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Health service capacity modelling.

This paper aims to describe a modelling tool that gives a framework for the estimation of future bed demand for hospital services. It also outlines some issues regarding the application of the model. A quantitative mathematical model was constructed that was based on two years of seasonally adjusted inpatient data. To calculate the number of beds required five years into the future, ten factors were applied to the number of bed-days used for each service. In the example given (Figure 1), 7,924 bed-days used in 1998-99 translated into a requirement for twenty-six beds in 2004. The value of this approach lies in the ability to describe and delineate each of the varying factors, and thus allowing clinicians, healthcare managers, the purchasers of health services and other stakeholders to be involved in a clear and explicit decision-making process.

Data Interpretation, Statistical↗

Design of a directed molecular network.

An ability to rationally design complex networks from the bottom up can offer valuable quantitative model systems for use in gaining a deeper appreciation for the principles governing the self-organization and functional characteristics of complex systems. We report herein the de novo design, graph prediction, experimental analysis, and characterization of simple self-organized, nonlinear molecular networks. Our approach makes use of the sequence-dependent auto- and cross-catalytic functional characteristics of template-directed peptide fragment condensation reactions in neutral aqueous solutions. Starting with an array of 81 sequence similar 32-residue coiled-coil peptides, we estimated the relative stability difference between all plausible A(2)B-type coiled-coil ensembles and used this information to predict the auto- and cross-catalysis pathways and the resulting plausible network motif and connectivities. Similar to most complex systems, the generated graph displays clustered nodes with an overall hierarchical architecture. To test the validity of the design principles used, nine nodes composing a main segment of the graph were experimentally analyzed for their capacity in establishing the predicted network connectivity. The resulting self-organized chemical network is shown to display 25 directed edges in good agreement with the graph analysis estimations. Moreover, we show that by varying the system parameters (presence or absence of certain substrates or templates), its operating network motif can be altered, even to the extremes of turning pathways on or off. We suggest that this approach can be expanded for the construction of large-scale networks, offering a means to study and to understand better the emergent, collective behaviors of networks.

Amino Acid Sequence↗

The nucleotide switch in Cdc42 modulates coupling between the GTPase-binding and allosteric equilibria of Wiskott-Aldrich syndrome protein.

The GTP/GDP nucleotide switch in Ras superfamily GTPases generally involves differential affinity toward downstream effectors, with the GTP-bound state having a higher affinity for effector than the GDP-bound state. We have developed a quantitative model of allosteric regulation of the Wiskott-Aldrich syndrome protein (WASP) by the Rho GTPase Cdc42 to better understand how GTPase binding is coupled to effector activation. The model accurately predicts WASP affinity for Cdc42, activity toward Arp2/3 complex, and activation by Cdc42 as functions of a two-state allosteric equilibrium in WASP. The ratio of GTPase affinities for the inactive and active states of WASP is appreciably larger for Cdc42-GTP than for Cdc42-GDP. The greater ability to distinguish between the two states of WASP makes Cdc42-GTP a full WASP agonist, whereas Cdc42-GDP is only a partial agonist. Thus, the nucleotide switch controls not only the affinity of Cdc42 for its effector but also the efficiency of coupling between the Cdc42-binding and allosteric equilibria in WASP. This effect can ensure high fidelity and specificity in Cdc42 signaling in crowded membrane environments.

Actin-Related Protein 2↗

Statistical analysis of MPSS measurements: application to the study of LPS-activated macrophage gene expression.

Massively Parallel Signature Sequencing (MPSS), a recently developed high-throughput transcription profiling technology, has the ability to profile almost every transcript in a sample without requiring prior knowledge of the sequence of the transcribed genes. As is the case with DNA microarrays, effective data analysis depends crucially on understanding how noise affects measurements. We analyze the sources of noise in MPSS and present a quantitative model describing the variability between replicate MPSS assays. We use this model to construct statistical hypotheses that test whether an observed change in gene expression in a pair-wise comparison is significant. This analysis is then extended to the determination of the significance of changes in expression levels measured over the course of a time series of measurements. We apply these analytic techniques to the study of a time series of MPSS gene expression measurements on LPS-stimulated macrophages. To evaluate our statistical significance metrics, we compare our results with published data on macrophage activation measured by using Affymetrix GeneChips.

Base Sequence↗

Multiple homeostatic mechanisms in the control of P1 plasmid replication.

Many organisms control initiation of DNA replication by limiting supply or activity of initiator proteins. In plasmids, such as P1, initiators are limited primarily by transcription and dimerization. However, the relevance of initiator limitation to plasmid copy number control has appeared doubtful, because initiator oversupply increases the copy number only marginally. Copy number control instead has been attributed to initiator-mediated plasmid pairing ("handcuffing"), because initiator mutations to handcuffing deficiency elevates the copy number significantly. Here, we present genetic evidence of a role for initiator limitation in plasmid copy number control by showing that autorepression-defective initiator mutants also can elevate the plasmid copy number. We further show, by quantitative modeling, that initiator dimerization is a homeostatic mechanism that dampens active monomer increase when the protein is oversupplied. This finding implies that oversupplied initiator proteins are largely dimeric, partly accounting for their limited ability to increase copy number. A combination of autorepression, dimerization, and handcuffing appears to account fully for control of P1 plasmid copy number.

DNA↗

Hydrophobic hydration from small to large lengthscales: Understanding and manipulating the crossover.

Small and large hydrophobic solutes exhibit remarkably different hydration thermodynamics. Small solutes are accommodated in water with minor perturbations to water structure, and their hydration is captured accurately by theories that describe density fluctuations in pure water. In contrast, hydration of large solutes is accompanied by dewetting of their surfaces and requires a macroscopic thermodynamic description. A unified theoretical description of these lengthscale dependencies was presented by Lum, Chandler, and Weeks [(1999) J. Phys. Chem. B 103, 4570-4577]. Here, we use molecular simulations to study lengthscale-dependent hydrophobic hydration under various thermodynamic conditions. We show that the hydration of small and large solutes displays disparate dependencies on thermodynamic variables, including pressure, temperature, and additive concentration. Understanding these dependencies allows manipulation of the small-to-large crossover lengthscale, which is nanoscopic under ambient conditions. Specifically, applying hydrostatic tension or adding ethanol decreases the crossover length to molecular sizes, making it accessible to atomistic simulations. With detailed temperature-dependent studies, we further demonstrate that hydration thermodynamics changes gradually from entropic to enthalpic near the crossover. The nanoscopic lengthscale of the crossover and its sensitivity to thermodynamic variables imply that quantitative modeling of biomolecular self-assembly in aqueous solutions requires elements of both molecular and macroscopic hydration physics. We also show that the small-to-large crossover is directly related to the Egelstaff-Widom lengthscale, the product of surface tension and isothermal compressibility, which is another fundamental lengthscale in liquids.

Biophysical Phenomena↗

General and variable features of varicosity spacing along unmyelinated axons in the hippocampus and cerebellum.

Along unmyelinated central axons, synapses occur at focal swellings called axonal varicosities (boutons). The mechanisms regulating how frequently synapses and varicosities occur along axons remain poorly understood. Here, to investigate varicosity distribution patterns and the extent to which they may be conserved across different axons, we analyzed varicosity numbers and positions along fluorescently labeled axon branches in hippocampal area CA1 (CA3-to-CA1 "Schaffer collateral" axons) and five other synaptic regions of rat hippocampus and cerebellum. Varicosity spacing varied by region; e.g., 3.7 +/- 0.6 microm (mean +/- SD) for CA3-to-CA1 axons and 5.2 +/- 1.0 microm for cerebellar parallel fibers. Surprisingly, when 56 axons from these different regions were pooled into a single heterogeneous group, a general relationship emerged: the spacing variability (SD) was a constant fraction of the mean spacing, suggesting that varicosities along different axons are distributed in a fundamentally similar, scaled manner. Varicosity spacing was neither regular nor random but followed a pattern consistent with random synaptic distributions and the occurrence of multiple-synapse boutons. A quantitative model reproduced the salient features of the data and distinguished between two proposed mechanisms relating axonal morphogenesis and synaptogenesis.

Animals↗

Endocytic vesicle scission by lipid phase boundary forces.

Endocytosis in budding yeast is thought to occur in several phases. First, the membrane invaginates and then elongates into a tube. A vesicle forms at the end of the tube, eventually pinching off to form a "free" vesicle. Experiments show that actin polymerization is an active participant in the endocytic process, along with a number of membrane-associated proteins. Here we investigate the possible roles of these components in driving vesiculation by constructing a quantitative model of the process beginning at the stage where the membrane invagination has elongated into a tube encased in a sheath of membrane-associated protein. This protein sheath brings about the scission step where the vesicle separates from the tube. When the protein sheath is dynamin, it is commonly assumed that scission is brought about by the constriction of the sheath. Here, we show that an alternative scenario can work as well: The protein sheath acts as a "filter" to effect a phase separation of lipid species. The resulting line tension tends to minimize the interface between the tube region and the vesicle region. Interestingly, large vesicle size can further facilitate the reduction of the interfacial diameter down to a few nanometers, small enough so that thermal fluctuations can fuse the membrane and pinch off the vesicle. To deform the membrane into the tubular vesicle shape, the membrane elastic resistance forces must be balanced by some additional forces that we show can be generated by actin polymerization and/or myosin I. These active forces are shown to be important in successful scission processes as well.

Endocytosis↗

Quantification of protein half-lives in the budding yeast proteome.

A complete description of protein metabolism requires knowledge of the rates of protein production and destruction within cells. Using an epitope-tagged strain collection, we measured the half-life of >3,750 proteins in the yeast proteome after inhibition of translation. By integrating our data with previous measurements of protein and mRNA abundance and translation rate, we provide evidence that many proteins partition into one of two regimes for protein metabolism: one optimized for efficient production or a second optimized for regulatory efficiency. Incorporation of protein half-life information into a simple quantitative model for protein production improves our ability to predict steady-state protein abundance values. Analysis of a simple dynamic protein production model reveals a remarkable correlation between transcriptional regulation and protein half-life within some groups of coregulated genes, suggesting that cells coordinate these two processes to achieve uniform effects on protein abundances. Our experimental data and theoretical analysis underscore the importance of an integrative approach to the complex interplay between protein degradation, transcriptional regulation, and other determinants of protein metabolism.

Fungal Proteins↗

Mg2+-RNA interaction free energies and their relationship to the folding of RNA tertiary structures.

Mg2+ ions are very effective at stabilizing tertiary structures in RNAs. In most cases, folding of an RNA is so strongly coupled to its interactions with Mg2+ that it is difficult to separate free energies of Mg2+-RNA interactions from the intrinsic free energy of RNA folding. To devise quantitative models accounting for this phenomenon of Mg2+-induced RNA folding, it is necessary to independently determine Mg2+-RNA interaction free energies for folded and unfolded RNA forms. In this work, the energetics of Mg2+-RNA interactions are derived from an assay that measures the effective concentration of Mg2+ in the presence of RNA. These measurements are used with other measures of RNA stability to develop an overall picture of the energetics of Mg2+-induced RNA folding. Two different RNAs are discussed, a pseudoknot and an rRNA fragment. Both RNAs interact strongly with Mg2+ when partially unfolded, but the two folded RNAs differ dramatically in their inherent stability in the absence of Mg2+ and in the free energy of their interactions with Mg2+. From these results, it appears that any comprehensive framework for understanding Mg2+-induced stabilization of RNA will have to (i) take into account the interactions of ions with the partially unfolded RNAs and (ii) identify factors responsible for the widely different strengths with which folded tertiary structures interact with Mg2+.

Base Sequence↗

On schemes of combinatorial transcription logic.

Cells receive a wide variety of cellular and environmental signals, which are often processed combinatorially to generate specific genetic responses. Here we explore theoretically the potentials and limitations of combinatorial signal integration at the level of cis-regulatory transcription control. Our analysis suggests that many complex transcription-control functions of the type encountered in higher eukaryotes are already implementable within the much simpler bacterial transcription system. Using a quantitative model of bacterial transcription and invoking only specific protein-DNA interaction and weak glue-like interaction between regulatory proteins, we show explicit schemes to implement regulatory logic functions of increasing complexity by appropriately selecting the strengths and arranging the relative positions of the relevant protein-binding DNA sequences in the cis-regulatory region. The architectures that emerge are naturally modular and evolvable. Our results suggest that the transcription regulatory apparatus is a "programmable" computing machine, belonging formally to the class of Boltzmann machines. Crucial to our results is the ability to regulate gene expression at a distance. In bacteria, this can be achieved for isolated genes via DNA looping controlled by the dimerization of DNA-bound proteins. However, if adopted extensively in the genome, long-distance interaction can cause unintentional intergenic cross talk, a detrimental side effect difficult to overcome by the known bacterial transcription-regulation systems. This may be a key factor limiting the genome-wide adoption of complex transcription control in bacteria. Implications of our findings for combinatorial transcription control in eukaryotes are discussed.

Bacteria↗

Evidence of nonspecific surface interactions between laser-polarized xenon and myoglobin in solution.

The high sensitivity of the magnetic resonance properties of xenon to its local chemical environment and the large (129)Xe NMR signals attainable through optical pumping have motivated the use of xenon as a probe of macromolecular structure and dynamics. In the present work, we report evidence for nonspecific interactions between xenon and the exterior of myoglobin in aqueous solution, in addition to a previously reported internal binding interaction. (129)Xe chemical shift measurements in denatured myoglobin solutions and under native conditions with varying xenon concentrations confirm the presence of nonspecific interactions. Titration data are modeled quantitatively with treatment of the nonspecific interactions as weak binding sites. Using laser-polarized xenon to measure (129)Xe spin-lattice relaxation times (T(1)), we observed a shorter T(1) in the presence of 1 mM denatured apomyoglobin in 6 M deuterated urea (T(1) = 59 +/- 1 s) compared with that in 6 M deuterated urea alone (T(1) = 291 +/- 2 s), suggesting that nonspecific xenon-protein interactions can enhance (129)Xe relaxation. An even shorter T(1) was measured in 1 mM apomyoglobin in D(2)O (T(1) = 15 +/- 0.3 s), compared with that in D(2)O alone (T(1) = 506 +/- 5 s). This difference in relaxation efficiency likely results from couplings between laser-polarized xenon and protons in the binding cavity of apomyoglobin that may permit the transfer of polarization between these nuclei via the nuclear Overhauser effect.

Animals↗

The HLA-DQ2 gene dose effect in celiac disease is directly related to the magnitude and breadth of gluten-specific T cell responses.

In patients with celiac disease, inflammatory T cell responses to HLA-DQ2-bound gluten peptides are thought to cause disease. Two types of HLA-DQ2 molecules exist, termed HLA-DQ2.5 and HLA-DQ2.2. Whereas HLA-DQ2.5 predisposes to celiac disease, HLA-DQ2.2 does not. We now provide evidence that the disease-associated HLA-DQ2.5 molecule presents a large repertoire of gluten peptides, whereas the non-disease-associated HLA-DQ2.2 molecule can present only a subset of these. Moreover, gluten presentation by HLA-DQ2 homozygous antigen-presenting cells was superior to presentation by HLA-DQ2/non-DQ2 heterozygous antigen-presenting cells in terms of T cell proliferation and cytokine secretion. Gluten presentation by HLA-DQ2.5/2.2 heterozygous antigen-presenting cells induced intermediate T cell stimulation. These results correlated with peptide binding to the antigen-presenting cells. Finally, we demonstrate that HLA-DQ trans dimers formed in HLA-DQ2.5/2.2 heterozygous individuals have properties identical with HLA-DQ2.5 dimers. Our findings explain the strongly increased risk of disease development for HLA-DQ2.5 homozygous and HLA-DQ2.2/2.5 heterozygous individuals, and they are indicative of a quantitative model for disease development, where HLA-DQ expression and the available number of T cell-stimulatory gluten peptides are critical limiting factors. This model may have important implications for disease prevention.

Antigen-Presenting Cells↗

Calculation of immigration and extinction curves from the species-area-distance relation.

Quantitative models of the species-area-distance relation, based on equilibria between immigration and extinction rates, have been tested against data for birds on 52 Solomon islands. Biologically reasonable models account for 98% of the variance in species number. The data are adequate to permit determination of immigration and extinction curves and the values of seven associated parameters. The resulting curves are very concave. Extinction rates vary almost exactly as the reciprocal of area, but the effect of area on immigration rates is slight. Recognition of major differences among species in immigration and extinction rates and in dispersal distances proves essential to a successful model.

Journal Article↗

Nonspecific DNA binding of genome-regulating proteins as a biological control mechanism: measurement of DNA-bound Escherichia coli lac repressor in vivo.

Binding of genome regulatory proteins to nonspecific DNA sites may play an important role in controlling the thermodynamics and kinetics of the interactions of these proteins with their specific target DNA sequences. An estimate of the fraction of Escherichia coli lac repressor molecules bound in vivo to the operator region and to nonoperator sites on the E. coli chromosome is derived by measurement of the distribution of repressor between a minicell-producing E. coli strain (P678-54) and the DNA-free minicells derived therefrom. Assuming the minicell cytoplasm to be representative of that of the parent E. coli cells, we find that less than 10% of the repressor tetramers of the average cell are free in solution; the remainder are presumed to be bound to the bacterial chromosome. The minimum in vivo value of the association constant for repressor to bulk nonoperator DNA (K(RD)) calculated from these results is about 10(3) M(-1), and analysis of the sources of error in the minicell experiment suggests that the actual in vivo value of K(RD) could be substantially greater. The value of K(RD), coupled with in vitro data on the ionic strength dependence of this parameter, can be used to estimate that the effective intracellular cation activity of E. coli is no greater than about 0.24 M (and probably no less than 0.17 M) in terms of sodium ion equivalents. The minicell distribution experiments also confirm that the association constant for the binding of inducer-repressor complex to bulk nonoperator DNA (K(RID)) is [unk] K(RD)in vivo. These results are used to calculate minimum in vivo values of K(RO) and K(RIO) (association constants for repressor and for inducer-repressor complex binding to operator) of about 10(12) M(-1) and about 10(9) M(-1), respectively. The results fit a quantitative model for operon regulation in which nonspecific DNA-repressor complexes play a key role in determining basal and constitutive levels of gene expression [von Hippel, P. H., Revzin, A., Gross, C. A. & Wang, A. C. (1974) Proc. Natl. Acad. Sci. USA 71, 4808-4812].

Bacterial Proteins↗

Gin-mediated DNA inversion: product structure and the mechanism of strand exchange.

Inversion of the G loop of bacteriophage Mu requires the phage-encoded Gin protein and a host factor. The topological changes in a supercoiled DNA substrate generated by the two purified proteins were analyzed. More than 99% of the inversion products were unknotted rings. This result excludes synapsis by way of a random collision of recombination sites, because the resulting entrapped supercoils would be converted into knots by recombination. Instead, the recombination sites must come together in the synaptic complex in an ordered fashion with a fixed number of supercoils between the sites. The linking number of the substrate DNA increases by four during recombination. Thus, in three successive rounds of inversion, the change in linking number was +4, +8, and +12, respectively. These results lead to a quantitative model for the mechanism of Gin recombination that includes the distribution of supercoils in the synaptic complex, their alteration by strand exchange, and specific roles for the two proteins needed for recombination.

Bacteriophage lambda↗

Kinetic discrimination in T-cell activation.

We propose a quantitative model for T-cell activation in which the rate of dissociation of ligand from T-cell receptors determines the agonist and antagonist properties of the ligand. The ligands are molecular complexes between antigenic peptides and proteins of the major histocompatibility complex on the surfaces of antigen-presenting cells. Binding of ligand to receptor triggers a series of biochemical reactions in the T cell. If the ligand dissociates after these reactions are complete, the T cell receives a positive activation signal. However, dissociation of ligand after completion of the first reaction but prior to generation of the final products results in partial T-cell activation, which acts to suppress a positive response. Such a negative signal is brought about by T-cell ligands containing the variants of antigenic peptides referred to as T-cell receptor antagonists. Results of recent experiments with altered peptide ligands compare favorably with T-cell responses predicted by this model.

Animals↗

Frontiers of finance: evolution and efficient markets.

In this review article, we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions of research, some focusing on more elaborate mathematical models that are capable of rationalizing the empirical facts, others taking a completely different tack in rejecting rationality altogether. One of the most promising directions is to view financial markets from a biological perspective and, specifically, within an evolutionary framework in which markets, instruments, institutions, and investors interact and evolve dynamically according to the "law" of economic selection. Under this view, financial agents compete and adapt, but they do not necessarily do so in an optimal fashion. Evolutionary and ecological models of financial markets is truly a new frontier whose exploration has just begun.

Economics↗