Parts List Research Articles

It's the Technology, Stupid

Living organisms are incredibly complex. Almost every biological function arises from the combined action of multiple components whose interactions generate functions and properties that are not currently predictable from the attributes of the individual parts. Because they evolved, living systems solve design problems in idiosyncratic ways that can only be resolved by experiment. Unraveling this complexity, moving toward the prediction of phenotype from genotype, is the major challenge that life scientists, including cell biologists, will face over the next 50 years. As always in biological research, it will be new technologies that will determine what is achievable. But predicting new technologies is impossible, so here I describe currently foreseeable developments. Iain W. Mattaj Cellular parts lists, RNAs, proteins, protein modifications, lipids, will be increasingly complete, as will catalogs of the interactions that occur between these components. Single cells will continue to be amenable to a variety of genetic, biochemical, and imaging approaches that cannot be simply applied to complex organisms and intracellular processes coupled to cell–cell interactions provide the basis for the development, structure, and function of tissues, organs, and multicellular organisms. Therefore, the cell will undoubtedly remain at the center of biology in the next few decades, even though the nature of cell biology will change significantly. Cell biology will become more interdisciplinary. The boundaries with other biomedical disciplines have already blurred and physics, chemistry, mathematics, and computer science are also beginning to have a heavy influence. The recent and ongoing radical advances in imaging have turned molecular cell biology from a discipline dominated by reductionist experimental methods and descriptive morphology into a quantitative science geared at measuring, dissecting, and understanding molecular mechanisms in their in vivo context. This trend will continue. Imaging in four dimensions captures real-time data that reflects the physiological conditions and dynamics of the biological system under study. Fluorescence-based light microscopy techniques use reporter molecules to monitor the localization, and in an increasing number of cases the activity, of molecules inside cells. These methods will allow biochemical and biophysical parameters of cellular processes, such as signaling cascades or the assembly and disassembly of subcellular structures, to be quantitatively determined and thus provide the raw material for the type of modeling and simulation methods that, when applied together with experimental manipulation, will enable detailed understanding of the information flow that underlies cellular processes and functions. Thus, I foresee a broad, significant increase in our understanding of “how cells work.” The major current limitation is the small variety of available in vivo reporters and the small number that can be studied simultaneously. I confidently expect both of these limitations to yield to energetic attack over the next two decades. The recent advent of super-resolution microscopy and electron microscopic tomography are important steps in bridging the resolution gaps between cell and structural biology. These and other developments have led to a new approach, sometimes called cellular structural biology, that integrates across scales to move toward a detailed, structure-based understanding of cellular organization and function. In my view, the insight gained will change our way of thinking about cellular processes and how to manipulate them. In parallel, automated high-throughput and high-content microscopy have revolutionized the scale at which cell biology experiments can be done. Phenotypes of thousands of cells can now be screened in parallel, and image-processing software recognizes patterns and phenotypes more reliably than the human eye. Microfluidics will enhance single-cell study methods and the parallelization of biochemical assays. This will have a big impact in the years to come, for example, in systematically studying aspects of cellular phenotype based on interindividual or interspecies genetic variation. All of these developments suggest that cell biology will probably be substantially redefined in terms of its scope, scale, and toolbox and in the questions it addresses over the next 50 years. I encourage those entering the field to train as broadly as possible, studying chemistry, physics, or mathematics as well as biology. However, given that cells have already been under study for 400 years, we shouldn't be too surprised if there are still more questions than answers in 2060.

My Dream of a Fantastic Voyage to See the Inner Workings of a Cell

What would I give to be allowed to embark on a Fantastic Voyage at the nanometer scale inside the cell! In the 1960's film, humans were shrunk down to merely micrometer scale, but we now know that “nano” is the ticket. Imagine being able to observe cellular structural biology in real time and to see proteins and nucleic acids in action, in the concentrated environment of the nucleus, let alone in the cytosol. I imagine a complex molecular ballroom full of many intricately choreographed dancers, changing partners, switching locations, dying and being born again. Imagine the purpose and chaos governing the survival of the cellular microcosm, there for me (for you) to see and ultimately understand. Eva Nogales. Photo by Paul Fetters for HHMI. As a structural biologist, initially trained as a physicist, cells often seem too complex and far afield from my own research. My scientific presentations typically borrow images from cell biologists' websites, and I warn my audience after the first introductory slides that no more cells will be seen for the rest of the talk. However, as a molecular electron microscopist working on the cytoskeleton and large macromolecular complexes, I boast in front of crystallographers and nuclear magnetic resonance experts that we study fully functional complexes, in as close to physiological conditions as one can possibly expect outside of a cell. However, this is obviously not as physiological as if we were visualizing the native complexes in their cellular context! With fully annotated genomes providing nearly complete cellular parts lists, and with ever more powerful light microscopy, among other 21st century techniques, we have come a long way toward understanding the inner workings of the cell. Still, the dream of visualizing the intact cell's anatomy with molecular resolution seems like science fiction. Is there any hope for visualizing these molecular machines where they function and when it matters, even if it is not through our atomically shrunk, craving eyes? I really want to think so. It may not come from a single instrument, like the Star Trek scope where magnification can be cranked until the bar code on individual atoms becomes clear. However, combining currently available methodologies and then taking them to the next level may, step by step, get us there. The first combined electron and light microscopes are already producing data wherein the fluorescent colors of choice are superimposed on the gray levels of individual molecular density. Spectroscopy readings, with nanometer cube mapping capability, are being carved out of cellular slices in futuristic attempts at spatial metabolomics. Three-dimensional maps of hydrated cells will soon become routine, and as the resolution moves from 100 to 10 Å in my life time (if I take good care of myself), we will be able to identify macromolecules by shapes, in snapshots of cellular life. We will be able to follow the paths of single proteins as they meander their way along the chaotic cellular freeways of the cytoskeleton, or fluidly traffic between cellular compartments. We are almost there. My own personal dream of “visualizing” the complete kinetochore protein network, carrying out the dynamic engagement of chromosomes to the mitotic spindle and thus revealing the force coupling mechanism, may be just around the corner. It is not that images are worth a thousand gels, or movies a million pulldowns (although perhaps they are), it's just my own preferred means of getting to know and understand nature. My wish for the future of cell biology: I want to “see” the cell (I leave smelling it and listening to it to biochemists and theoretical physicists, respectively).

Mining metabolites: extracting the yeast metabolome from the literature

Text mining methods have added considerably to our capacity to extract biological knowledge from the literature. Recently the field of systems biology has begun to model and simulate metabolic networks, requiring knowledge of the set of molecules involved. While genomics and proteomics technologies are able to supply the macromolecular parts list, the metabolites are less easily assembled. Most metabolites are known and reported through the scientific literature, rather than through large-scale experimental surveys. Thus it is important to recover them from the literature. Here we present a novel tool to automatically identify metabolite names in the literature, and associate structures where possible, to define the reported yeast metabolome. With ten-fold cross validation on a manually annotated corpus, our recognition tool generates an f-score of 78.49 (precision of 83.02) and demonstrates greater suitability in identifying metabolite names than other existing recognition tools for general chemical molecules. The metabolite recognition tool has been applied to the literature covering an important model organism, the yeast Saccharomyces cerevisiae, to define its reported metabolome. By coupling to ChemSpider, a major chemical database, we have identified structures for much of the reported metabolome and, where structure identification fails, been able to suggest extensions to ChemSpider. Our manually annotated gold-standard data on 296 abstracts are available as supplementary materials. Metabolite names and, where appropriate, structures are also available as supplementary materials.Electronic supplementary materialThe online version of this article (doi:10.1007/s11306-010-0251-6) contains supplementary material, which is available to authorized users.

Study on Statistical Method of Steel Bridge Parts Information Based on Three-Dimensional CAD

Parts information of steel bridge with tens of thousands of parts is difficult to be managed and be executed statistics. On the platform of three-dimensional CAD systems, steel bridge node is the study object in this paper, according to the assembly relationship of all parts in the three-dimensional assembly model, the parts list, quantity, geometrical information and weight of the parts of the steel bridge nodes are extracted from a three-dimensional model by the application interface provided by three-dimensional CAD systems. On the basis of geometrical information of the parts, the minimum boundary dimension of the parts is computed by use of the principle of computer graphics. The method can rapidly and accurately obtain parts information, and can provide basis for assembly process and processing technology.

LIFE SCIENCE TECHNOLOGIES: Protein-Protein Interaction Technologies Toward a Human Interactome

The human genome has been called the "blueprint of life," but it's really more of a parts list. Cellular architecture is better defined by its complexes, the molecular machines that actually make a cell, a cell. French researchers first coined the term "interactome" in 1999; the first protein-protein interactome data appeared in 2000. Today the field--like the 11-year-old it is--is maturing rapidly. Interactome research has racked up more than 560 publications, and databases now house interactions numbering in the hundreds of thousands. Still, as international efforts to map the human protein-interaction network get under way, it's clear interactomics has a long way to go.

Focus on the Spatial Organization of Signalling

Since the early days of light microscopy it has been apparent that cells are highly organized and compartmentalized. However, only in recent decades has the molecular basis of this spatial organization and its functional role in cellular signalling events emerged. Furthermore, modern molecular and imaging techniques, together with the intricate combination of cellular and developmental biological approaches, are extending our understanding of how individual cells respond to their environment and are organized within a tissue. Years of molecular and genetic analysis, coupled with recent advances in large‐scale approaches, may have identified many of the core components of signalling pathways, although new layers of regulation, such as small RNAs and alternative splicing, continue to add complexity. Although the parts list may soon be completed, our understanding at the level of signal integration and cross‐talk remains limited. The key to understanding cellular regulation is to complement biochemical assays in vitro with analysis on how spatial organization contributes to the properties of intra‐ and intercellular communication. This requires a real‐time quantitative analysis of endogenous components in the cellular context, which has only recently became possible with advanced microscopy techniques and biosensors. These developments open a new era in the analysis of spatial organization on different biological scales from molecules to cells to tissues and organs. The EMBO Journal covers a broad spectrum of subject areas and approaches, ranging from biochemical to cell biological, as well as those at the organism level. However, the journal has a longstanding tradition of hosting important papers on signalling, which …

A systems biology approach to understanding atherosclerosis

Atherosclerosis, a chronic inflammatory disease of the vascular system, presents significant challenges to developing effective molecular diagnostics and novel therapies. A systems biology approach integrating data from large-scale measurements (e.g. transcriptomics, proteomics and genomics) is successfully contributing to deciphering regulatory networks underlying the response of many different cellular systems to perturbations. Such a network analysis strategy using pathway information and data from multiple measurement platforms, tissues and species is a promising approach to elucidate the mechanistic underpinnings of complex diseases. Here, we present our views on the contributions that a systems approach can bring to the study of atherosclerosis, propose ways to tackle the complexity of the disease in a systems manner and review recent systems-level studies of the disease.

Anti-Diabetic Agents from Natural Products — An Update from 2004 to 2009

Diabetes mellitus (DM), the third killer of the mankind health along with cancer, cardiovascular and cerebrovascular diseases, is one of the most challenging diseases facing health care professionals today. The World Health Organization (WHO) has declared that a DM epidemic is underway. Primary DM and its complications are costly to manage, not only for affected individuals, but also for healthcare systems around the world. Screening of anti-diabetic agents has been extensively investigated in the past decades. Natural products (NPs) have served as a major source of drugs for centuries, and about half of the pharmaceuticals in use today are derived from natural substances. Many natural products especially plants-derived medicines have been recommended for the treatment of DM. The present paper reviews NPs appeared in the literature with potential for DM and also identifies the research needs in this area. It mainly covers the time period from January 2004 to October 2008. The current review is divided into three major sections based on classification of the natural materials involved. The first part focuses on known and some new chemical entities isolated mainly from medicinal plants possessing anti-diabetic properties, including saponins, flavonoids, alkaloids, anthraquinones, terpenes, coumarins, phenolics, polysaccharides, and some other compounds. The second part summarizes crude extract of medicinal plants which are commonly used in the traditional Chinese medical system and have been demonstrated experimental or/and clinical anti-diabetic effectiveness, mainly including Leguminosae, Cucurbitaceae, Araliaceae, Liliaceae, Chenopodiaceae, Solanaceae, Compositae, Campanulaceae, Cornaceae, Rhamnaceae, Scrophulariaceae, Euphorbiaceae, Ginkgoceae, Gramineae, Myrtaceae, Sterculiaceae, Annonaceae, Labiatae, Crassulaceae, and Miscellaneous. The third part lists some compound formulae consisting of extracts of several plants that have been reported as beneficial for the treatment of DM, major involving Xiaokeling tablet, Ba-Wei-Di-Huang-Wan and Formula 1.

How to Understand the Cell by Breaking It: Network Analysis of Gene Perturbation Screens

Modern high-throughput gene perturbation screens are key technologies at the forefront of genetic research. Combined with rich phenotypic descriptors they enable researchers to observe detailed cellular reactions to experimental perturbations on a genome-wide scale. This review surveys the current state-of-the-art in analyzing perturbation screens from a network point of view. We describe approaches to make the step from the parts list to the wiring diagram by using phenotypes for network inference and integrating them with complementary data sources. The first part of the review describes methods to analyze one- or low-dimensional phenotypes like viability or reporter activity; the second part concentrates on high-dimensional phenotypes showing global changes in cell morphology, transcriptome or proteome.

Cardiovascular Networks

“If there is any area in which a network thinking could trigger a revolution, I believe that biology is it.” — Albert Laszlo Barabasi 1 Traditional biological and biochemical studies deal with relatively few components, allowing intuitive reasoning to guide hypotheses and experiments. For example, a popular experimental protocol in cardiovascular research is to examine gene functions through the use of transgenic or gene-targeted mice. Although clearly informative, it is becoming increasingly clear that such studies alone are not sufficient to explain complex processes such as arrhythmias, heart failure, and atherogenesis. Even a basic behavior, the action potential of a cardiomyocyte, requires the coordinated actions of >20 different ion transporters and channels.2 Perturbing proteins individually will help establish their functions, but it will not provide a full understanding of how they function together (quantitatively, temporally, and spatially). For this, a more global analysis, in which the activities of all of the relevant proteins are tracked over time and then integrated into a quantitative mathematical model, is required to provide a deeper level of understanding of cardiomyocyte dynamics. A new branch of biology, called systems biology, seeks to identify the components of complex systems and to model their dynamic interactions.3 The approach arose in large part as a result of new technical and analytical developments. The Human Genome Project provided a biological “parts list,” and technologies such as massively parallel DNA sequencing, expression microarrays, and tandem mass spectrometric analyses of proteins and metabolites have made high-throughput analysis of biological systems feasible. To deal with the data explosion, novel statistical and other mathematical modeling approaches are being developed. Basically, systems-based approaches involve 4 steps. The first is to define the system to be examined (eg, a cardiomyocyte). The second is to identify the components of the system (eg, the set …

Examining Mechanical Properties of Vertebrate Meiotic Spindles

Accurate chromosome segregation during cell division relies on the self-organization of a dynamic multi-component apparatus, the microtubule-based bipolar spindle. Through genetic, biochemical, and cell biological approaches, the complete ‘parts list’ of the components, including microtubule-based motor proteins, which are responsible for the assembly and maintenance of the meiotic spindle are now available. However, how spindle self-organization is controlled through integration of forces generated by multiple biomolecular processes remains mysterious. Here we report a calibrated microneedle-based system that allows application of sub-nanoNewton forces at specific sites within the metaphase spindle assembled in Xenopus egg extracts. Our set-up allows direct force measurements and can be combined with multi-mode high resolution microscopy along with chemical perturbations of specific spindle components. Using this system we applied sinusoidal strain to the metaphase spindle, keeping the range <5% to minimize nonlinearities of the response. The stress response was measured over the frequency ranged between 0.01 Hz and 2 Hz. Based on the resultant stress-strain relationship we determined the frequency-dependent mechanical properties of the spindle. The spindle response showed a typical characteristic time-scale of ∼50 s, at which the mechanical property changed from solid-like to liquid-like. Additional experiments examining stress relaxation, which may reflect the dynamics of structural reorganization, revealed a similar time-scale. This transition disappeared when the spindles were treated with AMPPNP, a slow-hydrolyzing ATP analog, suggesting that the characteristic time-scale is determined by an ATP-dependent processes within the spindle. The contribution of key mitotic motors such as dynein and kinesin is being examined by pharmacological or immunological perturbations. Together, these analyses will allow us discuss models for how forces in the self-organizing meiotic spindle are integrated.

And they said it wouldn't last...

In the 10 years that Genome Biology has been published the scientific changes have been amazing, as have the changes in the culture of science.

Nuclear physics: quantitative single-cell approaches to nuclear organization and gene expression.

The internal workings of the nucleus remain a mystery. A list of component parts exists, and in many cases their functional roles are known for events such as transcription, RNA processing, or nuclear export. Some of these components exhibit structural features in the nucleus, regions of concentration or bodies that have given rise to the concept of functional compartmentalization--that there are underlying organizational principles to be described. In contrast, a picture is emerging in which transcription appears to drive the assembly of the functional components required for gene expression, drawing from pools of excess factors. Unifying this seemingly dual nature requires a more rigorous approach, one in which components are tracked in time and space and correlated with onset of specific nuclear functions. In this chapter, we anticipate tools that will address these questions and provide the missing kinetics of nuclear function. These tools are based on analyzing the fluctuations inherent in the weak signals of endogenous nuclear processes and determining values for them. In this way, it will be possible eventually to provide a computational model describing the functional relationships of essential components.

A multi-scale parts list for the brain: community-based ontology curation for neuroinformatics with NeuroLex.org

Event Abstract Back to Event A multi-scale parts list for the brain: community-based ontology curation for neuroinformatics with NeuroLex.org Stephen Larson1*, Fahim Imam1, Rembrandt Bakker2, Luan Pham1 and Maryann Martone1 1 University of California, San Diego, Center for Research of Biological Systems, United States 2 Radboud UMC Nijmegen, Donders Institute for Brain, Cognition and Behaviour, Netherlands What makes up the nervous system? What are the inhibitory neurons? What brain regions are they in? What ion channels do they express? Do their dendrites have spines? What fiber bundles do they participate in? These questions and many more could be answered by a multi-scale parts list for the brain, where each part was uniquely indexed and unambiguously defined. Unfortunately, no such standard list has come into widespread use by the neuroscience community. Our effort to address this challenge has resulted in the instantiation of a semantic wiki, NeuroLex.org. For many years we have been building community ontologies for neuroscience, first through the Biomedical Informatics Research Network and now through the Neuroscience Information Framework (http://neuinfo.org) projects. These projects resulted in the construction of a large modular ontology, constructed by importing existing ontologies where possible, called the NIF Standard Ontology (NIFSTD; Bug et al, 2008). It covers behavioral activity, behavioral paradigms, brain regions, cells, diseases, molecules, nervous system function, subcellular components, information resources, resource types, and qualities. NeuroLex.org was originally populated with the NIFSTD in an effort to improve the process of editing and maintaining it. The initial update processes created one wiki page from each ontological "class", which refers to an entity relevant to neuroscience. Content that is added or updated in NeuroLex.org is contributed back to the NIFSTD. This content is not directly added to NIFSTD, but is incorporated into the NIFSTD OWL file by a knowledge engineer after curation by the NIF ontology group. NeuroLex.org's structuring of knowledge allows classes to be rendered using tables, trees, and lists which combine the asserted content of the class with queried content derived from other classes. For example, the page for "Cerebellum" displays a dynamic tree that lists the brain region classes that have been asserted as "part-of" the Cerebellum. This page also lists the neuron classes that have been asserted as "located-in" the Cerebellum. Neither of these property assertions are made on the Cerebellum page itself; rather they are displayed via dynamic queries that find classes related to the Cerebellum throughout the wiki. NeuroLex.org has served as a test bed for a rallying point for the efforts of the Program of Ontologies of Neural System (PONS), an activity of the International Neuroinformatics Coordinating Facility (INCF). In the last year, content and edits have been contributed by several members of the task forces in this activity. In addition, NeuroLex.org has incorporated a lightweight web application for digital atlasing called the Scalable Brain Atlas (http://scalablebrainatlas.incf.org), which generates atlas plate images that highlight a given brain region, in order to more clearly define it. NeuroLex.org has been online since October 2008 and has evolved into a powerful platform for collaboratively maintaining and extending the NIFSTD ontology. It has received 110,000 edits and has 104 registered users. It regularly receives 225 hits per day on average, 80% of which come directly from search engine hit results. NeuroLex.org is built on top of the open source Semantic Mediawiki platform (http://semantic-mediawiki.org) and incorporates several open source extensions such as Semantic Forms and the Halo Extension. We conclude that NeuroLex.org is a good starting point for the collaborative maintenance of ontologies. Other groups are also using a similar approach, e.g., BioMedGT (http://biomedgt.nci.nih.gov). While we are still working through some issues, e.g., synchronizing the NIFSTD with the content on NeuroLex, exporting and importing OWL, and bulk uploading concepts, we believe that semantic wikis are a good tool for providing community contribution and feedback to projects like NIF.

‘Unknown’ proteins and ‘orphan’ enzymes: the missing half of the engineering parts list – and how to find it

Like other forms of engineering, metabolic engineering requires knowledge of the components (the 'parts list') of the target system. Lack of such knowledge impairs both rational engineering design and diagnosis of the reasons for failures; it also poses problems for the related field of metabolic reconstruction, which uses a cell's parts list to recreate its metabolic activities in silico. Despite spectacular progress in genome sequencing, the parts lists for most organisms that we seek to manipulate remain highly incomplete, due to the dual problem of 'unknown' proteins and 'orphan' enzymes. The former are all the proteins deduced from genome sequence that have no known function, and the latter are all the enzymes described in the literature (and often catalogued in the EC database) for which no corresponding gene has been reported. Unknown proteins constitute up to about half of the proteins in prokaryotic genomes, and much more than this in higher plants and animals. Orphan enzymes make up more than a third of the EC database. Attacking the 'missing parts list' problem is accordingly one of the great challenges for post-genomic biology, and a tremendous opportunity to discover new facets of life's machinery. Success will require a co-ordinated community-wide attack, sustained over years. In this attack, comparative genomics is probably the single most effective strategy, for it can reliably predict functions for unknown proteins and genes for orphan enzymes. Furthermore, it is cost-efficient and increasingly straightforward to deploy owing to a proliferation of databases and associated tools.

Ihor Lemischka: stem cells meet systems biology

How to become whole from a list of parts

Lipidomics: a mass spectrometry based systems level analysis of cellular lipids

Lipidomics is a logical outcome of the history and traditions of lipid biochemistry and advances in mass spectrometry are at the heart of a renaissance in understanding the roles of lipids in cellular functions. Our desire to understand the complexity of lipids in biology has led to new techniques that allow us to identify over 1000 phospholipids in mammalian cell types and tissues. Improvements in chromatographic separation and mass spectrometry have positioned us to determine not only the lipid composition (i.e. parts list) of cells and tissues, but also address questions regarding lipid substrates and products that previously overwhelmed traditional analytical technologies. In the decade since lipidomics was conceived much of the efforts have been on new methodologies, development of computer programs to decipher the gigabytes of raw data, and struggling with the highly variable nature of biological systems where absolute quantities of a given metabolite may be less important than its relative change in concentration. It is clear that the technology is now sufficiently developed to address fundamental questions about the roles of lipids in cellular signaling and metabolic pathways.

Mechanical Design of Translocating Motor Proteins

Translocating motors generate force and move along a biofilament track to achieve diverse functions including gene transcription, translation, intracellular cargo transport, protein degradation, and muscle contraction. Advances in single molecule manipulation experiments, structural biology, and computational analysis are making it possible to consider common mechanical design principles of these diverse families of motors. Here, we propose a mechanical parts list that include track, energy conversion machinery, and moving parts. Energy is supplied not just by burning of a fuel molecule, but there are other sources or sinks of free energy, by binding and release of a fuel or products, or similarly between the motor and the track. Dynamic conformational changes of the motor domain can be regarded as controlling the flow of free energy to and from the surrounding heat reservoir. Multiple motor domains are organized in distinct ways to achieve motility under imposed physical constraints. Transcending amino acid sequence and structure, physically and functionally similar mechanical parts may have evolved as nature's design strategy for these molecular engines.

Structural Memory in the Contractile Ring Makes the Duration of Cytokinesis Independent of Cell Size

Cytokinesis is accomplished by constriction of a cortical contractile ring. We show that during the early embryonic divisions in C. elegans, ring constriction occurs in two phases--an initial phase at a constant rate followed by a second phase during which the constriction rate decreases in proportion to ring perimeter. Cytokinesis completes in the same amount of time, despite the reduction in cell size during successive divisions, due to a strict proportionality between initial ring size and the constant constriction rate. During closure, the myosin motor in the ring decreases in proportion to perimeter without turning over. We propose a "contractile unit" model to explain how the ring retains a structural memory of its initial size as it disassembles. The scalability of constriction may facilitate coordination of mitotic events and cytokinesis when cell size, and hence the distance traversed by the ring, varies during embryogenesis and in other contexts.

Network Formulations of Mixed-Integer Programs

We consider mixed-integer sets described by system of linear inequalities in which the constraint matrix A is totally unimodular; the right-hand side is arbitrary vector; and a subset of the variables is required to be integer. We show that the problem of checking nonemptiness of a set of this type is NP-complete, even in the case in which the linear system describes mixed-integer network flows with half-integral requirement on the nodes. This is in contrast to the case in which A is totally unimodular and contains at most two nonzeros per row. In this case, we provide an extended formulation for the convex hull of solutions whose constraint matrix is a dual-network matrix with an integral right-hand-side vector. The size of this formulation depends on the number of distinct fractional parts taken by the continuous variables in the extreme points of the convex hull of the given set. When this number is polynomial in the dimension of A, the extended formulation is of polynomial size. If, in addition, the corresponding list of fractional parts can be computed efficiently, then our result provides a polynomial algorithm for the optimization problem over these sets. We show that there are instances for which this list is of exponential size, and we also give conditions under which it is short and can be efficiently computed. Finally, we show that these results provide a unified framework leading to polynomial-size extended formulations for several generalizations of mixing sets and lot-sizing sets studied in the last few years.