPMs) are used as a modeling framework to elucidate mechanisms of biological development. They allow a spatial resolution below the cellular scale and are applied particularly when problems are studied where multiple spatial and temporal scales are involved. Despite the increasing usage of CPMs in theoretical biology, this model class has received little attention from mathematical theory. To narrow this gap, the CPMs are subjected to a theoretical study here. It is asked to which extent the updating rules establish an appropriate dynamical model of intercellular interactions and what the principal behavior at different time scales characterizes. It is shown that the longtime behavior of a CPM is degenerate in the sense that the cells consecutively die out, independent of the specific interdependence structure that characterizes the model. While CPMs are naturally defined on finite, spatially bounded lattices, possible extensions to spatially unbounded systems are explored to assess to which extent spatio-temporal limit procedures can be applied to describe the emergent behavior at the tissue scale. To elucidate the mechanistic structure of CPMs, the model class is integrated into a general multiscale framework. It is shown that the central role of the surface fluctuations, which subsume several cellular and intercellular factors, entails substantial limitations for a CPM's exploitation both as a mechanistic and as a phenomenological model.

Within a fully microscopic setting, we derive a variational principle for the non-equilibrium steady states of chemical reaction networks, valid for time-scales over which chemical potentials can be taken to be slowly varying: at stationarity the system minimizes a global function of the reaction fluxes with the form of a Hopfield Hamiltonian with Hebbian couplings, that is explicitly seen to correspond to the rate of decay of entropy production over time. Guided by this analogy, we show that reaction networks can be formally re-cast as systems of interacting reactions that optimize the use of the available compounds by competing for substrates, akin to agents competing for a limited resource in an optimal allocation problem. As an illustration, we analyze the scenario that emerges in two simple cases: that of toy (random) reaction networks and that of a metabolic network model of the human red blood cell., 10 pages, 2 figures, 2 tables, to appear in PLoS One

Many bird species do not make their own nests; therefore, selection of existing sites that provide adequate microclimates is critical. This is particularly true for owls in north temperate climates that often nest early in the year when inclement weather is common. Spotted owls use three main types of nest structures, each of which are structurally distinct and may provide varying levels of protection to the eggs or young. We tested the hypothesis that spotted owl nest configuration influences nest microclimate using both experimental and observational data. We used a wind tunnel to estimate the convective heat transfer coefficient (h(c)) of eggs in 25 potential nest configurations that mimicked 2 nest types (top-cavity and platform nests), at 3 different wind speeds. We then used the estimates of h(c) in a biophysical heat transfer model to estimate how long it would take unattended eggs to cool from incubation temperature (~36 °C) to physiological zero temperature (PZT; ~26 °C) under natural environmental conditions. Our results indicated that the structural configuration of nests influences the cooling time of the eggs inside those nests, and hence, influences the nest microclimate. Estimates of time to PZT ranged from 10.6 minutes to 33.3 minutes. Nest configurations that were most similar to platform nests always had the fastest egg cooling times, suggesting that platform nests were the least protective of those nests we tested. Our field data coupled with our experimental results suggested that nest choice is important for the reproductive success of owls during years of inclement weather or in regions characterized by inclement weather during the nesting season.

By funneling protein effectors through needle complexes located on the cellular membrane, bacteria are able to infect host cells during type III secretion events. The spatio-temporal mechanisms through which these events occur are however not fully understood, due in part to the inherent challenges in tracking single molecules moving within an intracellular medium. As a result, theoretical predictions of secretion times are still lacking. Here we provide a model that quantifies, depending on the transport characteristics within bacterial cytoplasm, the amount of time for a protein effector to reach either of the available needle complexes. Using parameters from Shigella flexneri we are able to test the role that translocators might have to activate the needle complexes and offer semi-quantitative explanations of recent experimental observations.

The integration of various types of genomic data into predictive models of biological networks is one of the main challenges currently faced by computational biology. Constraint-based models in particular play a key role in the attempt to obtain a quantitative understanding of cellular metabolism at genome scale. In essence, their goal is to frame the metabolic capabilities of an organism based on minimal assumptions that describe the steady states of the underlying reaction network via suitable stoichiometric constraints, specifically mass balance and energy balance (i.e. thermodynamic feasibility). The implementation of these requirements to generate viable configurations of reaction fluxes and/or to test given flux profiles for thermodynamic feasibility can however prove to be computationally intensive. We propose here a fast and scalable stoichiometry-based method to explore the Gibbs energy landscape of a biochemical network at steady state. The method is applied to the problem of reconstructing the Gibbs energy landscape underlying metabolic activity in the human red blood cell, and to that of identifying and removing thermodynamically infeasible reaction cycles in the Escherichia coli metabolic network (iAF1260). In the former case, we produce consistent predictions for chemical potentials (or log-concentrations) of intracellular metabolites; in the latter, we identify a restricted set of loops (23 in total) in the periplasmic and cytoplasmic core as the origin of thermodynamic infeasibility in a large sample ($10^6$) of flux configurations generated randomly and compatibly with the prior information available on reaction reversibility., 11 pages, 6 figures, 1 table; for associated supporting material see http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002562