Instabilities in complex mixtures with a large number of components

Inside living cells are complex mixtures of thousands of components. It is hopeless to try to characterise all the individual interactions in these mixtures. Thus, we develop a statistical approach to approximating them, and examine the conditions under which the mixtures phase separate. The approach approximates the matrix of second virial coefficients of the mixture by a random matrix, and determines the stability of the mixture from the spectrum of such random matrices.Comment: 4 pages, uses RevTeX 4.

A Markov Chain based method for generating long-range dependence

This paper describes a model for generating time series which exhibit the statistical phenomenon known as long-range dependence (LRD). A Markov Modulated Process based upon an infinite Markov chain is described. The work described is motivated by applications in telecommunications where LRD is a known property of time-series measured on the internet. The process can generate a time series exhibiting LRD with known parameters and is particularly suitable for modelling internet traffic since the time series is in terms of ones and zeros which can be interpreted as data packets and inter-packet gaps. The method is extremely simple computationally and analytically and could prove more tractable than other methods described in the literatureComment: 8 pages, 2 figure

Vacuum orbit and spontaneous symmetry breaking in hyperbolic sigma models

We present a detailed study of quantized noncompact, nonlinear SO(1,N) sigma-models in arbitrary space-time dimensions D \geq 2, with the focus on issues of spontaneous symmetry breaking of boost and rotation elements of the symmetry group. The models are defined on a lattice both in terms of a transfer matrix and by an appropriately gauge-fixed Euclidean functional integral. The main results in all dimensions \geq 2 are: (i) On a finite lattice the systems have infinitely many nonnormalizable ground states transforming irreducibly under a nontrivial representation of SO(1,N); (ii) the SO(1,N) symmetry is spontaneously broken. For D =2 this shows that the systems evade the Mermin-Wagner theorem. In this case in addition: (iii) Ward identities for the Noether currents are derived to verify numerically the absence of explicit symmetry breaking; (iv) numerical results are presented for the two-point functions of the spin field and the Noether current as well as a new order parameter; (v) in a large N saddle-point analysis the dynamically generated squared mass is found to be negative and of order 1/(V \ln V) in the volume, the 0-component of the spin field diverges as \sqrt{\ln V}, while SO(1,N) invariant quantities remain finite.Comment: 60 pages, 12 Figures, AMS-Latex; v2: results on vacuum orbit and spontaneous symmetry breaking extended to all dimension

Taylor approximations of operator functions

This survey on approximations of perturbed operator functions addresses recent advances and some of the successful methods.Comment: 12 page

Strong negative self regulation of Prokaryotic transcription factors increases the intrinsic noise of protein expression

Background Many prokaryotic transcription factors repress their own transcription. It is often asserted that such regulation enables a cell to homeostatically maintain protein abundance. We explore the role of negative self regulation of transcription in regulating the variability of protein abundance using a variety of stochastic modeling techniques. Results We undertake a novel analysis of a classic model for negative self regulation. We demonstrate that, with standard approximations, protein variance relative to its mean should be independent of repressor strength in a physiological range. Consequently, in that range, the coefficient of variation would increase with repressor strength. However, stochastic computer simulations demonstrate that there is a greater increase in noise associated with strong repressors than predicted by theory. The discrepancies between the mathematical analysis and computer simulations arise because with strong repressors the approximation that leads to Michaelis-Menten-like hyperbolic repression terms ceases to be valid. Because we observe that strong negative feedback increases variability and so is unlikely to be a mechanism for noise control, we suggest instead that negative feedback is evolutionarily favoured because it allows the cell to minimize mRNA usage. To test this, we used in silico evolution to demonstrate that while negative feedback can achieve only a modest improvement in protein noise reduction compared with the unregulated system, it can achieve good improvement in protein response times and very substantial improvement in reducing mRNA levels. Conclusions Strong negative self regulation of transcription may not always be a mechanism for homeostatic control of protein abundance, but instead might be evolutionarily favoured as a mechanism to limit the use of mRNA. The use of hyperbolic terms derived from quasi-steady-state approximation should also be avoided in the analysis of stochastic models with strong repressors

Membranes by the Numbers

Many of the most important processes in cells take place on and across membranes. With the rise of an impressive array of powerful quantitative methods for characterizing these membranes, it is an opportune time to reflect on the structure and function of membranes from the point of view of biological numeracy. To that end, in this article, I review the quantitative parameters that characterize the mechanical, electrical and transport properties of membranes and carry out a number of corresponding order of magnitude estimates that help us understand the values of those parameters.Comment: 27 pages, 12 figure

A manganese photosensitive tricarbonyl molecule [Mn(CO)3(tpa-κ(3)N)]Br enhances antibiotic efficacy in a multi-drug-resistant Escherichia coli

Carbon monoxide-releasing molecules (CORMs) are a promising class of new antimicrobials, with multiple modes of action that are distinct from those of standard antibiotics. The relentless increase in antimicrobial resistance, exacerbated by a lack of new antibiotics, necessitates a better understanding of how such novel agents act and might be used synergistically with established antibiotics. This work aimed to understand the mechanism(s) underlying synergy between a manganese-based photoactivated carbon monoxide-releasing molecule (PhotoCORM), [Mn(CO)3(tpa-κ(3)N)]Br [tpa=tris(2-pyridylmethyl)amine], and various classes of antibiotics in their activities towards Escherichia coli EC958, a multi-drug-resistant uropathogen. The title compound acts synergistically with polymyxins [polymyxin B and colistin (polymyxin E)] by damaging the bacterial cytoplasmic membrane. [Mn(CO)3(tpa-κ(3)N)]Br also potentiates the action of doxycycline, resulting in reduced expression of tetA, which encodes a tetracycline efflux pump. We show that, like tetracyclines, the breakdown products of [Mn(CO)3(tpa-κ(3)N)]Br activation chelate iron and trigger an iron starvation response, which we propose to be a further basis for the synergies observed. Conversely, media supplemented with excess iron abrogated the inhibition of growth by doxycycline and the title compound. In conclusion, multiple factors contribute to the ability of this PhotoCORM to increase the efficacy of antibiotics in the polymyxin and tetracycline families. We propose that light-activated carbon monoxide release is not the sole basis of the antimicrobial activities of [Mn(CO)3(tpa-κ(3)N)]Br

Ionization Probabilities through ultra-intense Fields in the extreme Limit

We continue our investigation concerning the question of whether atomic bound states begin to stabilize in the ultra-intense field limit. The pulses considered are essentially arbitrary, but we distinguish between three situations. First the total classical momentum transfer is non-vanishing, second not both the total classical momentum transfer and the total classical displacement are vanishing together with the requirement that the potential has a finite number of bound states and third both the total classical momentum transfer and the total classical displacement are vanishing. For the first two cases we rigorously prove, that the ionization probability tends to one when the amplitude of the pulse tends to infinity and the pulse shape remains fixed. In the third case the limit is strictly smaller than one. This case is also related to the high frequency limit considered by Gavrila et al.Comment: 16 pages LateX, 2 figure

Improving the batch-to-batch reproducibility in microbial cultures during recombinant protein production by guiding the process along a predefined total biomass profile

In industry Escherichia coli is the preferred host system for the heterologous biosynthesis of therapeutic proteins that do not need posttranslational modifications. In this report, the development of a robust high-cell-density fed-batch procedure for the efficient production of a therapeutic hormone is described. The strategy is to guide the process along a predefined profile of the total biomass that was derived from a given specific growth rate profile. This profile might have been built upon experience or derived from numerical process optimization. A surprisingly simple adaptive procedure correcting for deviations from the desired path was developed. In this way the batch-to-batch reproducibility can be drastically improved as compared to the process control strategies typically applied in industry. This applies not only to the biomass but, as the results clearly show, to the product titer also

A systems approach to model natural variation in reactive properties of bacterial ribosomes

<p>Abstract</p> <p>Background</p> <p>Natural variation in protein output from translation in bacteria and archaea may be an organism-specific property of the ribosome. This paper adopts a systems approach to model the protein output as a measure of specific ribosome reactive properties in a ribosome-mediated translation apparatus. We use the steady-state assumption to define a transition state complex for the ribosome, coupled with mRNA, tRNA, amino acids and reaction factors, as a subsystem that allows a focus on the completed translational output as a measure of specific properties of the ribosome.</p> <p>Results</p> <p>In analogy to the steady-state reaction of an enzyme complex, we propose a steady-state translation complex for mRNA from any gene, and derive a maximum specific translation activity, <it>T</it>_{<it>a</it>(max)}, as a property of the ribosomal reaction complex. <it>T</it>_{<it>a</it>(max)}has units of <it>a</it>-protein output per time per <it>a</it>-specific mRNA. A related property of the ribosome, <inline-formula><m:math name="1752-0509-2-62-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:semantics><m:mrow><m:msub><m:mover accent="true"><m:mi>T</m:mi><m:mo>˜</m:mo></m:mover><m:mrow><m:mi>a</m:mi><m:mo stretchy="false">(</m:mo><m:mi>max</m:mi><m:mo>⁡</m:mo><m:mo stretchy="false">)</m:mo></m:mrow></m:msub></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafmivaqLbaGaadaWgaaWcbaGaemyyaeMaeiikaGIagiyBa0MaeiyyaeMaeiiEaGNaeiykaKcabeaaaaa@3464@</m:annotation></m:semantics></m:math></inline-formula>, has units of <it>a</it>-protein per time per total RNA with the relationship <inline-formula><m:math name="1752-0509-2-62-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:semantics><m:mrow><m:msub><m:mover accent="true"><m:mi>T</m:mi><m:mo>˜</m:mo></m:mover><m:mrow><m:mi>a</m:mi><m:mo stretchy="false">(</m:mo><m:mi>max</m:mi><m:mo>⁡</m:mo><m:mo stretchy="false">)</m:mo></m:mrow></m:msub></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafmivaqLbaGaadaWgaaWcbaGaemyyaeMaeiikaGIagiyBa0MaeiyyaeMaeiiEaGNaeiykaKcabeaaaaa@3464@</m:annotation></m:semantics></m:math></inline-formula> = <it>ρ</it>_{<it>a </it>}<it>T</it>_{<it>a</it>(max)}, where <it>ρ</it>_{<it>a </it>}represents the fraction of total RNA committed to translation output of <it>P</it>_{<it>a </it>}from gene <it>a </it>message. <it>T</it>_{<it>a</it>(max)}as a ribosome property is analogous to <it>k</it>_catfor a purified enzyme, and <inline-formula><m:math name="1752-0509-2-62-i1" xmlns:m="http://www.w3.org/1998/Math/MathML"><m:semantics><m:mrow><m:msub><m:mover accent="true"><m:mi>T</m:mi><m:mo>˜</m:mo></m:mover><m:mrow><m:mi>a</m:mi><m:mo stretchy="false">(</m:mo><m:mi>max</m:mi><m:mo>⁡</m:mo><m:mo stretchy="false">)</m:mo></m:mrow></m:msub></m:mrow><m:annotation encoding="MathType-MTEF"> MathType@MTEF@5@5@+=feaagaart1ev2aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGaciGaaiaabeqaaeqabiWaaaGcbaGafmivaqLbaGaadaWgaaWcbaGaemyyaeMaeiikaGIagiyBa0MaeiyyaeMaeiiEaGNaeiykaKcabeaaaaa@3464@</m:annotation></m:semantics></m:math></inline-formula> is analogous to enzyme specific activity in a crude extract.</p> <p>Conclusion</p> <p>Analogy to an enzyme reaction complex led us to a ribosome reaction model for measuring specific translation activity of a bacterial ribosome. We propose to use this model to design experimental tests of our hypothesis that specific translation activity is a ribosomal property that is subject to natural variation and natural selection much like <it>V</it>_maxand <it>K</it>_mfor any specific enzyme.</p