The Berg-Purcell Limit Revisited

Biological systems often have to measure extremely low concentrations of chemicals with high precision. When dealing with such small numbers of molecules, the inevitable randomness of physical transport processes and binding reactions will limit the precision with which measurements can be made. An important question is what the lower bound on the noise would be in such measurements. Using the theory of diffusion-influenced reactions, we derive an analytical expression for the precision of concentration estimates that are obtained by monitoring the state of a receptor to which a diffusing ligand can bind. The variance in the estimate consists of two terms, one resulting from the intrinsic binding kinetics and the other from the diffusive arrival of ligand at the receptor. The latter term is identical to the fundamental limit derived by Berg and Purcell (Biophys. J., 1977), but disagrees with a more recent expression by Bialek and Setayeshgar. Comparing the theoretical predictions against results from particle-based simulations confirms the accuracy of the resulting expression and reaffirms the fundamental limit established by Berg and Purcell.     

Revising Berg-Purcell for finite receptor kinetics

From nutrient uptake to chemoreception to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors. Mathematical analysis of such systems often neglects the fact that receptors process molecules at finite kinetic rates. A key example is the celebrated formula of Berg and Purcell for the rate that cell surface receptors capture extracellular molecules. Indeed, this influential result is only valid if receptors transport molecules through the cell wall at a rate much faster than molecules arrive at receptors. From a mathematical perspective, ignoring receptor kinetics is convenient because it makes the diffusing molecules independent. In contrast, including receptor kinetics introduces correlations between the diffusing molecules because, for example, bound receptors may be temporarily blocked from binding additional molecules. In this work, we present a modeling framework for coupling bulk diffusion to surface receptors with finite kinetic rates. The framework uses boundary homogenization to couple the diffusion equation to nonlinear ordinary differential equations on the boundary. We use this framework to derive an explicit formula for the cellular uptake rate and show that the analysis of Berg and Purcell significantly overestimates uptake in some typical biophysical scenarios. We confirm our analysis by numerical simulations of a many-particle stochastic system.     

The ``hitchhiking Effect'''' Revisited

The number of selectively neutral polymorphic sites in a random sample of genes can be affected by ancestral selectively favored substitutions at linked loci. The degree to which this happens depends on when in the history of the sample the selected substitutions happen, the strength of selection and the amount of crossing over between the sampled locus and the loci at which the selected substitutions occur. This phenomenon is commonly called hitchhiking. Using the coalescent process for a random sample of genes from a selectively neutral locus that is linked to a locus at which selection is taking place, a stochastic, finite population model is developed that describes the steady state effect of hitchhiking on the distribution of the number of selectively neutral polymorphic sites in a random sample. A prediction of the model is that, in regions of low crossing over, strongly selected substitutions in the history of the sample can substantially reduce the number of polymorphic sites in a random sample of genes from that expected under a neutral model.     

The Northwest Passage Revisited

The Chinese annual fishing ban in the northwestern area of the South China Sea has been a cause for tension between Vietnam and China in recent years. This article advocates for the replacement of this unilateral fishing ban with a bilateral network of marine protected areas between China and Vietnam. Such a network, if properly implemented, could not only help to preserve the living resources of the South China Sea, but also contribute toward decreasing the tension between the two countries.     

The Pinwheel Experiment Revisited

The critical point hypothesis explains the origin of some cardiac arrhythmias, and the bidomain model describes electrical stimulation of the heart. In this paper, the critical point hypothesis is combined with the bidomain model. The result is four new predictions about the pinwheel experiment, a fundamental experiment in cardiac electrophysiology. These are: (1) The duration of the vulnerable period during cathodalS₂stimulation is longer for anS₁wavefront propagating perpendicular to the fibers than for anS₁wavefront propagating parallel to the fibers. (2) For anodalS₂stimulation with theS₁wavefront propagating parallel to the fibers, the vulnerable period splits into two periods with an “invulnerable period” between them. (3) For anodalS₂stimulation with theS₁wavefront propagating perpendicular to the fibers, the vulnerable period consists of only one period. (4) A previously suggested mechanism for the upper limit of vulnerability (S₂is so strong that the entire tissue is depolarized by an amount greater thanS*) is no longer applicable.     

The Darwinian Revolution Revisited

The Darwinian revolution remains an acceptable phrase to describe the change in thought brought about by the theory of evolution, provided that the revolution is seen as occurring over an extended period of time. The decades from the 1790s through the 1850s are at the focus of this article. Emphasis is placed on the issue of species extinction and on generational shifts in opinion.     

The Common Ancestor Process Revisited

We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Probab. 39 (2002), 38–54) and Taylor (Electron. J. Probab. 12 (2007), 808–847), we characterise this distribution via the fixation probability of the offspring of all individuals of favourable type (regardless of the offspring’s types). We concentrate on a finite population and stay with the resulting discrete setting all the way through. This way, we extend previous results and gain new insight into the underlying particle picture.     

The Gigantocellular Depressor Area Revisited

1. In studies conducted with Dr Donald Reis we described a functionally distinct region of the rat medullary reticular formation that we called the Gigantocellular Depressor Area (GiDA). The GiDA was defined as a region from which vasodepressor and sympathoinhibitory responses were evoked by nanoinjections of glutamate. We later showed that cells in the GiDA project to autonomic nuclei in the medulla, brainstem, and spinal cord, including the intermediolateral cell column. We also showed that kainic acid lesions of the GiDA induce hypertension and block the baroreceptor reflex evoked by electrical stimulation of the aortic depressor nerve. The present studies describe the effects of muscimol nanoinjections into the GiDA.2. Nanoinjections of muscimol were made in the GiDA of anesthetized rats and changes in arterial pressure, heart rate, and responses to aortic depressor nerve stimulation were measured.3. Bilateral nanoinjections of muscimol into the GiDA evoke an increase in arterial pressure and lead to fulminating hypertension. Unilateral injections of muscimol into the GiDA block the baroreflex response evoked by electrical stimulation of the ipsilateral aortic depressor nerve. However, these unilateral injections of muscimol into the GiDA evoked profound falls in arterial pressure to nearly spinal levels. In spite of this fall in blood pressure, heart rate also decreased significantly and there was not a compensatory tachycardia. Both the arterial pressure and baroreceptor responses required several hours to recover following the muscimol injections.4. Although these data are consistent with the proposal that the GiDA is critical for the baroreflex, the opposing effects on blood pressure of unilateral and bilateral injections of muscimol are difficult to reconcile with our current models of central sympathetic regulation.     

The Elementary Nervous System Revisited

Parker's theory of the origin of the nervous system is discussedalong with later interpretations. Attention today has shiftedfrom the cellular to the molecular level, and it has becomeclear that many of the molecules and mechanisms thought of astypically neuronal have homologs or counterparts in non-nervouscells and unicellular organisms. This applies to signallingchemicals, receptors, second messenger systems and ion channels,and also to the production of electrical events. Parker's viewof sponges as a group lacking nerves but possessing independenteffectors is still acceptable, but some sponges (and also higheranimals) employ non-nervous signalling pathways to coordinatetheir effectors. Thus, nerves are not always necessary for coordinatedbehavior. Cnidarians like hydra have seemingly simple, two-dimensionalnervous systems with little or no centralization, but even suchsystems can be surprisingly complex, and the more advanced cnidariansshow neurophysiological specializations as sophisticated asthose of many higher invertebrates. Examples of ingenious cnidariansolutions to behavioral problems are given. No existing animalshave ‘elementary’ nervous systems if that term impliesthe existence of crude or inefficient functional adaptations     

The Central Plains Tradition Revisited

Abstract

Recent interpretations of the Central Plains Tradition are critically evaluated. In the process special attention is given to:( 1) alternative interpretations of the extant data base, (2) the cogency of taxonomic proposals, and (3) the construal of radiocarbon determinations. Blakeslee’s ”trade network thesis” is examined and an origin in the exigencies of population growth and spread is suggested.     

The NBS1-ATM Connection Revisited

Nijmegen Breakage syndrome (NBS) is a rare autosomal recessive disorder characterized by microcephaly, immunodeficiency, and increased predisposition to the development of malignancy.^1,2 Due to the overlap of clinical and cellular features of patients with ataxia telangiectasia (AT), NBS was described as an AT variant syndrome until the underlying gene product mutation was identified.^3-5 Cells from both AT and NBS patients show increased sensitivity to ionizing radiation (IR), genomic instability and cell cycle checkpoint defects following DNA damage,^6,7 suggesting that both gene products participate in the same DNA damage response pathway. Here we highlight recent developments and refinements in our understanding of the interplay between NBS1 and ATM in vivo.     

The boylston street fishweir: Revisited

Excavations for the Boston subway system early in this century and later for building sites revealed the presence of waterlogged wood in the peat and silt deep beneath the present surface. Beginning more than 50 yr ago, the investigation of geological and biological materials recovered from these sites, especially the wood remains, believed to have been set in place by prehistoric Native Americans, became a benchmark for the multidisciplinary application of scientific methods in archaeology and environmental reconstruction. Recent excavations for building foundations in Boston have exposed additional wooden materials. We have analyzed 216 specimens recently recovered from an excavation at 500 Boylston Street where older office buildings were demolished to make way for a new commercial structure. Although some of our findings differ from those of the previous investigators we find support for the earlier supposition that the remains represent an ancient Native American fishweir, a fencelike barrier and trap for fish on an ancient shoreline.     

The Willey And Phillips System Revisited:

Abstract

The purpose of this paper is to evaluate the logical structure of the Willey and Phillips system of culture historic-integration and propose the expansion of that logical structure to its inherent limits. The dimensions and features of this expanded paradigm are discussed and the resulting classes defined. Previous evaluations of the Willey and Phillips system by Plains archeologists are reviewed in light of the original and expanded paradigm.