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The ribosome flow model (RFM) is a phenomenological model for the flow of particles along a one-dimensional chain of n sites. It has been extensively used to study ribosome flow along the mRNA molecule during translation. When the transition rates along the chain are time-varying and jointly T -periodic the RFM entrains, i.e. every trajectory of the RFM converges to a unique T -periodic solution that depends on the transition rates, but not on the initial condition. In general, entrainment to periodic excitations like the 24 h solar day or the 50 Hz frequency of the electric grid is important in numerous natural and artificial systems. An interesting question, called the gain of entrainment (GOE) in the RFM, is whether proper coordination of the periodic translation rates along the mRNA can lead to a larger average protein production rate. Analysing the GOE in the RFM is non-trivial and partial results exist only for the RFM with dimensions n = 1, 2. We use a new approach to derive several results on the GOE in the general n -dimensional RFM. Perhaps surprisingly, we rigorously characterize several cases where there is no GOE, so to maximize the average production rate in these cases, the best choice is to use constant transition rates all along the chain.

During translation, mRNAs 'compete' for shared resources. Under stress conditions, during viral infection and also in high-throughput heterologous gene expression, these resources may become scarce, e.g. the pool of free ribosomes is starved, and then the competition may have a dramatic effect on the global dynamics of translation in the cell. We model this scenario using a network that includes m ribosome flow models (RFMs) interconnected via a pool of free ribosomes. Each RFM models ribosome flow along an mRNA molecule, and the pool models the shared resource. We assume that the number of mRNAs is large, so many ribosomes are attached to the mRNAs, and the pool is starved. Our analysis shows that adding an mRNA has an intricate effect on the total protein production. The new mRNA produces new proteins, but the other mRNAs produce less proteins, as the pool that feeds these mRNAs now has a smaller abundance of ribosomes. As the number of mRNAs increases, the marginal utility of adding another mRNA diminishes, and the total protein production rate saturates to a limiting value. We demonstrate our approach using an example of insulin protein production in a cell-free system.

We present a new theoretical framework for large-scale mRNA translation using a network of models called the ribosome flow model with Langmuir kinetics (RFMLK), interconnected via a pool of free ribosomes. The input to each RFMLK depends on the pool density, and it affects the initiation rate and potentially also the internal ribosome entry rates along each RFMLK. Ribosomes that detach from an RFMLK owing to termination or premature drop-off are fed back into the pool. We prove that the network always converges to a steady state, and study its sensitivity to variations in the parameters. For example, we show that if the drop-off rate at some site in some RFMLK is increased then the pool density increases and consequently the steady-state production rate in all the other RFMLKs increases. Surprisingly, we also show that modifying a parameter of a certain RFMLK can lead to arbitrary effects on the densities along the modified RFMLK, depending on the parameters in the entire network. We conclude that the competition for shared resources generates an indirect and intricate web of mutual effects between the mRNA molecules that must be accounted for in any analysis of translation.

A dynamical system entrains to a periodic input if its state converges globally to an attractor with the same period. In particular, for a constant input, the state converges to a unique equilibrium point for any initial condition. We consider the problem of maximizing a weighted average of the system's output along the periodic attractor. The gain of entrainment is the benefit achieved by using a non-constant periodic input relative to a constant input with the same time average. Such a problem amounts to optimal allocation of resources in a periodic manner. We formulate this problem as a periodic optimal control problem, which can be analysed by means of the Pontryagin maximum principle or solved numerically via powerful software packages. We then apply our framework to a class of nonlinear occupancy models that appear frequently in biological synthesis systems and other applications. We show that, perhaps surprisingly, constant inputs are optimal for various architectures. This suggests that the presence of non-constant periodic signals, which frequently appear in biological occupancy systems, is a signature of an underlying time-varying objective functional being optimized., (© 2021 The Authors.)

Since current recommendations call for a substantial reduction in overall sodium consumption, we tested whether or not these recommendations are implemented in common large subpopulations such as those with abnormal weight or hypertension in the current high sodium, high-calorie nutritional environment. In a national representative cross-sectional survey of the community-dwelling subjects aged 25-65 years conducted in Israel between 2015 and 2017, 582 randomly selected subjects completed health and dietary questionnaires, underwent blood pressure and anthropometric measurements and collected 24-h urine specimens, to assess dietary sodium intake. Overall mean 24-h sodium excretion was 3834 mg, more than double the recommended upper intake for adults < 1500 mg/day. Sodium excretion was directly related to caloric intake and blood pressure and linked to the presence of hypertension and overweight/obesity. The highest sodium excretion was seen in overweight/obese hypertensive subjects. This recent national survey shows a high consumption of sodium in the Israeli population and a dose-response association between caloric intake and urinary sodium excretion, independent of BMI and hypertension. Nevertheless, overweight/obese subjects with hypertension consume (excrete) more sodium than other BMI/ blood pressure-related phenotypes and may thus comprise a target subpopulation for future efforts to reduce sodium intake., (© 2021. The Author(s).)

A balanced diet and weight loss are the first lines of treatment for the prevention of metabolic syndrome (MS). Dietary strategies may include changing the composition of macronutrients, adopting a particular dietary pattern as a Mediterranean diet. However, the role of micronutrients, particularly potassium, in the propensity for or treatment of the syndrome is unclear. The study aimed to examine the relationship between the presence of the MS and its risk factors and the 24-h potassium excretion as the most valid proxy for dietary intake. The analyses were performed as part of the national survey estimating sodium and other electrolytes excretion conducted between 2014-2016 in Israel. The survey included urine collection, anthropometric and blood pressure measurements, and a comprehensive medical questionnaire that included details on the intake of medications that may affect electrolyte secretion. A model was constructed to evaluate the probability for the MS. MS score and its probability were examined in relation to potassium excretion at different levels and in stratification to sex. A total of 581 participants were included in the analysis. The mean potassium excretion was 2818 ± 1417 mg. The prevalence of the MS was 18.5% among participants with above-average potassium excretion and about 10.4% among participants with lower-than-average excretion ( p = 0.007). A dose-response relationship was observed between MS score and potassium: the higher the score, the lower was the excretion of potassium. Potassium excretion, rather than sodium excretion, correlated with all components of the MS and even predicted MS independently from other variables. This is the first study based on a national survey showing that potassium consumption, as represented by daily excretion in urine, is inversely related to the presence of MS components after adjustment for several leading variables and careful exclusion of participants taking drugs which may interfere in potassium excretion.

The rate of mRNA translation depends on the initiation, elongation, and termination rates of ribosomes along the mRNA. These rates depend on many "local" factors like the abundance of free ribosomes and tRNA molecules in the vicinity of the mRNA molecule. All these factors are stochastic and their experimental measurements are also noisy. An important question is how protein production in the cell is affected by this considerable variability. We develop a new theoretical framework for addressing this question by modeling the rates as identically and independently distributed random variables and using tools from random matrix theory to analyze the steady-state production rate. The analysis reveals a principle of universality: the average protein production rate depends only on the of the set of possible values that the random variable may attain. This explains how total protein production can be stabilized despite the overwhelming stochasticticity underlying cellular processes.

Background: In the treatment of obesity/metabolic syndrome, dietary measures traditionally focus on reducing carbohydrate/fat-related caloric intake. The possibility that changes in potassium consumption may be related to the achieved weight loss has not been previously explored., Methods: Sixty-eight participants, with a mean age of 51.6 ± 11.0 years (F/M-30/38), who fulfilled the ATPIII criteria for the metabolic syndrome (MS) were enrolled into a 1-year intensive multidisciplinary program. Nutritional recommendation consisted of a moderate low calorie/high protein Mediterranean diet. Baseline assessment included clinical and biochemical profiling, and body composition. Nutritional components were registered over 7 days before and at the end of 1 year of treatment., Results: Mean baseline body mass index (BMI) was 35 ± 4 kg/m², which declined by 9.4 ± 0.1% after one year of combined intervention. Linear stepwise regression analysis revealed that 45% of the predicted variance of the % decline in BMI was related to increased consumption of dietary potassium (β = -0.865) and caproic acid (β = -0.423) and reduction in the consumption of dietary vitamin B6 (β = 0.542), calcium (β = 0.335), total carbohydrates (β = 0.239) and total caloric intake (β = 0.238; p < 0.001). Notably, the strongest correlate of the decline in BMI was the increase in dietary potassium intake (β = -0.865). Subjects whose achieved decrease in BMI was above the average ( n = 30) increased potassium intake by 25% as compared to an increase in dietary potassium intake of only 3% by those whose decline in BMI was below the average ( n = 36; p < 0.05). The change in dietary potassium was related to the percent increase in dietary protein (r = 0.433; p < 0.001)., Conclusion: An increase in dietary potassium consumption is a previously unrecognized predictor of the achieved reduction in BMI in a weight-loss-oriented multidisciplinary intervention in obesity/MS. Prospective trials are underway to confirm this post-hoc finding., Competing Interests: The authors declare no conflict of interest.

The ribosome flow model with input and output (RFMIO) is a deterministic dynamical system that has been used to study the flow of ribosomes during mRNA translation. The input of the RFMIO controls its initiation rate and the output represents the ribosome exit rate (and thus the protein production rate) at the 3' end of the mRNA molecule. The RFMIO and its variants encapsulate important properties that are relevant to modeling ribosome flow such as the possible evolution of "traffic jams" and non-homogeneous elongation rates along the mRNA molecule, and can also be used for studying additional intracellular processes such as transcription, transport, and more. Here we consider networks of interconnected RFMIOs as a fundamental tool for modeling, analyzing and re-engineering the complex mechanisms of protein production. In these networks, the output of each RFMIO may be divided, using connection weights, between several inputs of other RFMIOs. We show that under quite general feedback connections the network has two important properties: (1) it admits a unique steady-state and every trajectory converges to this steady-state; and (2) the problem of how to determine the connection weights so that the network steady-state output is maximized is a convex optimization problem. These mathematical properties make these networks highly suitable as models of various phenomena: property (1) means that the behavior is predictable and ordered, and property (2) means that determining the optimal weights is numerically tractable even for large-scale networks. For the specific case of a feed-forward network of RFMIOs we prove an additional useful property, namely, that there exists a spectral representation for the network steady-state, and thus it can be determined without any numerical simulations of the dynamics. We describe the implications of these results to several fundamental biological phenomena and biotechnological objectives.

The ribosomal density along different parts of the coding regions of the mRNA molecule affects various fundamental intracellular phenomena including: protein production rates, global ribosome allocation and organismal fitness, ribosomal drop off, co-translational protein folding, mRNA degradation, and more. Thus, regulating translation in order to obtain a desired ribosomal profile along the mRNA molecule is an important biological problem. We study this problem by using a dynamical model for mRNA translation, called the ribosome flow model (RFM). In the RFM, the mRNA molecule is modeled as an ordered chain of $n$ sites. The RFM includes $n$ state-variables describing the ribosomal density profile along the mRNA molecule, and the transition rates from each site to the next are controlled by $n+1$ positive constants. To study the problem of controlling the density profile, we consider some or all of the transition rates as time-varying controls. We consider the following problem: given an initial and a desired ribosomal density profile in the RFM, determine the time-varying values of the transition rates that steer the system to the desired density profile, if they exist. More specifically, we consider two control problems. In the first, all transition rates can be regulated separately, and the goal is to steer the ribosomal density profile and the protein production rate from a given initial value to a desired value. In the second problem, one or more transition rates are jointly regulated by a single scalar control, and the goal is to steer the production rate to a desired value within a certain set of feasible values. In the first case, we show that the system is controllable, i.e., the control is powerful enough to steer the system to any desired value in finite time, and provide simple closed-form expressions for constant positive control functions (or transition rates) that asymptotically steer the system to the desired value. In the second case, we show that the system is controllable, and provide a simple algorithm for determining the constant positive control value that asymptotically steers the system to the desired value. We discuss some of the biological implications of these results.

The master equation plays an important role in many scientific fields including physics, chemistry, systems biology, physical finance and sociodynamics. We consider the master equation with periodic transition rates. This may represent an external periodic excitation like the 24 h solar day in biological systems or periodic traffic lights in a model of vehicular traffic. Using tools from systems and control theory, we prove that under mild technical conditions every solution of the master equation converges to a periodic solution with the same period as the rates. In other words, the master equation entrains (or phase locks) to periodic excitations. We describe two applications of our theoretical results to important models from statistical mechanics and epidemiology., Competing Interests: We declare we have no competing interests.

We study a deterministic mechanistic model for the flow of ribosomes along the mRNA molecule, called the ribosome flow model with extended objects  (RFMEO). This model encapsulates many realistic features of translation including non-homogeneous transition rates along mRNA, the fact that every ribosome covers several codons, and the fact that ribosomes cannot overtake one another. The RFMEO is a mean-field approximation of an important model from statistical mechanics called the totally asymmetric simple exclusion process with extended objects (TASEPEO). We demonstrate that the RFMEO describes biophysical aspects of translation better than previous mean-field approximations, and that its predictions correlate well with those of TASEPEO. However, unlike TASEPEO, the RFMEO is amenable to rigorous analysis using tools from systems and control theory. We show that the ribosome density profile along the mRNA in the RFMEO converges to a unique steady-state density that depends on the length of the mRNA, the transition rates along it, and the number of codons covered by every ribosome, but not on the initial density of ribosomes along the mRNA. In particular, the protein production rate also converges to a unique steady state. Furthermore, if the transition rates along the mRNA are periodic with a common period  T then the ribosome density along the mRNA and the protein production rate converge to a unique periodic pattern with period  T , that is, the model entrains to periodic excitations in the transition rates. Analysis and simulations of the RFMEO demonstrate several counterintuitive results. For example, increasing the ribosome footprint may sometimes lead to an increase in the production rate. Also, for large values of the footprint the steady-state density along the mRNA may be quite complex (e.g. with quasi-periodic patterns) even for relatively simple (and non-periodic) transition rates along the mRNA. This implies that inferring the transition rates from the ribosome density may be non-trivial. We believe that the RFMEO could be useful for modelling, understanding and re-engineering translation as well as other important biological processes., (© 2017 The Author(s).)

The ribosome flow model on a ring (RFMR) is a deterministic model for ribosome flow along a circularized mRNA. We derive a new spectral representation for the optimal steady-state production rate and the corresponding optimal steady-state ribosomal density in the RFMR. This representation has several important advantages. First, it provides a simple and numerically stable algorithm for determining the optimal values even in very long rings. Second, it enables efficient computation of the sensitivity of the optimal production rate to small changes in the transition rates along the mRNA. Third, it implies that the optimal steady-state production rate is a strictly concave function of the transition rates. Maximizing the optimal steady-state production rate with respect to the rates under an affine constraint on the rates thus becomes a convex optimization problem that admits a unique solution. This solution can be determined numerically using highly efficient algorithms. This optimization problem is important, for example, when re-engineering heterologous genes in a host organism. We describe the implications of our results to this and other aspects of translation.

In many important cellular processes, including mRNA translation, gene transcription, phosphotransfer, and intracellular transport, biological "particles" move along some kind of "tracks". The motion of these particles can be modeled as a one-dimensional movement along an ordered sequence of sites. The biological particles (e.g., ribosomes or RNAPs) have volume and cannot surpass one another. In some cases, there is a preferred direction of movement along the track, but in general the movement may be bidirectional, and furthermore the particles may attach or detach from various regions along the tracks. We derive a new deterministic mathematical model for such transport phenomena that may be interpreted as a dynamic mean-field approximation of an important model from mechanical statistics called the asymmetric simple exclusion process (ASEP) with Langmuir kinetics. Using tools from the theory of monotone dynamical systems and contraction theory we show that the model admits a unique steady-state, and that every solution converges to this steady-state. Furthermore, we show that the model entrains (or phase locks) to periodic excitations in any of its forward, backward, attachment, or detachment rates. We demonstrate an application of this phenomenological transport model for analyzing ribosome drop off in mRNA translation.

Natural phenomena frequently involve a very large number of interacting molecules moving in confined regions of space. Cellular transport by motor proteins is an example of such collective behavior. We derive a deterministic compartmental model for the unidirectional flow of particles along a one-dimensional lattice of sites with nearest-neighbor interactions between the particles. The flow between consecutive sites is governed by a "soft" simple exclusion principle and by attracting or repelling forces between neighboring particles. Using tools from contraction theory, we prove that the model admits a unique steady-state and that every trajectory converges to this steady-state. Analysis and simulations of the effect of the attracting and repelling forces on this steady-state highlight the crucial role that these forces may play in increasing the steady-state flow, and reveal that this increase stems from the alleviation of traffic jams along the lattice. Our theoretical analysis clarifies microscopic aspects of complex multi-particle dynamic processes.

[This corrects the article DOI: 10.1371/journal.pone.0166481.].

Down regulation of mRNA translation is an important problem in various bio-medical domains ranging from developing effective medicines for tumors and for viral diseases to developing attenuated virus strains that can be used for vaccination. Here, we study the problem of down regulation of mRNA translation using a mathematical model called the ribosome flow model (RFM). In the RFM, the mRNA molecule is modeled as a chain of n sites. The flow of ribosomes between consecutive sites is regulated by n + 1 transition rates. Given a set of feasible transition rates, that models the outcome of all possible mutations, we consider the problem of maximally down regulating protein production by altering the rates within this set of feasible rates. Under certain conditions on the feasible set, we show that an optimal solution can be determined efficiently. We also rigorously analyze two special cases of the down regulation optimization problem. Our results suggest that one must focus on the position along the mRNA molecule where the transition rate has the strongest effect on the protein production rate. However, this rate is not necessarily the slowest transition rate along the mRNA molecule. We discuss some of the biological implications of these results.

During mRNA translation, several ribosomes attach to the same mRNA molecule simultaneously translating it into a protein. This pipelining increases the protein translation rate. A natural and important question is what ribosomal density maximizes the protein translation rate. Using mathematical models of ribosome flow along both a linear and a circular mRNA molecules we prove that typically the steady-state protein translation rate is maximized when the ribosomal density is one half of the maximal possible density. We discuss the implications of our results to endogenous genes under natural cellular conditions and also to synthetic biology., Competing Interests: The authors have declared that no competing interests exist.

A single mammalian cell includes an order of 10(4)-10(5) mRNA molecules and as many as 10(5)-10(6) ribosomes. Large-scale simultaneous mRNA translation induces correlations between the mRNA molecules, as they all compete for the finite pool of available ribosomes. This has important implications for the cell's functioning and evolution. Developing a better understanding of the intricate correlations between these simultaneous processes, rather than focusing on the translation of a single isolated transcript, should help in gaining a better understanding of mRNA translation regulation and the way elongation rates affect organismal fitness. A model of simultaneous translation is specifically important when dealing with highly expressed genes, as these consume more resources. In addition, such a model can lead to more accurate predictions that are needed in the interconnection of translational modules in synthetic biology. We develop and analyse a general dynamical model for large-scale simultaneous mRNA translation and competition for ribosomes. This is based on combining several ribosome flow models (RFMs) interconnected via a pool of free ribosomes. We use this model to explore the interactions between the various mRNA molecules and ribosomes at steady state. We show that the compound system always converges to a steady state and that it always entrains or phase locks to periodically time-varying transition rates in any of the mRNA molecules. We then study the effect of changing the transition rates in one mRNA molecule on the steady-state translation rates of the other mRNAs that results from the competition for ribosomes. We show that increasing any of the codon translation rates in a specific mRNA molecule yields a local effect, an increase in the translation rate of this mRNA, and also a global effect, the translation rates in the other mRNA molecules all increase or all decrease. These results suggest that the effect of codon decoding rates of endogenous and heterologous mRNAs on protein production is more complicated than previously thought. In addition, we show that increasing the length of an mRNA molecule decreases the production rate of all the mRNAs., (© 2016 The Author(s).)

Blood pressure (BP) variability (BPV) contributes to target organ damage independent of BP. The authors examined the effect of a 1-year multidisciplinary intervention on BPV in patients with the metabolic syndrome (MetS) as defined by criteria from the Third Report of the Adult Treatment Panel. Forty-four nondiabetic patients underwent clinical and biochemical profiling, 24-hour ambulatory BP monitoring (ABPM), body composition, carotid intima-media thickness, and carotid-femoral pulse wave velocity (PWV). The intervention targeted all MetS components. BPV was assessed by the standard deviation of daytime systolic BP derived from ABPM. Patients with low and high BPV (lower or higher than the median daytime standard deviation of 11.6 mm Hg) did not differ in regards to systolic and diastolic BP, age, fasting glucose, glycated hemoglobin, and body mass index, but the high-variability group had higher values of low-density lipoprotein and leg fat. The 1-year intervention resulted in weight reduction but not BP-lowering. BPV declined in the high-variability group in association with lowering of PWV, C-reactive protein, glycated hemoglobin, alanine aminotransferase, asymmetric dimethylarginine, and increased high-density lipoprotein cholesterol. A multidisciplinary intervention independent of BP-lowering normalized BPV, lowered PWV, and enhanced metabolic control., (© 2015 Wiley Periodicals, Inc.)

The asymmetric simple exclusion process (ASEP) is an important model from statistical physics describing particles that hop randomly from one site to the next along an ordered lattice of sites, but only if the next site is empty. ASEP has been used to model and analyze numerous multiagent systems with local interactions including the flow of ribosomes along the mRNA strand. In ASEP with periodic boundary conditions a particle that hops from the last site returns to the first one. The mean field approximation of this model is referred to as the ribosome flow model on a ring (RFMR). The RFMR may be used to model both synthetic and endogenous gene expression regimes. We analyze the RFMR using the theory of monotone dynamical systems. We show that it admits a continuum of equilibrium points and that every trajectory converges to an equilibrium point. Furthermore, we show that it entrains to periodic transition rates between the sites. We describe the implications of the analysis results to understanding and engineering cyclic mRNA translation in-vitro and in-vivo.

Using the dynamic mean-field approximation of the totally asymmetric simple exclusion process (TASEP), we investigate the effect of small changes in the initiation, elongation, and termination rates along the mRNA strand on the steady-state protein translation rate. We show that the sensitivity of mRNA translation is equal to the sensitivity of the maximal eigenvalue of a symmetric, nonnegative, tridiagonal, and irreducible matrix. This leads to new analytical results as well as efficient numerical schemes that are applicable for large-scale models. Our results show that in the usual endogenous case, when initiation is more rate-limiting than elongation, the sensitivity of the translation rate to small mutations rapidly increases towards the 5' end of the ORF. When the initiation rate is high, as may be the case for highly expressed and/or heterologous optimized genes, the maximal sensitivity is with respect to the elongation rates at the middle of the mRNA strand. We also show that the maximal possible effect of a small increase/decrease in any of the rates along the mRNA is an increase/decrease of the same magnitude in the translation rate. These results are in agreement with previous molecular evolutionary and synthetic biology experimental studies.

Translation is an important stage in gene expression. During this stage, macro-molecules called ribosomes travel along the mRNA strand linking amino acids together in a specific order to create a functioning protein. An important question, related to many biomedical disciplines, is how to maximize protein production. Indeed, translation is known to be one of the most energy-consuming processes in the cell, and it is natural to assume that evolution shaped this process so that it maximizes the protein production rate. If this is indeed so then one can estimate various parameters of the translation machinery by solving an appropriate mathematical optimization problem. The same problem also arises in the context of synthetic biology, namely, re-engineer heterologous genes in order to maximize their translation rate in a host organism. We consider the problem of maximizing the protein production rate using a computational model for translation-elongation called the ribosome flow model (RFM). This model describes the flow of the ribosomes along an mRNA chain of length n using a set of n first-order nonlinear ordinary differential equations. It also includes n + 1 positive parameters: the ribosomal initiation rate into the mRNA chain, and n elongation rates along the chain sites. We show that the steady-state translation rate in the RFM is a strictly concave function of its parameters. This means that the problem of maximizing the translation rate under a suitable constraint always admits a unique solution, and that this solution can be determined using highly efficient algorithms for solving convex optimization problems even for large values of n. Furthermore, our analysis shows that the optimal translation rate can be computed based only on the optimal initiation rate and the elongation rate of the codons near the beginning of the ORF. We discuss some applications of the theoretical results to synthetic biology, molecular evolution, and functional genomics., (© 2014 The Author(s) Published by the Royal Society. All rights reserved.)

Gene translation is the process in which intracellular macro-molecules, called ribosomes, decode genetic information in the mRNA chain into the corresponding proteins. Gene translation includes several steps. During the elongation step, ribosomes move along the mRNA in a sequential manner and link amino-acids together in the corresponding order to produce the proteins. The homogeneous ribosome flow model (HRFM) is a deterministic computational model for translation-elongation under the assumption of constant elongation rates along the mRNA chain. The HRFM is described by a set of n first-order nonlinear ordinary differential equations, where n represents the number of sites along the mRNA chain. The HRFM also includes two positive parameters: ribosomal initiation rate and the (constant) elongation rate. In this paper, we show that the steady-state translation rate in the HRFM is a concave function of its parameters. This means that the problem of determining the parameter values that maximize the translation rate is relatively simple. Our results may contribute to a better understanding of the mechanisms and evolution of translation-elongation. We demonstrate this by using the theoretical results to estimate the initiation rate in M. musculus embryonic stem cell. The underlying assumption is that evolution optimized the translation mechanism. For the infinite-dimensional HRFM, we derive a closed-form solution to the problem of determining the initiation and transition rates that maximize the protein translation rate. We show that these expressions provide good approximations for the optimal values in the n-dimensional HRFM already for relatively small values of n. These results may have applications for synthetic biology where an important problem is to re-engineer genomic systems in order to maximize the protein production rate.

Periodic oscillations play an important role in many biomedical systems. Proper functioning of biological systems that respond to periodic signals requires the ability to synchronize with the periodic excitation. For example, the sleep/wake cycle is a manifestation of an internal timing system that synchronizes to the solar day. In the terminology of systems theory, the biological system must entrain or phase-lock to the periodic excitation. Entrainment is also important in synthetic biology. For example, connecting several artificial biological systems that entrain to a common clock may lead to a well-functioning modular system. The cell-cycle is a periodic program that regulates DNA synthesis and cell division. Recent biological studies suggest that cell-cycle related genes entrain to this periodic program at the gene translation level, leading to periodically-varying protein levels of these genes. The ribosome flow model (RFM) is a deterministic model obtained via a mean-field approximation of a stochastic model from statistical physics that has been used to model numerous processes including ribosome flow along the mRNA. Here we analyze the RFM under the assumption that the initiation and/or transition rates vary periodically with a common period T. We show that the ribosome distribution profile in the RFM entrains to this periodic excitation. In particular, the protein synthesis pattern converges to a unique periodic solution with period T. To the best of our knowledge, this is the first proof of entrainment in a mathematical model for translation that encapsulates aspects such as initiation and termination rates, ribosomal movement and interactions, and non-homogeneous elongation speeds along the mRNA. Our results support the conjecture that periodic oscillations in tRNA levels and other factors related to the translation process can induce periodic oscillations in protein levels, and may suggest a new approach for re-engineering genetic systems to obtain a desired, periodic, protein synthesis rate.

Gene translation is a central stage in the intracellular process of protein synthesis. Gene translation proceeds in three major stages: initiation, elongation, and termination. During the elongation step, ribosomes (intracellular macromolecules) link amino acids together in the order specified by messenger RNA (mRNA) molecules. The homogeneous ribosome flow model (HRFM) is a mathematical model of translation-elongation under the assumption of constant elongation rate along the mRNA sequence. The HRFM includes $(n)$ first-order nonlinear ordinary differential equations, where $(n)$ represents the length of the mRNA sequence, and two positive parameters: ribosomal initiation rate and the (constant) elongation rate. Here, we analyze the HRFM when $(n)$ goes to infinity and derive a simple expression for the steady-state protein synthesis rate. We also derive bounds that show that the behavior of the HRFM for finite, and relatively small, values of $(n)$ is already in good agreement with the closed-form result in the infinite-dimensional case. For example, for $(n=15)$, the relative error is already less than 4 percent. Our results can, thus, be used in practice for analyzing the behavior of finite-dimensional HRFMs that model translation. To demonstrate this, we apply our approach to estimate the mean initiation rate in M. musculus, finding it to be around 0.17 codons per second.

Eukaryotic mRNAs usually form a circular structure; thus, ribosomes that terminate translation at the 3' end can diffuse with increased probability to the 5' end of the transcript, initiating another cycle of translation. This phenomenon describes ribosomal flow with positive feedback--an increase in the flow of ribosomes terminating translating the open reading frame increases the ribosomal initiation rate. The aim of this paper is to model and rigorously analyse translation with feedback. We suggest a modified version of the ribosome flow model, called the ribosome flow model with input and output. In this model, the input is the initiation rate and the output is the translation rate. We analyse this model after closing the loop with a positive linear feedback. We show that the closed-loop system admits a unique globally asymptotically stable equilibrium point. From a biophysical point of view, this means that there exists a unique steady state of ribosome distributions along the mRNA, and thus a unique steady-state translation rate. The solution from any initial distribution will converge to this steady state. The steady-state distribution demonstrates a decrease in ribosome density along the coding sequence. For the case of constant elongation rates, we obtain expressions relating the model parameters to the equilibrium point. These results may perhaps be used to re-engineer the biological system in order to obtain a desired translation rate.

A central biological process in all living organisms is gene translation. Developing a deeper understanding of this complex process may have ramifications to almost every biomedical discipline. Reuveni et al. recently proposed a new computational model of gene translation called the Ribosome Flow Model (RFM). In this paper, we consider a particular case of this model, called the Homogeneous Ribosome Flow Model (HRFM). From a biological viewpoint, this corresponds to the case where the transition rates of all the coding sequence codons are identical. This regime has been suggested recently based on experiments in mouse embryonic cells. We consider the steady-state distribution of the HRFM. We provide formulas that relate the different parameters of the model in steady state. We prove the following properties: 1) the ribosomal density profile is monotonically decreasing along the coding sequence; 2) the ribosomal density at each codon monotonically increases with the initiation rate; and 3) for a constant initiation rate, the translation rate monotonically decreases with the length of the coding sequence. In addition, we analyze the translation rate of the HRFM at the limit of very high and very low initiation rate, and provide explicit formulas for the translation rate in these two cases. We discuss the relationship between these theoretical results and biological findings on the translation process.

Gene translation is a central process in all living organisms. Developing a better understanding of this complex process may have ramifications to almost every biomedical discipline. Recently, Reuveni et al. proposed a new computational model of this process called the ribosome flow model (RFM). In this study, we show that the dynamical behavior of the RFM is relatively simple. There exists a unique equilibrium point e and every trajectory converges to e. Furthermore, convergence is monotone in the sense that the distance to e can never increase. This qualitative behavior is maintained for any feasible set of parameter values, suggesting that the RFM is highly robust. Our analysis is based on a contraction principle and the theory of monotone dynamical systems. These analysis tools may prove useful in studying other properties of the RFM as well as additional intracellular biological processes.

Introduction: Mobile phones are in extensive use worldwide and concerns regarding their role in tumor formation were raised. Over the years multiple studies were published in order to investigate this issue using several approaches. The current study looks at secular trends of brain gliomas (low and high grade) incidence and changes in tumor's laterality over 30 years in a population extensively using this technology with a possible correlation to the spread of use of mobile phones., Materials and Methods: All brain gliomas that were diagnosed from 1980-2009 were included and subdivided into two groups--low and high grade. Secular and periodic time trend analyses of incidence rates and changes in laterality were performed. Preferred side of head using mobile phones was assessed with a questionnaire in a sample of adult individuals., Results: A decrease in incidence of low grade giomas (LGG) that correlated with introduction of mobile technology was found from 2.57, 2.34 and 2.79 for every 100,000 in the period 1980 to the end of 1994 to 1.72, 1.82 and 1.57, respectively, over the last three 5-years periods (1995-2009). High-grade glioma incidences increased significantly from 1980-2009 but in the period after mobile phones were introduced (1994-2009) a lower, non significant, rate of increase was observed in males and a lower one (significant) in females. A shift towards left sided tumor location for all adult gliomas combined and separately for LGG and HGG was noted from 1995 onward. The shift was more marked for those who were diagnosed in ages 20-49 (p=0.03)., Conclusions: We found a statistically significant decrease in LGG's over 30-years period that correlates with introducing of mobile phones technology and a shift in laterality towards left-sided tumors, the latter occurred in both low and high-grade gliomas.

Some studies found that cognitive functions of human beings may be altered while exposed to radiofrequency radiation (RFR) emitted by cellular phones. In two recent studies, we have found that experiment duration and exposure side (i.e., phone's location--right or left) may have a major influence on the detection of such effects. In this brief follow-up experiment, 29 right-handed male subjects were divided into two groups. Each subject had two standard cellular phones attached to both sides of his head. The subjects performed a spatial working memory task that required either a left-hand or a right-hand response under one of the two exposure conditions: left side of the head or right side. Contrary to our previous studies, in this work external antennas located far away from the subjects were connected to the cellular phones. This setup prevents any emission of RFR from the internal antenna, thus drastically reducing RFR exposure. Despite that, the results remain similar to those obtained in our previous work. These results indicate that some of the effects previously attributed to RFR can be the result of some confounders., (Copyright © 2011 Wiley-Liss, Inc.)

Gene regulation plays a central role in the development and functioning of living organisms. Gaining a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the Lambda switch.

This study examined the time dependence effects of exposure to radiofrequency radiation (RFR) emitted by standard GSM cellular phones on the cognitive functions of humans. A total of 48 healthy right-handed male subjects performed a spatial working memory task (that required either a left-hand or a right-hand response) while being exposed to one of two GSM phones placed at both sides of the head. The subjects were randomly divided into three groups. Each group was exposed to one of three exposure conditions: left-side of the head, right-side, or sham-exposure. The experiment consisted of 12 blocks of trials. Response times (RTs) and accuracy of the responses were recorded. It was found that the average RT of the right-hand responses under left-side exposure condition was significantly longer than those of the right-side and sham-exposure groups averaged together during the first two time blocks. These results confirmed the existence of an effect of exposure on RT, as well as the fact that exposure duration (together with the responding hand and the side of exposure) may play an important role in producing detectable RFR effects on performance. Differences in these parameters might be the reason for the failure of certain studies to detect or replicate RFR effects., ((c) 2008 Wiley-Liss, Inc.)

The present study examined the effects of exposure to Electromagnetic Radiation emitted by a standard GSM phone at 890 MHz on human cognitive functions. This study attempted to establish a connection between the exposure of a specific area of the brain and the cognitive functions associated with that area. A total of 36 healthy right-handed male subjects performed four distinct cognitive tasks: spatial item recognition, verbal item recognition, and two spatial compatibility tasks. Tasks were chosen according to the brain side they are assumed to activate. All subjects performed the tasks under three exposure conditions: right side, left side, and sham exposure. The phones were controlled by a base station simulator and operated at their full power. We have recorded the reaction times (RTs) and accuracy of the responses. The experiments consisted of two sections, of 1 h each, with a 5 min break in between. The tasks and the exposure regimes were counterbalanced. The results indicated that the exposure of the left side of the brain slows down the left-hand response time, in the second-later-part of the experiment. This effect was apparent in three of the four tasks, and was highly significant in only one of the tests. The exposure intensity and its duration exceeded the common exposure of cellular phone users.

A new method for non-invasive measurement of the human state of hydration is presented. This method is based on frequency-dependent absorptiometry of radio-waves passing through tissues. A device utilizing this method was constructed and applied to 12 young (24 +/- 1) male volunteers, who were dehydrated for 1-2.5% of their weight by performance of a physical effort (two 30 min bouts of treadmill walking/running at 2, 3, 4, 5, 6 and 7 mph, 5 min at each speed, separated by 10 min rest), under moderate heat stress (40 degrees C, 40% RH). Hypohydration level was determined by body weight measurements taken before each session, after 30 min and at the end of each session. Concomitantly, measurements of radio frequency (RF) absorption were taken. Each volunteer underwent the heat stress exercise twice: one in which no drinking was permitted, and another with free drinking. A correlation (R2 = 0.734) between weight loss and a change in the radio-waves absorption pattern was observed in most of the volunteers, in both hypo and euhydration sessions. Further work to establish the reproducibility and validity of the RF methodology in larger and different populations, i.e., females, other age groups and different health conditions, is already being researched.

Of a population of 400 patients treated with amiodarone, 97 underwent thyroid function evaluation. Of these, 20 patients proved to be thyrotoxic and 16 hypothyroid. In thyrotoxic patients, symptoms developed 2 to 36 months after starting treatment with amiodarone, the most specific laboratory finding being a high total T3 (TT3). No antithyroid treatment proved useful. Thyroid function returned to normal 3 to 7 months after stopping amiodarone therapy. In the hypothyroid group, a high thyroid-stimulating hormone was the most specific laboratory finding. These patients were treated with substitute therapy with or without withdrawal of amiodarone. The iodine content of the thyroid gland in part of this population taking amiodarone was measured by in vivo x-ray fluorescence. Patients in whom thyrotoxicosis developed showed especially high iodine contents. During treatment with amiodarone, patients at high risk of thyrotoxicosis were recognized by increasing TT3 values and higher iodine thyroid levels. A reduction in maintenance dose should be considered in this specific population.