Semiconservative Replication in the Quasispecies Model

This paper extends Eigen's quasispecies equations to account for the semiconservative nature of DNA replication. We solve the equations in the limit of infinite sequence length for the simplest case of a static, sharply peaked fitness landscape. We show that the error catastrophe occurs when $\mu$, the product of sequence length and per base pair mismatch probability, exceeds $2 \ln \frac{2}{1 + 1/k}$, where $k > 1$ is the first order growth rate constant of the viable ``master'' sequence (with all other sequences having a first-order growth rate constant of $1$). This is in contrast to the result of $\ln k$ for conservative replication. In particular, as $k \to \infty$, the error catastrophe is never reached for conservative replication, while for semiconservative replication the critical $\mu$ approaches $2 \ln 2$. Semiconservative replication is therefore considerably less robust than conservative replication to the effect of replication errors. We also show that the mean equilibrium fitness of a semiconservatively replicating system is given by $k (2 e^{-\mu/2} - 1)$ below the error catastrophe, in contrast to the standard result of $k e^{-\mu}$ for conservative replication (derived by Kimura and Maruyama in 1966).Comment: 15 pages, 7 figures, to be submitted to Phys. Rev.

The Emergence of Scaling in Sequence-based Physical Models of Protein Evolution

It has recently been discovered that many biological systems, when represented as graphs, exhibit a scale-free topology. One such system is the set of structural relationships among protein domains. The scale-free nature of this and other systems has previously been explained using network growth models that, while motivated by biological processes, do not explicitly consider the underlying physics or biology. In the present work we explore a sequence-based model for the evolution protein structures and demonstrate that this model is able to recapitulate the scale-free nature observed in graphs of real protein structures. We find that this model also reproduces other statistical feature of the protein domain graph. This represents, to our knowledge, the first such microscopic, physics-based evolutionary model for a scale-free network of biological importance and as such has strong implications for our understanding of the evolution of protein structures and of other biological networks.Comment: 20 pages (including figures), 4 figures, to be submitted to PNA

Enhanced Condition Assessment for Maine Lakes

The Influence of anthropogenic activities on lake water quality is well documented, but how those influences interact with the effects of natural features, such as watershed geology or lake morphometry, has been less explored. Further, some aspects of lake condition are influenced by factors that are not lake or watershed specific, but occur across large regions, such as weather patterns. All these factors may be interrelated in some instances, which can complicate lake condition assessments which have the purpose of determining how lakes are being affected by human activities. This dissertation investigates how lake assessments can integrate the interactions among natural features of lakes, their watersheds, and anthropogenic influences. Chapter 1 discusses the variety of factors that may affect lake condition and how those influences may confound lake condition assessments. Chapter 2 details the creation of a hydrogeomorphic lake classification, based on ecoregions and lake depth, that partitioned lakes into groups that share similarities in background water quality condition. In chapter 3, a logistic regression model is described that uses maximum depth and relative lake area beneath the epilimnion to predict which low-nutrient lakes (total phosphorus \u3c 15 μg/L) may exhibit naturally-occurring anoxia. In chapter 4, water clarity patterns from different types of reference lakes (detailed in chapter 2) were modeled to allow for comparisons between yearly water clarity values in non-reference lakes and a reference baseline that shifts over time. Cumulative precipitation during the lake stratification season was the primary driver of yearly differences in background lake water clarity. In chapter 5, methods were developed to measure the effect of anthropogenic shoreland disturbance on the condition of littoral habitat. Multi-metric indices based on various habitat measures were established that determine if the littoral habitat is different from a natural reference condition. Chapter 6 summarizes the research in this dissertation and offers potential foci of future lake research in Maine. The overall goal of this dissertation was to advance our collective understanding of how lakes may be variably affected by natural and anthropogenic factors, thereby allowing for better-informed lake assessments and the development of more comprehensive, achievable lake management goals. The research presented herein underscores the importance of considering the interactions of multiple cross-scale factors when evaluating lake condition, especially those related to landscape traits that influence runoff water chemistry, natural lake-specific features such as basin morphometry, large-scale weather patterns, and localized shoreland development

Risk, Families, and Interventions in Early Childhood Special Education

The purpose of this paper is to provide a comprehensive review of key characteristics of early childhood special education and early intervention services. This paper seeks to explain key concepts that will aid professionals in their daily interactions with students, families, other professionals, and the outside community. The major topics that will be addressed are the determination of risk in ECSE, types of interventions used with young children with disabilities, and the family as an important collaborator in providing ECSE and EI services. The paper will then conclude with a discussion that addresses the salient point of the article and makes recommendations for professionals to remember in their interactions working in ECSE and EI programs

A Comparison of Multiple Frequency and Pulsed Eddy Current Techniques

In principle, the same information should be obtainable from. either pulsed or multiple frequency eddy current techniques, provided they utilize comparable frequency ranges. In practice, there are important differences and advantages for each method. Pulse instrumentation is generally cheaper, simpler, and less sophisticated. On the other hand, there has been greater development of theory and instrumentation using sinusoidal eddy currents, so that the equipment is generally more quantitative at present. The basic problem of determining certain paramenters when others may also be varying can be solved by measuring enough quantities to eliminate the unwanted variables, for example, by measuring the pulse response at various time delays or the sinusoidal response at various frequencies. In practice, the number of useful frequencies is strictly limited. Little additional information is obtainable from frequencies for which the skin depth is much greater or much less than the thickness of the sample. Since the frequencies must be spaced to. permit separation by filters, this puts a practical limit of about four on the number of frequencies useful for a given problem. This is not a serious limitation, since one can measure two quantities for each frequency and the total number of pertinent parameters rarely exceeds six. Pulse equipment can more readily handle a wide range of frequencies, but the instrumentation tends to become more elaborate, especially if high frequencies are needed for a particular application, and the repetition rate becomes low if low frequencies are necessary. The reproducibility of pulses is a problem which can be circumvented by the use of bridge techniques, differential coils and other standard techniques. New computer programs and microprocessor equipment have been developed which now make it possible to set up tests and measure parameters directly and precisely without the lengthy optimization calculations once necessary, though the latter will continue to be useful for the design of optimized coils and experiments

Rhythmic Clay: A View of Jun Kaneko\u27s Process

In this diverse age of artistic pluralism, retrospection and cynicism, Jun Kaneko\u27s ceramic sculptures prevail as confirmations of essential constancies. The certainties of man\u27s elemental graphic urge, the determinism of archetypal shapes, and the symbiosis of time and space are all revealed in Kaneko\u27s three dimensional abstractions. Kaneko employs abstraction, not to transcend contemporary complexities, but to reveal the inherent synchrony of the natural world. From a position of acceptance, rather than control, Kaneko is but one participant in a private conversation with his media. And though this internal conversation is not directed at Kaneko\u27s audience, we partake of his direct access to the absolute of form evolving in space. Kaneko\u27s bi-cultural experience and non-hierarchical sense of reality enable him to interpret the sculptural properties, rather than to predict them. His response to the organic pliability of the raw clay and transparent glazes permits the revelation of the underlying equilibrium of the world in flux. Thus Kaneko\u27s role is more collaborative than singular. His is a process based on intuitive observation of the interacting materials. It is his reception, rather than his manipulation of the innate sculptural qualities that determines the ultimate resolution of the work. Kaneko\u27s measured orchestration of the interplay of clay and form, surface and pattern, is toward the extraction of a visible harmony. The pattemed surfaces and emphatic shapes emerge from a gestalt of eastern and western aesthetics as precise distillations of Kaneko\u27s vision--a vision seen from within nature, ordered by mark-making and time