arXiv subjects

Patrick B. Warren

Publications and source records attributed to Patrick B. Warren.

49 records · Page 3Linked to original sources

arXiv2007

Flory-Huggins theory for the solubility of heterogeneously-modified polymers

Many water soluble polymers are chemically modified versions of insoluble base materials such as cellulose. A Flory-Huggins model is solved to determine the effects of heterogeneity in modification on the solubility of such polymers. It is found that heterogeneity leads to decreased solubility, with the effect increasing with increasing blockiness. In the limit of extreme blockiness, the nature of the phase coexistence crosses over to a polymer-polymer demixing transition. Some consequences are discussed for the synthesis of partially modified polymers, and the experimental characterisation of such systems.

cond-mat.soft↗

arXiv2006

Signal detection, modularity and the correlation between extrinsic and intrinsic noise in biochemical networks

Understanding cell function requires an accurate description of how noise is transmitted through biochemical networks. We present an analytical result for the power spectrum of the output signal of a biochemical network that takes into account the correlations between the noise in the input signal (the extrinsic noise) and the noise in the reactions that constitute the network (the intrinsic noise). These correlations arise from the fact that the reactions by which biochemical signals are detected necessarily affect the signaling molecules and the detection components of the network simultaneously. We show that anti-correlation between the extrinsic and intrinsic noise enhances the robustness of zero-order ultrasensitive networks to biochemical noise. We discuss the consequences of the correlation between extrinsic and intrinsic noise for a modular description of noise transmission through large biochemical networks in the context of the mitogen-activated protein kinase cascade.

q-bio.MN↗

arXiv2005

Exact results for noise power spectra in linear biochemical reaction networks

We present a simple method for determining the exact noise power spectra in linear chemical reaction networks. We apply the method to networks which are representative of biochemical processes such as gene expression and signal detection. Our results clarify how noise is transmitted by signal detection motifs, and indicate how to coarse-grain networks by the elimination of fast reactions.

q-bio.SC↗

arXiv2005

Density functional theory for a macroion suspension

A density functional theory for a macroion suspension is examined, where the excess free energy corresponds to the macroion self energy arising from the polarisation of the supporting electrolyte solution. This is treated within a linearised or Debye-Huckel approximation. The model predicts liquid-liquid phase separation at low ionic strength. The interface structure and surface tension between coexisting phases is calculated using a variational approximation. Results are also obtained for structure factors, which are shown to obey the Stillinger-Lovett moment conditions. As one approaches the critical points, the structure factors may diverge at a non-zero wavevector, indicating that the critical points could be replaced by charge-density-wave phases.

cond-mat.soft↗

arXiv2004

Chemical models of genetic toggle switches

We study by mean-field analysis and stochastic simulations chemical models for genetic toggle switches formed from pairs of genes that mutually repress each other. In order to determine the stability of the genetic switches, we make a connection with reactive flux theory and transition state theory. The switch stability is characterised by a well defined lifetime $τ$. We find that $τ$ grows exponentially with the mean number $\Nmean$ of transcription factor molecules involved in the switching. In the regime accessible to direct numerical simulations, the growth law is well characterised by $τ\sim\Nmean{}^α\exp(b\Nmean)$, where $α$ and $b$ are parameters. The switch stability is decreased by phenomena that increase the noise in gene expression, such as the production of multiple copies of a protein from a single mRNA transcript (shot noise), and fluctuations in the number of proteins produced per transcript. However, robustness against biochemical noise can be drastically enhanced by arranging the transcription factor binding domains on the DNA such that competing transcription factors mutually exclude each other on the DNA. We also elucidate the origin of the enhanced stability of the exclusive switch with respect to that of the general switch: while the kinetic prefactor is roughly the same for both switches, the `barrier' for flipping the switch is significantly higher for the exclusive switch than for the general switch.

q-bio.MN↗

arXiv2004

Sampling rare switching events in biochemical networks

Bistable biochemical switches are ubiquitous in gene regulatory networks and signal transduction pathways. Their switching dynamics, however, are difficult to study directly in experiments or conventional computer simulations, because switching events are rapid, yet infrequent. We present a simulation technique that makes it possible to predict the rate and mechanism of flipping of biochemical switches. The method uses a series of interfaces in phase space between the two stable steady states of the switch to generate transition trajectories in a ratchet-like manner. We demonstrate its use by calculating the spontaneous flipping rate of a symmetric model of a genetic switch consisting of two mutually repressing genes. The rate constant can be obtained orders of magnitude more efficiently than using brute-force simulations. For this model switch, we show that the switching mechanism, and consequently the switching rate, depends crucially on whether the binding of one regulatory protein to the DNA excludes the binding of the other one. Our technique could also be used to study rare events and non-equilibrium processes in soft condensed matter systems.

q-bio.MN↗

arXiv2003

Late stage kinetics for various wicking and spreading problems

The kinetics of spreading of a liquid drop in a wedge or V-shaped groove, in a network of such grooves, and on a hydrophilic strip, is re-examined. The length of a droplet of volume Omega spreading in a wedge after a time t is predicted to scale as Omega^(1/5) * t^(2/5), and the height profile is predicted to be a parabola in the distance along the wedge. If the droplet is spreading radially in a sparse network of V-shaped grooves on a surface, the radius is predicted to scale as Omega^(1/6) * t^(1/3), provided the liquid is completely contained within the grooves. A number of other results are also obtained.

cond-mat.stat-mech↗

arXiv2003

Enhancement of the stability of genetic switches by overlapping upstream regulatory domains

We study genetic switches formed from pairs of mutually repressing operons. The switch stability is characterised by a well defined lifetime which grows sub-exponentially with the number of copies of the most-expressed transcription factor, in the regime accessible by our numerical simulations. The stability can be markedly enhanced by a suitable choice of overlap between the upstream regulatory domains. Our results suggest that robustness against biochemical noise can provide a selection pressure that drives operons, that regulate each other, together in the course of evolution.

q-bio.MN↗

arXiv2002

Simple models for charge and salt effects in protein crystallisation

A simple extension of existing models for protein crystallisation is described, in which salt ions and charge neutrality are explicitly incorporated. This provides a straightforward explanation for the shape of protein crystallisation boundaries, the associated scaling properties seen for lysozyme, and can also explain much of the salt dependence of the second virial coefficient. The analysis has wider implications for the use of pair potentials to understand protein crystallisation.

cond-mat.soft↗

arXiv2001

Hydrodynamic bubble coarsening in off-critical vapour-liquid phase separation

Late-stage coarsening in off-critical vapour-liquid phase separation is re-examined. In the limit of bubbles of vapour distributed throughout a continuous liquid phase, it is argued that coarsening proceeds via inertial hydrodynamic bubble collapse. This replaces the Lifshitz-Slyozov-Wagner mechanism seen in binary liquid mixtures. The arguments are strongly supported by simulations in two dimensions using a novel single-component soft sphere fluid.

cond-mat.stat-mech↗

arXiv2000

Charged colloids at low ionic strength: macro- or microphase separation?

Phase separation in charged systems may involve the replacement of critical points by microphase separated states, or charge-density-wave states. A density functional theory for highly charged colloids at low ionic strength is developed to examine this possibility. It is found that the lower critical solution point is most susceptible to microphase separation. Moreover the tendency can be quantified, and related to the importance of small ion entropy in suppressing phase separation at low added salt. The theory also gives insights into the colloid structure factor in these systems.

cond-mat.soft↗

arXiv1999

A theory of void formation in charge-stabilised colloidal suspensions at low ionic strength

Using a carefully justified development of Debye-Huckel theory for highly asymmetric electrolytes, one finds that a region of expanded phase instability, or miscibility gap, can appear for charge-stabilised colloidal suspensions at high charges and low ionic strengths. It is argued that this is offers a straightforward explanation for the observations of void structures and other anomalies in such suspensions in this region. The nature of the interface between coexisting phases, and general arguments that many-body attractions form a key part of the underlying physical picture, are also examined. The present analysis may also generate new insights into old problems such as coacervation in oppositely charged colloid or protein / polyelectrolyte mixtures, and suggests interesting new possibilities such as the appearance of charge density wave phases in colloidal systems in the vicinity of the critical solution points.

cond-mat.stat-mech↗

arXiv1999

Re-entrant Melting in Polydisperse Hard Spheres

The effect of polydispersity on the freezing transition of hard spheres is examined within a moment description. At low polydispersities a single fluid-to-crystal transition is recovered. With increasing polydispersity we find a density above which the crystal melts back into an amorphous phase. The range of densities over which the crystalline phase is stable shrinks with increasing polydispersity until, at a certain level of polydispersity, the crystal disappears completely from the equilibrium phase diagram. The two transitions converge to a single point which we identify as the polydisperse analogue of a point of equal concentration. At this point, the freezing transition is continuous in a thermodynamic sense.

cond-mat.soft↗