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We propose a 3D stochastic cellular automaton model, governed by evolutionary game theory, to simulate bone remodeling dynamics. The model includes four voxel states: Formation, Quiescence, Resorption, and Environment. We simulate the Resorption and Formation processes on separate time scales to explore the parameter space and derive a phase diagram that illustrates the sensitivity of these processes to parameter changes. Combining these results, we simulate a full bone remodeling cycle. Furthermore, we show the importance of modeling small neighborhoods for studying local bone microenvironment controls. This model can guide experimental design and, in combination with other models, it could assist to further explore external impacts on bone remodeling. Consequently, this model contributes to an improved understanding of complex dynamics in bone remodeling dynamics and exploring alterations due to disease or drug treatment. [ABSTRACT FROM AUTHOR]

Complex Markov models are widely used and powerful predictive tools to analyze stochastic biochemical processes. However, when the network of states is unknown, it is necessary to extract information from the data to partially build the network and estimate the values of the rates. The short-time behavior of the first-passage time distributions between two states in linear chains has been shown recently to behave as a power of time with an exponent equal to the number of intermediate states. For a general Markov model we derive the complete Taylor expansion of the first-passage time distribution between two arbitrary states. By combining algebraic methods and graph theory approaches it is shown that the first term of the Taylor expansion is determined by the shortest path from the initial state to the final state. When this path is unique, we prove that the coefficient of the first term can be written in terms of the product of the transition rates along the path. It is argued that the application of our results to first-return times may be used to estimate the dependence of rates on external parameters in experimentally measured time distributions. [ABSTRACT FROM AUTHOR]

In this work, we consider the reversible reaction between reactants of species A and B to form the product C. We consider this reaction as a prototype of many pseudobiomolecular reactions in biology, such as for instance molecular motors. We derive the exact probability density for the stochastic waiting time that a molecule of species A needs until the reaction with a molecule of species B takes place. We perform this computation taking fully into account the stochastic fluctuations in the number of molecules of species B. We show that at low numbers of participating molecules, the exact probability density differs from the exponential density derived by assuming the law of mass action. Finally, we discuss the condition of detailed balance in the exact stochastic and in the approximate treatment. [ABSTRACT FROM AUTHOR]

We investigate the role of degradation of mRNA on protein synthesis using the totally asymmetric simple exclusion process (TASEP) as the underlying model for ribosome dynamics. mRNA degradation has a strong effect on the lifetime distribution of the mRNA, which in turn affects polysome statistics such as the number of ribosomes present on an mRNA strand of a given size. An average over mRNA of all ages is equivalent to an average over possible configurations of the corresponding TASEP-both before steady state and in steady state. To evaluate the relevant quantities for the translation problem, we first study the approach towards steady state of the TASEP, starting with an empty lattice representing an unloaded mRNA. When approaching the high density phase, the system shows two distinct phases with the entry and exit boundaries taking control of the density at their respective ends in the second phase. The approach towards the maximal current phase exhibits the surprising property that the ribosome entry flux can exceed the maximum possible steady state value. In all phases, the averaging over the mRNA age distribution shows a decrease in the average ribosome density profile as a function of distance from the entry boundary. For entry/exit parameters corresponding to the high density phase of TASEP, the average ribosome density profile also has a maximum near the exit end. [ABSTRACT FROM AUTHOR]

Using the generic example of Ising spins on scale-free networks, we demonstrate that degree-degree correlations can induce a large number of thermodynamically stable states in networks that otherwise exhibit only the two completely ordered states. The additional stable states are related to the layered network structure. As one increases the temperature, a cascade of first-order phase transitions is found, at which some layers of the network become disordered, while others remain ordered. Negative degree-degree correlations are found to stabilize ordered layers against thermal fluctuations. Positively correlated networks can exhibit an infinite number of ground states and phase transitions, while in negatively correlated networks both numbers are finite. [ABSTRACT FROM AUTHOR]

A simple measure for the efficiency of protein synthesis by ribosomes is provided by the steady state amount of protein per messenger RNA (mRNA), the so-called translational ratio, which is proportional to the translation rate. Taking the degradation of mRNA into account, we show theoretically that both the translation rate and the translational ratio decrease with increasing mRNA length, in agreement with available experimental data for the prokaryote Escherichia coli. We also show that, compared to prokaryotes, mRNA degradation in eukaryotes leads to a less rapid decrease of the translational ratio. This finding is consistent with the fact that, compared to prokaryotes, eukaryotes tend to have longer proteins. [ABSTRACT FROM AUTHOR]

This special issue of Biophysical Reviews and Letters describes recent advances in the area of active biomimetic systems, which are inspired by the cytoskeletal architecture found in all eukaryotic cells. The main building blocks of these systems are provided by two types of cytoskeletal filaments, F-actin and microtubules, as well as molecular stepping motors such as kinesins and myosins. All of these building blocks represent molecular machines: They are coupled to nucleotide hydrolysis and are able to convert the chemical energy released from this process into mechanical work. Bundles of filaments and teams of stepping motors generate strong pushing forces and perform long-ranged cargo transport. [ABSTRACT FROM AUTHOR]

Abstract: In this study we consider a population subdivided in groups. Each group is connected to two neighboring groups by means of migration channels. The migration channels are used with different probability, according to a gradient that gives a preferential direction of colonization. Within groups we have a fast population dynamics modeled with a Moran process. Between groups we have a process of colonization selection at low migration rate, based on the propagule model. We consider resident and invading individuals, with the invading individuals having a relative fitness r. Groups composed only of invaders will also have a relative group fitness R. We show that, independently of the value of r, a strong gradient reduces the advantage of groups with large fitness and thus works against group selection. [Copyright &y& Elsevier]

Abstract: We investigate the effect of auto-correlated yield on the evolutionarily stable germination fraction of dormant seeds. By using both analytics and numerics, we first show that in a regime of small fluctuations a positive correlation reduces dormancy and a negative correlation enhances dormancy. By extending the numerical analysis we also show that in the regime of large fluctuations a more complex picture emerges where also negative correlations can reduce dormancy. [Copyright &y& Elsevier]

Abstract: Dormant seeds in permanent soil seed banks change their germination probability with age, but little is known about the causes of this behavior. Since current adaptive models do not consider the age structure of the seed bank, the sole explanation is that changes in germination probability with age are due to passive accidental factors or to decay of seeds. Here we present a theory, which shows that such changes might be adaptive. In particular, in density-regulated populations, the evolutionarily stable fraction of germinating seeds in each age class increases with age whenever age-dependent mortality of dormant seeds remains constant or increases with age. [Copyright &y& Elsevier]

Annual plants in unpredictable environments maintain dormant seeds to avoid extinction. Here, we present results for four desert annual species suggesting that germination rates are variable even in the absence of abiotic cues. Namely, seeds produced in a copious year had lower germination rates than seeds produced in drought years. Inspired by our data, we have extended previous bet-hedging models by including a structured seed bank. With density-dependence, the ESS (environmental stable strategy) involved a negative relationship between seed yield and subsequent germination probability. We suggest that heterogeneous germination rates are selected for by competition among seedlings after years with high seed production. In summary, our findings are suggestive of an intriguingly simple and effective mechanism that may allow annual plants to partly predict their future success. [ABSTRACT FROM AUTHOR]

Abstract: In this article, we consider a bet-hedging model with density dependence for germination behavior of dormant seeds. We show how to compute accurate values of the evolutionary stable germination fraction using a method based on expansion around the average seed bank size. The expansion is made up to the fourth order and is expressed in terms of the first four moments of the distribution of the year-to-year variation in the average yield per adult plant. This method leads to a simple algebraic equation, which can be solved without recurring to simulations of the seed bank dynamics. We first show the analytical derivation under general assumptions about the effect of density dependence. We then test our results with a numerical analysis where an explicit form of the density dependence has been taken. [Copyright &y& Elsevier]

Adapting a simple biological model, we study the effects of control on the market. Companies are depicted as sites on a lattice and labelled by a fitness parameter (some `company-size' indicator). The chance of survival of a company on the market at any given time is related to its fitness, its position on the lattice and on some particular external influence, which may be considered to represent regulation from governments or central banks. The latter is rendered as a penalty for companies which show a very fast betterment in fitness space. As a result, we find that the introduction of regulation on the market contributes to lower the average fitness of companies. [ABSTRACT FROM AUTHOR]

Analysis of complex networks has been widely used as a powerful tool for investigating various physical, chemical, and biological processes. To understand the emergent properties of these complex systems, one of the most basic issues is to determine the structure and topology of the underlying networks. Recently, a new theoretical approach based on first-passage analysis has been developed for investigating the relationship between structure and dynamic properties for network systems with exponential dwell time distributions. However, many real phenomena involve transitions with nonexponential waiting times. We extend the first-passage method to uncover the structure of distinct pathways in complex networks with non-exponential dwell time distributions. It is found that the analysis of early time dynamics provides explicit information on the length of the pathways associated to their dynamic properties. It reveals a universal relationship that we have condensed in one general equation, which relates the number of intermediate states on the shortest path to the early time behavior of the first-passage distributions. Our theoretical predictions are confirmed by extensive Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Myoviruses, bacteriophages with T4-like architecture, must contract their tails prior to DNA release. However, quantitative kinetic data on myovirus particle opening are lacking, although they are promising tools in bacteriophage-based antimicrobial strategies directed against Gram-negative hosts. For the first time, we show time-resolved DNA ejection from a bacteriophage with a contractile tail, the multi-O-antigen-specific Salmonella myovirus Det7. DNA release from Det7 was triggered by lipopolysaccharide (LPS) O-antigen receptors and notably slower than in noncontractile-tailed siphoviruses. Det7 showed two individual kinetic steps for tail contraction and particle opening. Our in vitro studies showed that highly specialized tailspike proteins (TSPs) are necessary to attach the particle to LPS. A P22-like TSP confers specificity for the Salmonella Typhimurium O-antigen. Moreover, crystal structure analysis at 1.63 Å resolution confirmed that Det7 recognized the Salmonella Anatum O-antigen via an 15-like TSP, DettilonTSP. DNA ejection triggered by LPS from either host showed similar velocities, so particle opening is thus a process independent of O-antigen composition and the recognizing TSP. In Det7, at permissive temperatures TSPs mediate O-antigen cleavage and couple cell surface binding with DNA ejection, but no irreversible adsorption occurred at low temperatures. This finding was in contrast to short-tailed Salmonella podoviruses, illustrating that tailed phages usecommonparticle-opening mechanisms but have specialized into different infection niches. [ABSTRACT FROM AUTHOR]

Dynamic single-molecule force spectroscopy (SMFS) is a powerful method to characterize the mechanical stability of biomolecules. We address the problem that the standard manner of reporting the extracted energy landscape parameters does not reveal the intrinsic statistical errors associated with them. This problem becomes particularly relevant when SMFS is used to compare two or more different molecular systems. Here, we propose two methods that allow for a straightforward test of statistical significance. We illustrate the power of the methods by applying them to the experimental results obtained for three dimeric coiled coils of different lengths. Both methods are general and may be applied to any problem involving the fit of models with two correlated parameters. [ABSTRACT FROM AUTHOR]

In recent years, the Ribosome profiling technique (Ribo–seq) has emerged as a powerful method for globally monitoring the translation process in vivo at single nucleotide resolution. Based on deep sequencing of mRNA fragments, Ribo–seq allows to obtain profiles that reflect the time spent by ribosomes in translating each part of an open reading frame. Unfortunately, the profiles produced by this method can vary significantly in different experimental setups, being characterized by a poor reproducibility. To address this problem, we have employed a statistical method for the identification of highly reproducible Ribo–seq profiles, which was tested on a set of E. coli genes. State-of-the-art artificial neural network models have been used to validate the quality of the produced sequences. Moreover, new insights into the dynamics of ribosome translation have been provided through a statistical analysis on the obtained sequences. [ABSTRACT FROM AUTHOR]

Pulse-chase experiments are often used to study the degradation of macromolecules such as proteins or mRNA. Considerations for the choice of pulse length include the toxicity of the pulse to the cell and maximization of labeling. In the general case of non-exponential decay, varying the length of the pulse results in decay patterns that look different. Analysis of these patterns without consideration to pulse length would yield incorrect degradation parameters. Here we propose a method that constructively includes pulse length in the analysis of decay patterns and extracts the parameters of the underlying degradation process. We also show how to extract decay parameters reliably from measurements taken during the pulse phase. [ABSTRACT FROM AUTHOR]

Recent experimental results on the effect of miRNA on the decay of its target mRNA have been analyzed against a previously hypothesized single molecule degradation pathway. According to that hypothesis, the silencing complex (miRISC) first interacts with its target mRNA and then recruits the protein complexes associated with NOT1 and PAN3 to trigger deadenylation (and subsequent degradation) of the target mRNA. Our analysis of the experimental decay patterns allowed us to refine the structure of the degradation pathways at the single molecule level. Surprisingly, we found that if the previously hypothesized network was correct, only about 7% of the target mRNA would be regulated by the miRNA mechanism, which is inconsistent with the available knowledge. Based on systematic data analysis, we propose the alternative hypothesis that NOT1 interacts with miRISC before binding to the target mRNA. Moreover, we show that when miRISC binds alone to the target mRNA, the mRNA is degraded more slowly, probably through a deadenylation-independent pathway. The new biochemical pathway proposed here both fits the data and paves the way for new experimental work to identify new interactions. [ABSTRACT FROM AUTHOR]

□ For an irreducible continuous time Markov chain, we derive the distribution of the first passage time from a given state i to another given state j and the reversed passage time from j to i, each under the condition of no return to the starting point. When these two distributions are identical, we say that i and j are intime duality. We introduce a new condition calledpermuted balancethat generalizes the concept of reversibility and provides sufficient criteria, based on the structure of the transition graph of the Markov chain. Illustrative examples are provided. [ABSTRACT FROM PUBLISHER]

Experimental studies on mRNA stability have established several, qualitatively distinct decay patterns for the amount of mRNA within the living cell. Furthermore, a variety of different and complex biochemical pathways for mRNA degradation have been identified. The central aim of this paper is to bring together both the experimental evidence about the decay patterns and the biochemical knowledge about the multi-step nature of mRNA degradation in a coherent mathematical theory. We first introduce a mathematical relationship between the mRNA decay pattern and the lifetime distribution of individual mRNA molecules. This relationship reveals that the mRNA decay patterns at steady state expression level must obey a general convexity condition, which applies to any degradation mechanism. Next, we develop a theory, formulated as a Markov chain model, that recapitulates some aspects of the multi-step nature of mRNA degradation. We apply our theory to experimental data for yeast and explicitly derive the lifetime distribution of the corresponding mRNAs. Thereby, we show how to extract single-molecule properties of an mRNA, such as the age-dependent decay rate and the residual lifetime. Finally, we analyze the decay patterns of the whole translatome of yeast cells and show that yeast mRNAs can be grouped into three broad classes that exhibit three distinct decay patterns. This paper provides both a method to accurately analyze non-exponential mRNA decay patterns and a tool to validate different models of degradation using decay data. [ABSTRACT FROM AUTHOR]

When transcription of a gene is induced by a stimulus, the number of its mRNA molecules changes with time. Here we discuss how this time evolution depends on the shape of the mRNA lifetime distribution. Analysis of the statistical properties of this change reveals transient effects on polysomes, ribosomal profiles, and rate of protein synthesis. Our studies reveal that transient phenomena in gene expression strongly depend on the specific form of the mRNA lifetime distribution. [ABSTRACT FROM AUTHOR]

Recent theoretical work on the energy conversion by molecular motors coupled to nucleotide hydrolysis is reviewed. The most abundant nucleotide is provided by adenosine triphosphate (ATP) which is cleaved into adenosine diphosphate (ADP) and inorganic phosphate. The motors have several catalytic domains (or active sites), each of which can be empty or occupied by ATP or ADP. The chemical composition of all catalytic domains defines distinct nucleotide states of the motor which form a discrete state space. Each of these motor states is connected to several other states via chemical transitions. For stepping motors such as kinesin, which walk along cytoskeletal filaments, some motor states are also connected by mechanical transitions, during which the motor is displaced along the filament and able to perform mechanical work. The different motor states together with the possible chemical and mechanical transitions provide a network representation for the chemomechanical coupling of the motor molecule. The stochastic motor dynamics on these networks exhibits several distinct motor cycles, which represent the dominant pathways for different regimes of nucleotide concentrations and load force. For the kinesin motor, the competition of two such cycles determines the stall force, at which the motor velocity vanishes and the motor reverses its direction of motion. In general, kinesin is found to be governed by the competition of three distinct chemomechanical cycles. The corresponding network representation provides a unified description for all motor properties that have been determined by single molecule experiments. [ABSTRACT FROM AUTHOR]

In cultures of unicellular algae, features of single cells, such as cellular volume and starch content, are thought to be the result of carefully balanced growth and division processes. Single-cell analyses of synchronized photoautotrophic cultures of the unicellular alga Chlamydomonas reinhardtii reveal, however, that the cellular volume and starch content are only weakly correlated. Likewise, other cell parameters, e.g., the chlorophyll content per cell, are only weakly correlated with cell size. We derive the cell size distributions at the beginning of each synchronization cycle considering growth, timing of cell division and daughter cell release, and the uneven division of cell volume. Furthermore, we investigate the link between cell volume growth and starch accumulation. This work presents evidence that, under the experimental conditions of light-dark synchronized cultures, the weak correlation between both cell features is a result of a cumulative process rather than due to asymmetric partition of biomolecules during cell division. This cumulative process necessarily limits cellular similarities within a synchronized cell population. [ABSTRACT FROM AUTHOR]

Living cells contain a large number of molecular motors that convert the chemical energy released from nucleotide hydrolysis into mechanical work. This review focusses on stepping motors that move along cytoskeletal filaments. The behavior of these motors involves three distinct nonequilibrium processes that cover a wide range of length and time scales: (i) Directed stepping of single motors bound to a filament; (ii) Composite motor walks of single motors consisting of directed stepping interrupted by diffusive motion; and (iii) Cooperative transport by teams of several motors. On the molecular scale, the energy conversion of these motors leads to single steps along the filaments with a step size of about 10 nm. The corresponding chemomechanical coupling is governed by several distinct motor cycles, which represent the dominant pathways for different values of nucleotide concentrations and load force. For the kinesin motor, the competition of two such cycles determines the stall force, at which the motor velocity vanishes and the motor reverses the direction of its motion. Because of thermal noise, the stepping motors unbind from the filaments after a certain run time and run length. For kinesin, the run time is about 1 s and the run length is about 1 μm for high ATP concentration and low load force. On length scales that are large compared to the run length, a single motor undergoes composite walks consisting of directed stepping interrupted by diffusive motion. The relative importance of bound and unbound motor states depends on the binding and unbinding rates of the motors. The effective transport velocity and diffusion coefficient of the motors are determined by the geometry of the compartments, in which the motors move. The effective diffusion coefficient can be enhanced by several orders of magnitude if the motors undergo active diffusion by interacting with certain filament patterns. In vivo, stepping motors are responsible for the transport of vesicles and other types of intracellular cargo particles that shuttle between the different cell compartments. This cargo transport is usually performed by teams of motors. If all motors belong to the same molecular species, the cooperative action of the motors leads to uni-directional transport with a strongly increased run length and to a characteristic force dependence of the velocity distributions. If two antagonistic species of motors pull on the cargo, they perform a stochastic tug-of-war, which is characterized by a subtle force balance between the two motor teams and leads to seven distinct patterns of uni- and bi-directional transport. So far, all experimental observations on bi-directional transport are consistent with such a tug-of-war. Finally, the traffic of interacting motors is also briefly discussed. Depending on their mutual interactions and the compartment geometry, the motors form various spatio-temporal patterns such as traffic jams, and undergo nonequilibrium phase transitions between such transport patterns. [ABSTRACT FROM AUTHOR]

Abstract: This is the second of two papers dedicated to the relationship between population models of competition and biodiversity. Here, we consider species assembly models where the population dynamics is kept far from fixed points through the continuous introduction of new species, and generalize to such models the coexistence condition derived for systems at the fixed point. The ecological overlap between species and shared preys, that we define here, provides a quantitative measure of the effective interspecies competition and of the trophic network topology. We obtain distributions of the overlap from simulations of a new model based both on immigration and speciation, and show that they are in good agreement with those measured for three large natural food webs. As discussed in the first paper, rapid environmental fluctuations, interacting with the condition for coexistence of competing species, limit the maximal biodiversity that a trophic level can host. This horizontal limitation to biodiversity is here combined with either dissipation of energy or growth of fluctuations, which in our model limit the length of food webs in the vertical direction. These ingredients yield an effective model of food webs that produce a biodiversity profile with a maximum at an intermediate trophic level, in agreement with field studies. [Copyright &y& Elsevier]

Abstract: This is the first of two papers where we discuss the limits imposed by competition to the biodiversity of species communities. In this first paper, we study the coexistence of competing species at the fixed point of population dynamic equations. For many simple models, this imposes a limit on the width of the productivity distribution, which is more severe the more diverse the ecosystem is (1994, Theor. Popul. Biol. 45, 227–276). Here we review and generalize this analysis, beyond the “mean-field”-like approximation of the competition matrix used in previous works, and extend it to structured food webs. In all cases analysed, we obtain qualitatively similar relations between biodiversity and competition: the narrower the productivity distribution is, the more species can stably coexist. We discuss how this result, considered together with environmental fluctuations, limits the maximal biodiversity that a trophic level can host. [Copyright &y& Elsevier]

Summary Do young and old protein molecules have the same probability to be degraded? We addressed this question using metabolic pulse-chase labeling and quantitative mass spectrometry to obtain degradation profiles for thousands of proteins. We find that >10% of proteins are degraded non-exponentially. Specifically, proteins are less stable in the first few hours of their life and stabilize with age. Degradation profiles are conserved and similar in two cell types. Many non-exponentially degraded (NED) proteins are subunits of complexes that are produced in super-stoichiometric amounts relative to their exponentially degraded (ED) counterparts. Within complexes, NED proteins have larger interaction interfaces and assemble earlier than ED subunits. Amplifying genes encoding NED proteins increases their initial degradation. Consistently, decay profiles can predict protein level attenuation in aneuploid cells. Together, our data show that non-exponential degradation is common, conserved, and has important consequences for complex formation and regulation of protein abundance. [ABSTRACT FROM AUTHOR]