Mathematical Models of Plant Morphogenesis

P ublic support for U.S. federal expenditures for basic research gained momentum with the science and technology breakthroughs that contributed to the Allies' victory in World War II. After World War II, the Korean and Cold Wars concentrated research appropriations in the Department of Defense (DOD). DOD research expenditures were massive from 1950 to 1990. They included not only direct investments in weapons and intelligence systems but support of the underlying science, centered in physical sciences and engineering. What is less well remembered today is that DOD's basic research investments were broadly based, ranging far beyond the physical sciences and engineering into the life and social sciences. Through its service research offices and the Advanced Research Projects agencies, DOD also fostered interdisciplinary research in promising new areas, such as computation, and developed new modes for the performance of research, as in university materials research laboratories. The large investment in the physical sciences also contributed indirectly to medical science and health care, giving rise to many technologies used today. The life sciences now account for more than 50 percent of U.S. federal investment in basic research. Biomedical research funding has followed a pattern of steady significant growth over four decades, and the National Institutes of Health (NIH) have slowly come to dominate that funding. Today's strong federal support for the life sciences is warranted, because biomedical research is on the cusp of a revolution in preventative medicine and treatment. Nevertheless, today's overall research budget is increasingly out of balance. Federal funding of many fields in the physical sciences and engineering is down substantially since 1993 (9 to 36% in real terms in fields such as chemistry, physics, and electrical and chemical engineering). This loss, if continued, will imperil advances in these disciplines and endanger the continued flow of valuable discoveries and technologies that have been important to biomedical research and health care. National science and technology (S&T) policy over the past four decades has largely been led by physical scientists who first gained national experience in World War II. They crafted policies for broad investment in basic research and infrastructure, including the life sciences. As we enter the 21st century, biological scientists must assume broader leadership responsibilities in S&T policy, and they must speak out about the importance of support for all disciplines, including the physical sciences and engineering. NIH's Harold Varmus and the National Science Foundation's Rita Colwell recognize the imbalance in the current federal research portfolio and have begun advocating increased investment in all areas of research. Their leadership is to be commended, but it is not enough. Government, organizations, institutions, and industry can and should do more to bolster all basic research. NIH must set the example by much more broadly supporting innovative interdisciplinary research embracing all science, just as DOD did when it was the prime funder of R&D. Some of this has already begun in NIH's cross-institute bioengineering initiative and in prospective increased NIH support of information technology for biocomputation. Similar initiatives should be launched in other areas of the physical sciences and in the social and behavioral sciences. Funding for these initiatives should become a much larger percentage of NIH's overall expenditures. The life science professional societies must speak broadly for basic research and not just argue their own disciplinary cases. Disease advocacy groups must also articulate the case for the physical sciences in their work with the public and before Congress. University leaders and corporate executives must make the case for investment in all research disciplines. Most of all, biologists in the laboratory—working scientists and their students—need to appreciate that their research rests on the legacy not only of the life sciences but also the physical and other sciences. Today's life scientists and the next generation they are training must be the national leaders of the future who will increasingly guide all of U.S. basic research policy in the 21st century.

SummaryBecause of their large sizes and simple shapes, giant‐celled algae have been used to study how the structural and mechanical properties of cell walls influence cell growth. Here we review known relationships between cell wall and cell growth properties that are characteristic of three representative taxa of giant‐celled algae, namely, Valonia ventricosa, internodal cells of characean algae, and Vaucheria frigida. Tip‐growing cells of the genus Vaucheria differ from cells undergoing diffuse growth in V. ventricosa and characean algae in terms of their basic architectures (non‐lamellate vs. multilamellate) and their dependence upon pH and Ca2+ for cell wall extensibility. To further understand the mechanisms controlling cell growth by cell walls, comparative analyses of cell wall structures and/or associated growth modes will be useful. The giant‐celled algae potentially serve as good models for such investigations because of their wide variety of developmental processes and cell shapes exhibited.

Numerous studies deal with composition and molecular processes involved in primary cell wall formation and alteration in Arabidopsis. However, it still remains difficult to assess the relation between physiological properties and mechanical function at the cell wall level. The thin and fragile structure of primary cell walls and their large biological variability, partly related to structural changes during growth, make mechanical experiments challenging. Since, to the best of our knowledge, there is no reliable data in the literature about how the properties of the fully elongated zone of hypocotyls change with age. We studied in a series of experiments on two different seed batches the tensile properties the region below the growth zone of 4 to 7 day old etiolated Arabidopsis hypocotyls. Additionally, we analysed geometrical parameters, hypocotyl density and cellulose content as individual traits and their relation to tissue mechanics. No significant differences of the mechanical parameters of the non-growing region between 5–7 day old plants could be found whereas in 4 day old plants both tensile stiffness and ultimate tensile stress were significantly lower than in the older plants. Furthermore hypocotyl diameters and densities remain almost the same for 5, 6 and 7 day old seedlings. Naturally, hypocotyl lengths increase with age. The evaluation whether the choice–age or length—influences the mechanical properties showed that both are equally applicable sampling parameters. Additionally, our detailed study allows for the estimation of biological variability, connections between mechanics and hypocotyl age could be established and complement the knowledge on biochemistry and genetics affecting primary plant cell wall growth. The application of two different micromechanical devices for testing living Arabidopsis hypocotyls allows for emphasizing and discussing experimental limitations and for presenting a wide range of possibilities to address current and future questions related to plant cell wall mechanics, synthesis and growth in combination with molecular biology methodologies.

Study of the cell wall growth in Bacillus megaterium by pulse-labeling a DAP- Lys- mutant with tritiated diaminopimelic acid (DAP) had revealed the presence of intracytoplasmic radioactivity. The nature of this radioactivity was studied on one hand by autoradiographic analysis of bacteria treated in different ways and on the other hand by chromatography of the radioactive compounds extracted with boiling water. It is shown that cytoplasmic radioactivity corresponds neither to free DAP nor to DAP metabolized into lysine, but to murein precursors. Autoradiographic analysis of bacteria in which all murein precursors were removed gives exactly the same cell wall growth pattern as the one previously obtained for untreated bacteria. It can be concluded that, in B. megaterium, cell wall elongation occurs by diffuse intercalation of newly synthesized murein along the cylindrical part of the cell wall and that only cross wall formation occurs in a precise growth zone.

At the end of the 19th century, an architectural style called Neomudéjar became quite popular in some areas of Spain. Very much like other historicist European styles in the same years, the Neomudéjar sought to recreate the local medieval architecture. The use of faced brick façades with complicated bonds -formed by stretchers and headers in and out the main wall plane- lead in term to a wide variety of results that resembled Arabic architecture. The brick façades of the Neomudéjar buildings are ideal case studies for the analysis of the local behaviour of masonry structures, especially regarding problems of stress concentration. There are several methods for studying the global behaviour of masonry structures – from the classic thrust line to the limit analysis tools – but, as the average stresses taken over by structural masonry elements are usually well below the compression strength of the constituent material, the classical methods of analysis are designed to verify only the global stability. Local behaviour, on the other hand, is quite elusive, especially when the properties of the material are uncertain. In such cases stress concentrations might appear, resulting on stress currents and low stress islets. A particular case of these phenomena occurs in the bonding of Neomudéjar façades. Local concentration of stresses is especially likely in these bonds, given the peculiar relative position of some bricks with respect to others. The paper proposed will use one of these buildings, the Aguirre Schools (Rodríguez Ayuso, Madrid, 1886), as a case study to evaluate local behaviour. Starting from a geometrical hypothesis of the internal distribution of the material based on recent photogrammetric surveys, and using conventional software of parametric design, the paper will describe a numerical model based on a non-deterministic random algorithm, although limited in its number of solutions, to discuss later the validity and scope of them. The limitations of the standard hardware in which these design tools are usually handled will also be considered in the discussion.

BACKGROUNDIn the molecular era, the Laurén system is still a cost-effective and widely implemented classification for gastric cancer (GC) and it has been recently associated with clinical, histological and molecular features of these tumors. Despite recent advances in the understanding of the molecular biology of GC, there is a need to develop new prognostic tools for patient stratification in clinical practice. Thus, the identification of easily available prognostic factors in patients with intestinal and diffuse-type tumors can significantly improve risk assessment and patient stratification in GC.AIMTo identify clinicopathological differences, risk factors, and to develop cost-effective prognostic scores for patients with intestinal and diffuse-type GC.METHODSRetrospective study of all patients undergoing surgery for GC at a tertiary referral center from 2001 to 2019. 286 cases met inclusion criteria (intestinal: 190, diffuse: 96). Clinical data and gross findings were collected. All specimens were reviewed by two independent pathologists and a detailed protocol for histologic evaluation was followed. Five tissue microarrays (TMAs) were constructed and sections of the TMA block were immunostained for HERCEPTEST, MSH2, MSH6, MLH1 and PMS2. Statistical analyses were performed and prognostic scores were developed based on hazard ratios.RESULTSIntestinal and diffuse-type GC showed different epidemiological, clinicopathological and prognostic features. Diffuse tumors were significantly associated with younger age, less symptomatology, flat morphology, deeper invasion, perineural infiltration, advanced stage at diagnosis, administration of adjuvant therapy and poorer prognosis. Intestinal lesions were fungoid or polypoid, showed necrosis, desmoplasia, microsatellite instability and HERCEPTEST positivity and were diagnosed at earlier stages. Tumor depth, desmoplasia, macroscopic type and lymph node involvement were independently related to the Laurén subtype. Furthermore, intestinal and diffuse GC were associated with different risk factors for progression and death. Vascular invasion, perineural infiltration and growth pattern were important prognostic factors in intestinal-type GC. On the contrary, tumor size and necrosis were significant prognosticators in diffuse-type GC. Our recurrence and cancer-specific death scores for patients with intestinal and diffuse-type GC showed an excellent patient stratification into three (diffuse GC) or four (intestinal) prognostic groups.CONCLUSIONOur findings support that Laurén subtypes represent different clinicopathological and biological entities. The development of specific prognostic scores is a useful and cost-effective strategy to improve risk assessment in GC.

Scum actinomycetes in sewage treatment plants—Part 1: Growth kinetics of Nocardia amarae in chemostat culture

Irreversible cell enlargement begins with cell wall loosening which induces wall stress relaxation, leading to cell water uptake and cell enlargement. Growing cell walls consist of a cohesive network of cellulose microfibrils embedded in hydrophilic pectins and cellulose‐binding hemicelluloses. Models of the growing cell wall are provisional hypotheses about how these wall polymers interact to make a strong yet extensible wall. Recent results clarify how wall strength, plasticity and elasticity depend mostly on the stretching, straightening and sliding of cellulose microfibril networks in the wall. Passive sliding of cellulose microfibrils is facilitated by nonenzymic proteins named expansins while various enzymes modify pectins and hemicelluloses, altering their interactions with each other and with cellulose. Growth cessation is correlated with reduced expression of genes that promote wall loosening as well as changes in the direction of cellulose deposition and the structure of matrix polysaccharides, leading to a less extensible cell wall. Key Concepts Irreversible cell enlargement is an essential aspect of plant growth and morphogenesis. Surface enlargement of the cell wall may be highly localised, as in tip‐growing cells, or more evenly distributed over the cell wall surface, a ‘diffuse growth’ pattern common to most cells in the plant body. Cells typically enlarge substantially after they leave the meristem and before they differentiate into mature cells. Cell growth entails simultaneous uptake of water into the cell and irreversible expansion of the cell wall. In physical terms, growth begins with molecular loosening of the cell wall which leads to wall stress relaxation ; this creates the water potential difference needed for water uptake by the cell, resulting in physical enlargement of the cell. The growing cell wall is composed of a strong noncovalent network of cellulose microfibrils embedded in highly hydrated pectins and hemicelluloses that comprise the soft wall matrix. The tensile (in‐plane) mechanics of growing walls is largely determined by the behaviour of the cellulose microfibril network while pectins influence the indentation (out‐of‐plane) mechanics. Growing plant cell walls typically enlarge more rapidly at low pH (called ‘acid growth’), a process that is mediated by nonenzymatic proteins named α‐expansins; α‐expansins facilitate the passive sliding of a network of cellulose microfibrils in response to tensile wall stresses originating from cell turgor pressure. Deposition of new polymers to the wall is usually coordinated with surface expansion, but these are separable processes. Several classes of enzymes modify the structure of pectins and hemicelluloses in the cell wall, potentially affecting cell wall structure and mechanics. Cell wall mechanical properties are complex, encompassing a number of different physical behaviours that often are not well correlated with each other or with cell wall growth. Cessation of cell enlargement likely involves multiple processes, including changes in the direction of cellulose deposition, stiffening of cellulose and matrix networks, and reduced expression of wall loosening proteins.

Actin homologues of the MreB family have an important role in specifying the morphology of many non-spherical eubacteria. The mreC and mreD genes have been implicated in control of cell morphology but their precise functions are unknown. In Bacillus subtilis the MreB homologue Mbl directs helical insertion of new cell wall material in the cylindrical part of the rod-shaped cell. Depletion of either MreC or MreD abolishes the control of cell shape. In the presence of high concentrations of magnesium cells depleted of MreC or MreD can be propagated indefinitely, although they have a spheroidal shape. We show that growth of the spheroidal mutants is based on insertion of new wall material at cell division sites and that this localized growth is dependent on cell division. Under some conditions the MreC and MreD proteins localize in a helical configuration. This localization pattern resembles that of the helical cables of Mbl protein. These results suggest that MreC and MreD act in a morphogenic pathway that couples the helical cytosolic Mbl cables to the extracellular cell wall synthetic machinery, which is critical for cylindrical elongation of the rod-shaped cells.

3D Microscopy of Rod-Shaped Bacteria Reveals Roles of MreB in Diameter Control and Center-Line Curvature

Three areas where time-independent disorder plays a key role in biological dynamics far from equilibrium are reviewed. We first discuss the anomalous localization dynamics that arises when a single species spreads in space and time via diffusion and fluid advection in the presence of frozen heterogeneities in the growth rate. Next we treat the unzipping of double-stranded DNA as a function of force and temperature, a challenge that must be surmounted every time a cell divides. Heterogeneity in the DNA sequence dominates the physics of single-molecule force-extension curves for a broad range of forces upon approaching a sharp unzipping transition. The dynamics of the unzipping fork exhibits anomalous drift and diffusion in a similar range above this transition, with energy barriers that scale as the square root of the genome size. Finally, we describe how activated peptidoglycan strand extension sites, called dislocations in materials science, can mediate the growth of bacterial cell walls. Enzymatically driven circumferential motions of a few dozen of these defects are sufficient to describe the exponential elongation rates observed in experiments on Escherichia coli in a nutrient-rich environment. However, long-range elastic forces transmitted by the peptidoglycan meshwork cause the moving dislocations to interact not only with each other, but also with a disorderly array of frozen, inactivated strand ends.

Formation, growth and regeneration of incomplete cell wall in spheroplasts of the blue-green algaAnacystis nidulans in liquid media

Cellulose and xyloglucan (XG) assemble to form the cellulose/XG network, which is considered to be the dominant load-bearing structure in the growing cell walls of non-graminaceous land plants. We have extended the most commonly accepted model for the macromolecular organization of XG in this network, based on the structural and quantitative analysis of three distinct XG fractions that can be differentially extracted from the cell walls isolated from etiolated pea stems. Approximately 8% of the dry weight of these cell walls consists of XG that can be solubilized by treatment of the walls with a XG-specific endoglucanase (XEG). This material corresponds to an enzyme-susceptible XG domain, proposed to form the cross-links between cellulose microfibrils. Another 10% of the cell wall consists of XG that can be solubilized by concentrated KOH after XEG treatment. This material constitutes another XG domain, proposed to be closely associated with the surface of the cellulose microfibrils. An additional 3% of the cell wall consists of XG that can be solubilized only when the XEG- and KOH-treated cell walls are treated with cellulase. This material constitutes a third XG domain, proposed to be entrapped within or between cellulose microfibrils. Analysis of the three fractions indicates that metabolism is essentially limited to the enzyme-susceptible domain. These results support the hypothesis that enzyme-catalyzed modification of XG cross-links in the cellulose/XG network is required for the growth and development of the primary plant cell wall, and demonstrate that the structural consequences of these metabolic events can be analyzed in detail.

In the preparation for missions to Mars, basic knowledge of the mechanisms of growth and development of living plants under microgravity (micro-g) conditions is essential. Focus has centered on the g-effects on rigidity, including mechanisms of signal perception, transduction, and response in gravity resistance. These components of gravity resistance are linked to the evolution and acquisition of responses to various mechanical stresses. An overview is given both on the basic effect of hypergravity as well as of micro-g conditions in the cell wall changes. The review includes plant experiments in the US Space Shuttle and the effect of short space stays (8–14 days) on single cells (plant protoplasts). Regeneration of protoplasts is dependent on cortical microtubules to orient the nascent cellulose microfibrils in the cell wall. The space protoplast experiments demonstrated that the regeneration capacity of protoplasts was retarded. Two critical factors are the basis for longer space experiments: a. the effects of gravity on the molecular mechanisms for cell wall development, b. the availability of facilities and hardware for performing cell wall experiments in space and return of RNA/DNA back to the Earth. Linked to these aspects is a description of existing hardware functioning on the International Space Station.

Elasticity, plasticity and fine structure of plant cell walls