Stochastic Simulations of the Repressilator Circuit

The genetic repressilator circuit consists of three transcription factors, or repressors, which negatively regulate each other in a cyclic manner. This circuit was synthetically constructed on plasmids in {\it Escherichia coli} and was found to exhibit oscillations in the concentrations of the three repressors. Since the repressors and their binding sites often appear in low copy numbers, the oscillations are noisy and irregular. Therefore, the repressilator circuit cannot be fully analyzed using deterministic methods such as rate-equations. Here we perform stochastic analysis of the repressilator circuit using the master equation and Monte Carlo simulations. It is found that fluctuations modify the range of conditions in which oscillations appear as well as their amplitude and period, compared to the deterministic equations. The deterministic and stochastic approaches coincide only in the limit in which all the relevant components, including free proteins, plasmids and bound proteins, appear in high copy numbers. We also find that subtle features such as cooperative binding and bound-repressor degradation strongly affect the existence and properties of the oscillations.Comment: Accepted to PR

A statistical method for revealing form-function relations in biological networks

Over the past decade, a number of researchers in systems biology have sought to relate the function of biological systems to their network-level descriptions -- lists of the most important players and the pairwise interactions between them. Both for large networks (in which statistical analysis is often framed in terms of the abundance of repeated small subgraphs) and for small networks which can be analyzed in greater detail (or even synthesized in vivo and subjected to experiment), revealing the relationship between the topology of small subgraphs and their biological function has been a central goal. We here seek to pose this revelation as a statistical task, illustrated using a particular setup which has been constructed experimentally and for which parameterized models of transcriptional regulation have been studied extensively. The question "how does function follow form" is here mathematized by identifying which topological attributes correlate with the diverse possible information-processing tasks which a transcriptional regulatory network can realize. The resulting method reveals one form-function relationship which had earlier been predicted based on analytic results, and reveals a second for which we can provide an analytic interpretation. Resulting source code is distributed via http://formfunction.sourceforge.net.Comment: To appear in Proc. Natl. Acad. Sci. USA. 17 pages, 9 figures, 2 table

Creation and Reproduction of Model Cells with Semipermeable Membrane

A high activity of reactions can be confined in a model cell with a semipermeable membrane in the Schl\"ogl model. It is interpreted as a model of primitive metabolism in a cell. We study two generalized models to understand the creation of primitive cell systems conceptually from the view point of the nonlinear-nonequilibrium physics. In the first model, a single-cell system with a highly active state confined by a semipermeable membrane is spontaneously created from an inactive homogeneous state by a stochastic jump process. In the second model, many cell structures are reproduced from a single cell, and a multicellular system is created.Comment: 11 pages, 7 figure

Sociobiological Control of Plasmid copy number

Background:
All known mechanisms and genes responsible for the regulation of plasmid replication lie with the plasmid rather than the chromosome. It is possible therefore that there can be copy-up mutants. Copy-up mutants will have within host selective advantage. This would eventually result into instability of bacteria-plasmid association. In spite of this possibility low copy number plasmids appear to exist stably in host populations. We examined this paradox using a computer simulation model.

Model:
Our multilevel selection model assumes a wild type with tightly regulated replication to ensure low copy number. A mutant with slightly relaxed replication regulation can act as a “cheater” or “selfish” plasmid and can enjoy a greater within-host-fitness. However the host of a cheater plasmid has to pay a greater cost. As a result, in host level competition, host cell with low copy number plasmid has a greater fitness. Furthermore, another mutant that has lost the genes required for conjugation was introduced in the model. The non-conjugal mutant was assumed to undergo conjugal transfer in the presence of another conjugal plasmid in the host cell.

Results:
The simulatons showed that if the cost of carrying a plasmid was low, the copy-up mutant could drive the wild type to extinction or very low frequencies. Consequently, another mutant with a higher copy number could invade the first invader. This process could result into an increasing copy number. However above a certain copy number within-host selection was overcompensated by host level selection leading to a rock-paper-scissor (RPS) like situation. The RPS situation allowed the coexistence of high and low copy number plasmids. The non-conjugal “hypercheaters” could further arrest the copy numbers to a substantially lower level.

Conclusions:
These sociobiological interactions might explain the stability of copy numbers better than molecular mechanisms of replication regulation alone

Quantification of very low-abundant proteins in bacteria using the HaloTag and epi-fluorescence microscopy.

Cell biology is increasingly dependent on quantitative methods resulting in the need for microscopic labelling technologies that are highly sensitive and specific. Whilst the use of fluorescent proteins has led to major advances, they also suffer from their relatively low brightness and photo-stability, making the detection of very low abundance proteins using fluorescent protein-based methods challenging. Here, we characterize the use of the self-labelling protein tag called HaloTag, in conjunction with an organic fluorescent dye, to label and accurately count endogenous proteins present in very low numbers (<7) in individual Escherichia coli cells. This procedure can be used to detect single molecules in fixed cells with conventional epifluorescence illumination and a standard microscope. We show that the detection efficiency of proteins labelled with the HaloTag is ≥80%, which is on par or better than previous techniques. Therefore, this method offers a simple and attractive alternative to current procedures to detect low abundance molecules

(Working title) Are We Meeting Oral Health Needs of Care Home Populations?

Aim: To evaluate care home (N) staff knowledge of oral care in comparison to NHS Quality Improvement Scotland (NHS QIS) guidelines. To identify barriers to delivering oral care and determine if Oral Health Educator (OHE) training had an effect upon staff knowledge of oral care delivery. Setting: The study was undertaken within Greater Glasgow, 2005 to 2007. Subjects and Methods: From 33 care homes (N), 28 participated in data gathering comprising 109 staff. A ‘knowledge check-list’ based upon daily oral care protocol from NHS QIS Best Practice Statement (BPS) served as template for knowledge assessment. An OHE undertook small group discussions related to the BPS in a sub-group of original participants and a second round of data collected. Results: The majority of staff (n=86, 79%) agreed that residents required assistance with oral care and placed oral care (n=85, 78%) as a moderate to high priority. Only 57% of managers and 49% of nurses had received training in oral care. Most staff (79% of managers, 85% of nurses) were unaware of the NHS QIS BPS. Deficiencies in knowledge of key areas within the BPS were identified. Between pre- and post-OHE training, significant differences were identified in prioritisation of oral care (p =0.009), perceived competence (p =0.005) and confidence giving advice (p =0.004). Following OHE intervention, knowledge of BPS protocol increased by 45%. Conclusion: Knowledge of oral care provision by carers for home residents requires substantial improvement. An OHE training programme structured around the NHS QIS BPS demonstrated a measurable increase in levels of staff knowledge of oral care

FeCoCp3 Molecular Magnets as Spin Filters

Metallorganic molecules have been proposed as excellent spin filters in molecular spintronics because of the large spin-polarization of their electronic structure. However, most of the studies involving spin transport, have disregarded fundamental aspects such as the magnetic anisotropy of the molecule and the excitation of spin-flip processes during electron transport. Here, we study a molecule containing a Co and an Fe atoms stacked between three cyclopentadienyl rings that presents a large magnetic anisotropy and a S=1. These figures are superior to other molecules with the same transition metal, and improves the spin-filtering capacities of the molecule. Non-equilibrium Green's functions calculations based on density functional theory predict excellent spin-filtering properties both in tunnel and contact transport regimes. However, exciting the first magnetic state drastically reduces the current's spin polarization. Furthermore, a difference of temperature between electrodes leads to strong thermoelectric effects that also suppress spin polarization. Our study shows that in-principle good molecular candidates for spintronics need to be confronted with inelastic and thermoelectric effects

Heat dissipation in atomic-scale junctions

Atomic and single-molecule junctions represent the ultimate limit to the miniaturization of electrical circuits. They are also ideal platforms to test quantum transport theories that are required to describe charge and energy transfer in novel functional nanodevices. Recent work has successfully probed electric and thermoelectric phenomena in atomic-scale junctions. However, heat dissipation and transport in atomic-scale devices remain poorly characterized due to experimental challenges. Here, using custom-fabricated scanning probes with integrated nanoscale thermocouples, we show that heat dissipation in the electrodes of molecular junctions, whose transmission characteristics are strongly dependent on energy, is asymmetric, i.e. unequal and dependent on both the bias polarity and the identity of majority charge carriers (electrons vs. holes). In contrast, atomic junctions whose transmission characteristics show weak energy dependence do not exhibit appreciable asymmetry. Our results unambiguously relate the electronic transmission characteristics of atomic-scale junctions to their heat dissipation properties establishing a framework for understanding heat dissipation in a range of mesoscopic systems where transport is elastic. We anticipate that the techniques established here will enable the study of Peltier effects at the atomic scale, a field that has been barely explored experimentally despite interesting theoretical predictions. Furthermore, the experimental advances described here are also expected to enable the study of heat transport in atomic and molecular junctions, which is an important and challenging scientific and technological goal that has remained elusive.Comment: supporting information available in the journal web site or upon reques

Master equation simulation analysis of immunostained Bicoid morphogen gradient

<p>Abstract</p> <p>Background</p> <p>The concentration gradient of Bicoid protein which determines the developmental pathways in early <it>Drosophila </it>embryo is the best characterized morphogen gradient at the molecular level. Because different developmental fates can be elicited by different concentrations of Bicoid, it is important to probe the limits of this specification by analyzing intrinsic fluctuations of the Bicoid gradient arising from small molecular number. Stochastic simulations can be applied to further the understanding of the dynamics of Bicoid morphogen gradient formation at the molecular number level, and determine the source of the nucleus-to-nucleus expression variation (noise) observed in the Bicoid gradient.</p> <p>Results</p> <p>We compared quantitative observations of Bicoid levels in immunostained <it>Drosophila </it>embryos with a spatially extended Master Equation model which represents diffusion, decay, and anterior synthesis. We show that the intrinsic noise of an autonomous reaction-diffusion gradient is Poisson distributed. We demonstrate how experimental noise can be identified in the logarithm domain from single embryo analysis, and then separated from intrinsic noise in the normalized variance domain of an ensemble statistical analysis. We show how measurement sensitivity affects our observations, and how small amounts of rescaling noise can perturb the noise strength (Fano factor) observed. We demonstrate that the biological noise level in data can serve as a physical constraint for restricting the model's parameter space, and for predicting the Bicoid molecular number and variation range. An estimate based on a low variance ensemble of embryos suggests that the steady-state Bicoid molecular number in a nucleus should be larger than 300 in the middle of the embryo, and hence the gradient should extend to the posterior end of the embryo, beyond the previously assumed background limit. We exhibit the predicted molecular number gradient together with measurement effects, and make a comparison between conditions of higher and lower variance respectively.</p> <p>Conclusion</p> <p>Quantitative comparison of Master Equation simulations with immunostained data enabled us to determine narrow ranges for key biophysical parameters, which for this system can be independently validated. Intrinsic noise is clearly detectable as well, although the staining process introduces certain limits in resolution.</p