Faculty of Science

RESEARCH Newsletter

Volume 14 No 1 June 2010

For more information on the publications, please contact Assoc Prof Loh Kian Ping (email: scilohkp@nus.edu.sg) or Ms Lim Ghim Pheng, Belinda (scilgpb@nus.edu.sg) at the Dean’s Office, Faculty of Science, National University of Singapore.

Faculty of Science research Newsletter is a publication of

Content

O1Adverse Drug-Drug Interactions in Cancer Patients

Dr Nancy Ko Yu, Department of Pharmacy

O3Trans-Ethnic Analyses in the Genetics and Genomics of Common PhenotypesAssoc Prof. Teo Yik Ying, Department of Statistics & Applied Probability

06Supersymmetric Surface Operators and Four-Manifold TheoryDr Tan Meng Chwan, Department of Physics

08Charge Transport and Rectification in SAM-Based JunctionsDr Christian A. Nijhuis, Department of Chemistry

11 Nuclear Mechanics and Genome RegulationAssoc Prof. G.V. Shivashankar, Department of Biological Sciences

13Numerical Methods for Incompressible Viscous Fluid and Fluid Structure InteractionDr Liu Jie, Department of Mathematics

Academic Profile:Dr. Nancy Ko obtained her B.Sc. in Pharmacy from the National Taiwan University and holds a Masters degree in Pharmacy Administration from the University of Illinois at Chicago. She received her Ph.D. in Pharmaceutical Economics, Policy, and Outcomes Research with a minor in Educational Psychology from the University of Arizona. She is a founding member and committee officer of the currently forming Singapore Chapter of the International Society of Pharmacoeconomics and Outcomes Research (ISPOR) and is collaborating with local pharmacists and other health care providers on several research projects that aim to improve the safety and cost-effectiveness of drug use in Singapore.

Research Interests:

• Pharmacoeconomics

• Healthservicesresearch

• Drugutilizationreview

• Psychometrics

Contact Details:Department of PharmacyNational University of SingaporeBlock S4, 18 Science Drive 4Singapore 117543

Office : S4A-01-07Telephone : (65) 6516 4182Email : phakyn@nus.edu.sg

Adverse Drug-Drug Interactions in Cancer PatientsDr. Nancy Ko Yu,Department of Pharmacy

DRUGDEX.2 Among the 184 DDIs examined, only 31.0% were listed in both compendia, 46.7% were listed in Micromedex only, and 15.2% were listed in DIF only. In addition, as shown in Table 1, the comparative assessment between the two compendia showed inconsistency in the severity and scientific ratings of the DDIs examined.

At present, the frequency with which these identified interacting drug combinations are actually prescribed in practice as well as their clinical impact is little understood and needs further investigation. Previous studies of the prevalence of DDI prescribing have been conducted mostly in general or elderly patients. Cancer patients, however, despite their particularly high risk for DDIs, have not been as frequently studied. The findings of the few DDI studies on cancer patients suggest that interacting drug combinations are commonly prescribed and usually involve medications for co-morbid conditions.3-6 An estimated 27 to 63 percent of the cancer patients studied were exposed to potential DDIs of varying severity.4-6 In the literature, most studies of DDIs examined the occurrence of DDIs in prescriptions only, while little attempt has been made to determine how often these interactions actually caused clinically important adverse effects. As reported by a recent systematic review of DDIs in oncology, most published data on interactions between chemotherapy and non-chemotherapy agents came from small clinical trials and case series, and very limited data exist on the frequency and clinical consequences of the DDIs.7

Considering the high risk and potential adverse clinical impact of DDIs on cancer patients and the paucity of literature on this topic, with the collaboration of oncologists (Dr. Yong Wei Peng at NUH and Dr. Ng RaymondChee Hui at NCC) and clinical pharmacists (Dr. Alexandre Chan at NCC and Ms Lim Siew Woon at NUH), I am working on a NationalMedical Research Council (NMRC)-funded study that aims to shed light on the existence and extent of DDI prescribing in oncology practice in Singapore with a focus on OAAs. In addition, the findings of this ongoing study can advance our understanding of the presence and likelihood of clinical consequences resulting from DDIs, which, in the short term, could help physicians recognize potentially dangerous drug combinations and aid them in weighing the benefits and risks of prescribing these drug pairs. In the long run, the evidence established and knowledge gained can be used to develop or refine prescribing guidelines or electronic drug alerts in computerized physician order entry systems, with the ultimate goal of protecting patients from DDI-associated harm.

INTRODUCTION

Medication is a two-edged sword. Despite its positive and potentially life-saving

effects, medical drugs can harm or even kill when used inappropriately. A main research area of mine, in addition to pharmacoeconomics and outcomes research, is to investigate an important but sometimes overlooked drug-related problem in clinical practice: drug-drug interactions (DDIs).

In Singapore, cancer is the number one killer; about one in four individuals dies of cancer. There were more than 8,000 incident cancers each year between 2002 and 2006. DDIs are of particular concern in cancer patients because of their narrow therapeutic indices and the inherent toxicity of antineoplastic agents. Moreover, cancer patients are at considerable risk for DDIs because most cancer patients are over 65 years old and, consequently, are more likely to have age-related organ dysfunction and co-morbid conditions that require multiple medications. These patients also undergo multi-drug chemotherapy regimens and typically take supportive care medications, such as antiemetics, analgesics, and anti-infective agents, further increasing their risk for DDIs. This is an important problem, particularly in Singapore, because the percentage of the population considered to be elderly is expected to increase from 7.2% to 18.4% by the year 2030.

With the recent increase in the number of oral anticancer agents (OAAs) being introduced in the market, there has been a paradigm shift in cancer treatment from intravenous (IV) to oral therapy.1 Compared to IV therapy, oral treatment offers greater convenience by increasing flexibility in location and timing of administration.1 In addition, OAAs give patients a greater sense of control over their own treatments. Despite these benefits, the DDIs involving OAAs are still a major concern in oncology practice due to the drugs’ narrow therapeutic indices and the potential for lethal adverse effects.

While identifying potential DDIs is essential in pharmaceutical therapy, unfortunately, no one list of DDIs is agreed-upon, nor is there a consensus of which DDIs are usually clinically significant. Recognizing the high risk and significant impact of DDIs in cancer patients and the need for a better understanding of this problem, my colleagues and I created drug profiles for a list of DDIs involving 28 OAAs based on primary and tertiary literature reviews; we also evaluated the agreement between two commonly used DDI compendia: Drug Interaction Facts (DIF) and Micromedex

Dr. Nancy Ko Yu

1

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Table 1. Classification of DDIs based on severity and scientific evidence in DIF and MicromedexSeverity Ratings

MicromedexDIF

Major Moderate Minor

Contraindicated/major 18.2% 13.6% 0%

Moderate 10.6% 53.0% 0%

Minor 0% 1.5% 3.0%

Scientific Ratings

MicromedexDIF

Established Probable/ Suspected/

Possible

Unlikely

Excellent 1.5% 18.2% 0%

Good/fair/poor 7.6% 72.7% 0%

Unlikely 0.% 0% 0%

(Table extracted from Wong CM, Ko Y, Chan A. 20082)

References

1. Aisner J. Overview of the changing paradigm in cancer treatment: oral chemotherapy. Am J HealthSystPharm2007;64(9Suppl5):S4-7.

2. Wong CM, Ko Y, Chan A. Clinically significant drug-drug interactions between oral anticancer agents and nonanticancer agents: profiling and comparison of two drug compendia. Ann Pharmacother 2008;42:1737-48.

3. Riechelmann RP. Drug combinations with the potential to interact among cancer patients. Support Care Cancer 2007;15:1113-4.

4. Riechelmann RP, Moreira F, Smaletz O, Saad ED. Potential for drug interactions in hospitalized cancer patients. Cancer Chemother Pharmacol 2005;56:286-90.

5. Riechelmann RP, Tannock IF, Wang L, Saad ED, Taback NA, Krzyzanowska MK. Potential drug interactions and duplicate prescriptions among cancer patients. J Natl Cancer Inst 2007; 99:592-600.

6. Riechelmann RP, Zimmermann C, Chin SN, et al. Potential drug interactions in cancer patients receiving supportive care exclusively. J Pain Symptom Manage 2008;35:535-43.

7. Riechelmann RP, Saad ED. A systematic review on drug interactions in oncology. Cancer Invest 2006;24:704-12.

2

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Trans-Ethnic Analyses in the Genetics and Genomics of Common PhenotypesAssoc Prof Teo Yik Ying, Department of Statistics & Applied Probability

Genetics and genomics of modern biology

The advent of genetics and genomics began the digitization of modern biology, moving

from the observational and empirical nature of medicine and biology to a more deterministic nature of the science, where physical traits, disease risks and drug responses are expected to be predictable within mathematical quantification of confidence and uncertainty. Major international efforts and collaborations have collectively contributed resources and funding to understand the genetic composition of different organisms, which include humans1,2 and pathogens3-6. These resources have been vital in establishing the framework for the progression towards addressing intra-species genomic variation, which can be introduced due to different geography and environments creating differential evolutionary pressures to alter the genomes. Understanding these genomic differences between different populations of the same species is important, since these often underpin the diverse physical traits, dissimilar risks to diseases, and variations in drug responses that are exhibited across different populations of the same species.

Advent of genome-wide association studies

Inthehumanspecies,theInternationalHapMapProject was a landmark international effort in

exploring and quantifying human genomic variation at a considerably dense level across eleven diverse groups of people7-9, while the Human Genome Diversity Project (HGDP)surveyed the range of human genetic diversity across 52 different populations10. These projects yielded remarkable understanding of the extent of genomic variation across different populations, and information from these studies have been cleverly distilled and utilized in designing large-scale genetic scans that survey most of the genome simultaneously for variants that are associated with phenotypic variations11,12. By exploiting the patterns of correlation that exist in the human genome as a result of co-inheritance of neighbouring genomic regions, genome-wide association studies (GWAS) can examine up to 80% of the human genome for trait association with the latest genotyping technologies.

The advent of GWAS has revolutionized the strategies for investigating the genetic etiology of common diseases and complex traits, unveiling more sequence variants that segregate between individuals with different phenotypes in the past 30 months than the past 30 years combined13-

16. For example, almost 20 loci for obesity alone have been identified since 200717-22. This rapid discovery is expected to accelerate, as the costs of

Academic Profile:Assoc Prof Teo Yik Ying obtained his DPhil in Statistics from the University of Oxford, under the mentorship by Professor Peter Donnelly. He iscurrently an Associate Professor with the Department of Statistics & Applied Probability, and the Department of Epidemiology & Public Health at the National University of Singapore. He is alsoan Adjunct Visiting Group Leader at the Genome Institute of Singapore, Agency for Science, Technology and Research (A*STAR). Currently, he oversees the Singapore Genome Variation Project of which he also holds the Chair of the Analysis Team. He is also a member of the MalariaGenomic Epidemiology Network.

Research Interests:

• Statisticalgenetics

• Genome-wideassociationstudies

Contact Details:Department of Statistics & Applied ProbabilityBlk S16, Level 76 Science Drive 2National University of SingaporeSingapore 117546

Telephone : (65) 6516 2760Fax :(65)68723919Email : statyy@nus.edu.sg

TEO Yik Ying undertaking these genome-wide scans continue to decrease and the increasing size of the cohorts improves the statistical ability to identify genuine variants possessing smaller biological effects. However, GWAS fundamentally rely ondetecting indirect associations, where signals of trait association that emerged in GWAS are by themselves not functional, but instead situated in the locality of unassayed causal variants. There is thus the additional challenge of deconvoluting the association signals identified in the GWAS to localize the actual functional variants.

Fine-mapping the causal variants

There are three stages in a typical GWAS: (i) the genome is first screened for regions

of phenotypic association using commercial genotyping microarrays; (ii) signals of associations that emerged are surveyed in additional populations to verify the authenticity of the initial findings; (iii) validated regions that consistently displayed evidence of phenotypic association are fine-mapped to localize the causal variants. Progressing from the observed and validated signals of associations in GWAS to establishing the mechanisms of the disease or trait through fine-mapping can happen via two approaches: (i) re-sequencing, where every genetic position in a prescribed region is directly genotyped and tested directly for trait association; or (ii) in silico genotyping, which utilizes a dense set of reference data to statistically infer, or impute, the genetic composition of the samples at SNPs that are found in a reference set of data but are not actually assayed in the GWAS23. As each of the two strategies for fine-mapping has its own challenges, an alternative approach combines both re-sequencing and imputation. By first re-sequencing a handful of samples from the genome-wide study (say from the 1000 Genomes Project), a dense reference panel that is population-specific can be assembled for imputing against. A proof-of-concept for this integrated approach was exemplified in Jallow,TeoandSmalletal.(2009)24. In any of the approaches, ideally the functional polymorphism will emerge as the variant carrying the strongest signal.However,thepresenceoflongstretchesofLD can confound this process of fine-mapping.

Quandary of long LD

The presence of long-range LD implies a high probability that at least a few

SNPs on commercial microarrays used in GWAS will be in useful levels of LD with the unobserved causal variants. This increases the chance of successfully detecting genuine genotype-phenotype associations in the first stage of a GWAS (see Fig. 1a). However,long stretches of high LD imply a number

3

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Figure 2. LD of neighbouring SNPs around the focal SNP rs7754840 in the CDKAL1 gene in populations with European, Chinese, Malay and Asian Indian ancestries.

Figure 1. (a) shows the statistical evidence emerging from a GWAS (red circles); (b) shows the additional statistical evidence from additional SNPs observed from targeted re-sequencing (blue circles).

Trans-population fine-mapping

In general, LD tends to be more conserved in non-African populations, stretching over longer regions7,25,26. However, due to different anthropology and evolutionary history, patterns of LD variation may be substantially different between different populations. For

example, the gene CDKAL1 which was recently implicated in obesity and Type-2 diabetes in populations with European ancestry27-30 and a number of Asian populations31-34 was found to display strong signals of LD variations between multiple populations35. These dissimilar patterns of LD variation can be leveraged on to narrow the regions that are likely to contain the causal variant. In the example with CDKAL1, we show the example of how different SNPs were in high levels of LD in European, Chinese, Malay and Indian populations (see Fig. 2).

The availability of reference haplotype data across 1.7 million SNPs from the Singapore Genome Variation Project (SGVP)35, together with the data from the International HapMap Project7,8 mean there is a wealth of genomic resource for addressing the similarities and differences in patterns of LD across the human genome. Coupled with the availability of rich GWAS resources in Singapore across common human diseases like Type 2 diabetes, obesity, hypertension, myopia, dengue, cancer and others, there is vast potential for the development and application of trans-ethnic fine-mapping strategies to localize functional polymorphisms that are directly responsible for the diseases. The prospects of such trans-population strategy that rely on differing patterns of LD between populations were enhanced with the development of a novel statistical solution (by the applicant) for identifying genomic regions where LD differs significantly across populations36. This sets the stage for the development of a sophisticated statistical solution to combine the available information from dense reference data (from SGVP, HapMap and subsequently the 1000 Genomes Project) with validated GWAS signals to pinpoint the likely candidate causal variants. The proposed solution is likely to adopt at least a 2-stage process: (i) assessing the extent of LD variation around SNPs that are confirmed and validated to be carrying genotype-phenotype associations; (ii) when LD variation are substantially different (the definition of substantial difference will be part of the investigation by the project), trans-population variation in LD patterns can be leveraged on to fine-map the causal variants.

of neighbouring SNPs will be at high or perfect LD with the causal variant. This means association analysis with sequence-resolution genotype data is unlikely to distinguish which is the causal variant, as there will be a number of SNPs displaying statistical signals of similarly strong magnitude. This introduces a currently unresolved challenge in the third stage of GWAS (see Fig. 1b).

4

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

References

1. Venter JC, Adams MD, Myers et al. (2001) The sequence of the human genome. Science 291:1304-1351.

2. International HumanGenome Sequencing Consortium (2001) Initial sequencing and analysis of the human genome. Nature 409:860-921.

3. NCBI Influenza Virus Resource. http://www.ncbi.nlm.nih.gov/genomes/ FLU

4. Cole ST, Brosch R, Parkhill J et al. (1998) Deciphering the biology of Mycobacterium tuberculosis from the complete genome sequence.Nature393:537-544.

5. Gardner MJ, Hall N, Fung E et al. (2002) Genome sequence of the human malaria parasite Plasmodium falciparum. Nature 419:498-511.

6. Ghedin E, Sengamalav NA, Shumway M et al. (2005) Large-scale sequencing of human influenza reveals the dynamic nature of viral genome evolution. Nature 437:1162-1166.

7. InternationalHapMapConsortium(2005)A haplotype map of the human genome. Nature 437:1299-1320.

8. InternationalHapMapConsortium(2007)A second generation human haplotype map of over3.1millionSNPs.Nature449:851-861.

9. InternationalHapMapProjectPhase3: http://www.sanger.ac.uk/humgen/ hapmap3/

10. Rosenberg NA, Pritchard JK, Weber JL et al. (2002) Genetic structure of human populations.Science298:2381-2385.

11. Hirschhorn JN, Daly MJ (2005) Genome- wide association studies for common diseases and complex traits. Nat Rev Genet 6:95-108.

12. Wang WY, Barratt BJ, Clayton DG et al. (2005) Genome-wide association studies: theoretical and practical concerns. Nat Rev Genet6:109-118.

13. The Wellcome Trust Case Control Consortium (2007) Genomewide association study of 14,000 cases of seven common diseases and 3,000 shared controls. Nature 447:661- 678.

14. McCarthy MI, Abecasis GR, Cardon LR et al. (2008) Genome-wide association studies for complex traits: consensus, uncertainty andchallenges.NatRevGenet9:356-369.

15. Manolio TA, Brooks LD, Collins FS (2008) A HapMapharvestofinsightsintothegenetics ofcommondisease.JClinInvest118:1590- 1625.

16. Donnelly P (2008) Progress and challenges in genome-wide association studies in humans. Nature 456:728-731.

17. Scuteri A, Sanna S, Chen WM et al. (2007) Genome-wide association scan shows genetic variants in the FTO gene are associated with obesity related traits. PLoS Genet 3:1200-1210.

18. Dina C, Meyre D, Gallina et al. (2007) Variation in FTO contributes to childhood obesity and severeadultobesity.NatGenet39:724-726.

19. Frayling TM, Timpson NJ, Weedon MN et al. (2007) A common variant in the FTO gene is associated with body mass index and predisposes to childhood and adult obesity.Science316:889-894.

20. Loos RJ, Lindgren CM, Li S et al. (2008) Common variants near MC4R are associated with fat mass, weight and risk of obesity. Nat Genet 40:768-775.

21. WillerCJ,SpeliotesEK,LoosRJetal.(2009) Six new loci associated with body mass index highlight a neuronal influence on body weight regulation. Nat Genet 41:25- 34.

22. Meyre D, Delplanque J, Chevre JC et al. (2009)Genome-wide association study for early-onset and morbid adult obesity identifies three new risk loci in European populations.NatGenet41:157-159.

23. Marchini J, Howie B, Myers S et al. (2007) A new multipoint method for genome-wide association studies by imputation of genotypes.NatGenet39:906-913.

24. Jallow M, Teo YY, Small KS et al. (2009) Genome-wide and fine-resolution association analysis of malaria in West Africa.NatGenet[epub24thMay2009].

25. de Bakker PI, Burtt NP, Graham RR et al. (2006) Transferability of tag SNPs in genetic association studies in multiple populations. NatGenet38:1298-1303.

26. Pe’er I, de Bakker PI, Maller J et al. (2006) Evaluating and improving power in whole- genome association studies using fixed marker sets. Nat Genet 38:663-667.

27. Saxena R, Voight BF, Lyssenko V et al. (2007) Genome-wide association analysis identifies loci for type 2 diabetes and triglyceride levels. Science 316:1331-1336.

28. Scott LJ, Mohlke KL, Bonnycastle LL et al. (2007) A genome-wide association study of type 2 diabetes in Finns detects multiple susceptibility variants. Science 316:1341- 1345.

29. Steinthorsdottir V, Thorleifsson G, Reynisdottir I et al. (2007) A variant in CDKAL1 influences insulin response and risk of type 2 diabetes. Nat Genet 39:770- 775.

30. Zeggini E, WEedon MN, Lindgren CM et al. (2007) Replication of genome-wide association signals in UK samples reveals risk loci for type 2 diabetes. Science 316:1336-1341.

31. Liu Y, Yu L, Zhang D et al. (2008) Positive association between variations in CDKAL1 and type 2 diabetes in Han Chinese individuals. Diabetologia 51:2134-2137.

32. WuY, Li H, Loos RJ et al. (2008) Common variants in CDKAL1, CDKN2A/B, IGF2BP2, SLC30A8, and HHEX/IDE genes are associated with type 2 diabetes and impairedcastingglucose inaChineseHan population. Diabetes 57:2834-2842.

33. Ng MC, Park KS, Oh B et al. (2008) Implications of genetic variants near TCF7L2, SLC30A8, HHEX, CDKAL1, CDKN2A/B, IGF2BP2 and FTO in type 2 diabetes and obesity in 6,719 Asians. Diabetes 57:2226-2233.

34. TabaraY,OsawaH,KawamotoRetal.(2008) Replication study of candidate genes associated with type 2 diabetes base don genome-wide screen. Diabetes [epub: 25th Nov2008].

35. Teo YY, Sim X, Ong RTH et al. (2009) Singapore Genome Variation Project: A haplotype map of three South-East Asian populations. Genome Res (Accepted – In press).

36. TeoYY,FryAE,BhattacharyaKetal. (2009) Genome-wide comparisons of variation in linkage disequilibrium. Genome Res [epub 18thJune2009].

5

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Introduction

It has been about twenty years since the connection between Donaldson theory [1]

and twisted Yang-Mills theory with N = 2 supersymmetry in four-dimensions, was first elucidated by Witten in [2]. Since then, therehave been several important developments, especially on the physics side [3], which haveculminated in our present understanding of the Donaldson invariants of four-manifolds in terms of the “simpler” Seiberg-Witten monopole invariants[4,5].

The effort [4, 6] that led to this understanding,however, was partially motivated by a prescient structure theorem proved by Kronheimer and Mrowkain[7,8].Oneofthecentralingredientsintheir proof is this notion of ”ramified” Donaldson invariants; these invariants can be understood as extensions of the ordinary Donaldson invariants to four-manifold with embedded surfaces [9,10]. Such embedded surfaces can be physicallyinterpreted as two-dimensional analogs of the ‘t Hooftlineorloopoperator;theywerefirstusedin the physics literature to probe the dynamics of gauge theory and black holes. Despite the apparent versatility of these embedded surfaces, their physical and mathematical applications have been somewhat limited ever since, with the exception of a few examples.

Nevertheless, there has been a strong revival of interest in these objects following the recent workofGukovandWitten in [11]; intheirwork,generalizations of such embedded surfaces - coined thereafter as surface operators - were studied in the context of a four-dimensional N = 4 gauge-theoretic interpretation of the “ramified”geometric Langlands conjecture [12].Of late, these surface operators have also been analyzed in string theory, as well as in four-dimensional N = 2 gauge theories.

In light of these new developments, and the fact that the proof of the structure theorem by Kronheimer and Mrowka lies squarely on the use of such embedded surfaces, it was deemed timely and important that the analysis by Moore and Witten in [5] be generalized to includearbitrarily-embedded surface operators. This led totherecentworkoftheauthorin[13,14],andthe present article is a summary of the results which have appeared therein.

Surface Operators And Four-Dimensional Geometric Topology

By considering trivially and nontrivially-embedded supersymmetric surface

operators in an N = 2 theory with SO(3) gauge

Supersymmetric Surface Operators And Four-Manifold TheoryDr Tan Meng Chwan, Department of Physics

Dr Tan Meng Chwansymmetry on a compact, oriented, smooth four-manifold X, various seminal results in four-dimensional geometric topology can be shown to arise from the physics of electric-magnetic duality, U(1)R - invariance, spontaneous gauge symmetry breaking and localization onto supersymmetric configurations in twisted quantum field theories.

As a first example, Kronheimer and Mrowka proved that on four-manifolds which are technically “admissible”, a universal formula exists which identifies the “ramified” Donald-son invariants as the ordinary Donaldson invariants [7, 9, 10]. One can understand this remarkablemathematical result to be a consequence of electric-magnetic duality in the low-energy limit of the SO(3) theory: electric-magnetic duality in the corresponding low-energy U(1) theory over a generic region in moduli space asserts that the surface operators in the relevant Seiberg-Witten theory are necessarily ordinary; as such, the underlying topological invariance of a twisted version of the SO(3) theory then implies that its “ramified” high-energy correlation functions are equivalent to their ordinary low-energy counterparts from the twisted Seiberg-Witten theory; this equivalence reproduces exactly the universal formula of Kronheimer and Mrowka.

A second example would be the various minimal genus formulas for embedded surfaces in X which have been proved by Kronheimer-Mrowka and Ozsváth-Szabó in a series of seminal papers [7,8,15,16].Theseformulasaregeneralizationsofthe celebrated Thom conjecture which concerns the topology of complex curves embedded in CP2. Again, one can understand these formulas to be a consequence of the U(1)R - invariance of the correlation functions in the twisted N = 2 theory with SO(3) gauge symmetry: in order for the relevant correlation functions to be non-vanishing, the number of fermion zero-modes must match the respective dimensions of the moduli space of (“ramified”) instantons, that is, the U(1)R- anomaly must be cancelled; these matching conditions then translate to bounds on the genus of the surface operators which represent the embedded surfaces in the mathematical context.

Our third example would be certain identities obeyed by the ordinary Seiberg-Witten invariants of X as proved by Ozsváth and Szabó in[15,16].Theseidentitiescanbeshowntoarisefrom the ordinary limit of the relation between the correlation functions of the twisted SO(3) theory - which represent the “ramified” Donaldson invariants - and the correlation functions of the twisted Seiberg-Witten theory - which represent the “ramified” Seiberg-Witten invariants.

Academic Profile:Dr. Tan Meng Chwan, who was previously a Major with the Republic of Singapore Airforce, received his M.Sc and Ph.D degrees in theoretical physics from the National University of Singapore in 2003 and 2007, respectively. He was subsequentlyawarded the NUS-Overseas Postdoctoral Fellowship, and went on to the legendary Institute for Advanced Study in Princeton to do his postdoctoral training with his mentor and thesis examiner, Edward Witten, whom many regard as the greatest theoretical physicist to ever live. Thereafter, he went on to do his second postdoctoral training at the prestigious California Institute of Technology with yet another leading figure in the field, Anton Kapustin. In Jan 2010, he was appointed Assistant Professor in the Department of Physics, NUS.

Research Interests:

• StringTheory

• QuantumFieldTheory

• MathematicalPhysics

Contact Details:Department of PhysicsNational University of Singapore2, Science Drive 3, Singapore 117542

Telephone : (65) 6516 2604Email : phytmc@nus.edu.sg

6

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Surface Operators And Taubes’ Spectacular Result

Inaseriesoffourlongpaperscollectedin[17],C.H. Taubes showed that on any compact,

oriented, symplectic four-manifold X with b+ > 1, the ordinary Seiberg-Witten invariants are (up to a sign) equal to what is now known as the Gromov-Taubes invariants which count (with signs) the number of pseudo-holomorphic two-surfaces which can be embedded in X. This astonishing result - as formidable as its mathematical proof may be - nonetheless lends itself to a simple and concrete physical derivation that we shall now describe.

Let us consider the gauge group to be SU(2) instead of SO(3), that is, w2(E) = 0, where w2(E) is the second Stiefel-Whitney class of the SO(3)-bundle E. Due to the spontaneous breaking of gauge symmetry from SU(2) to U(1) at low-energies, and the electric-magnetic duality of the resulting U(1) theory, we find that the partition function in the sector where the corresponding dimension of the moduli space of “ramified” instantons is zero, can be identified as the Seiberg-Witten invariant SW(ŝ) determined by a particular basic class ŝ.

Because the path-integral in twisted quantum field theories localize onto supersymmetric configurations - these are “ramified” instantons in our case - the partition function will count (with signs) the number of solutions to the “ramified” instanton equation; in other words, it will count (with signs) the number of points in the zero-dimensional moduli space of “ramified” instantons. In the ordinary limit, each solution to the “ramified” instanton equation corresponds to a surface operator that is a pseudo-holomorphic curve whose fun-damental class is Poincaré-dual to the first Chern class c1 (L) of a complex line bundle L with self-dual connection; thus, the partition function is simply the Gromov-Taubes invariant Gr(c1 (L)) as defined mathematically by Taubes. Since the partition function can be identified as the Seiberg-Witten invariant determined by ŝ, we have SW(ŝ) = ±Gr(c1 (L)); this is just Taubes’ result.

Novel Mathematical Results From The Physics

Our physical setup goes further to suggest several novel mathematical results

which involve the (“ramified”) Donaldson and Seiberg-Witten invariants, and the Gromov-Taubes invariants.

Firstly, it can be shown - via an electric magnetic duality of a trivially-embedded “classical” surface operator - that the universal formula of Kronheimer and Mrowka can be generalized to hold for embedded surfaces with non-negative (as opposed to just positive) self-intersection.

Secondly, it can also be shown - via an electric-magnetic duality of a trivially-embedded “quantum” surface operator - that a Seiberg-Witten analog of the universal formula exists.In other words, a “ramified” Seiberg-Witten invariant of X - determined by a singular gauge field that picks up a nontrivial holonomy around a closed loop which links a trivially-embedded surface D⊂X - is equal to an ordinary Seiberg-Witten invariant of X.

Thirdly, via the Seiberg-Witten analog of the universal formula, one can deduce - via Taubes’ result derived earlier - that the Gromov-Taubes invariants are simply the “ramified” Seiberg-Witten invariants.

Last but not least, the intermediate computations in our physical derivation of Taubes’ result also suggest various identities among the Gromov-Taubes and Seiberg-Witten invariants. These identities can in turn be used to derive various important results about the Seiberg-Witten invariants of symplectic four-manifolds determined by the canonical basic class, and about the symplectic four-manifolds themselves.

Concluding Remarks

It is clear by now that there is a rich and deep connection between the physics of super-

symmetric surface operators in N = 2 gauge theory and the mathematics of four-manifold theory. One can certainly extend the present analysis to gauge groups of higher rank; the physical results would then indicate how Taubes’ result can be generalized accordingly. Other physical incarnations of Taubes’ result have also been proposed - albeit somewhat heuristically - via vortex strings in gauge theory[18]andthetopologicalGreen-Schwarzstring [19]; a close analogy with the physicsof superconductors has also been described in [20]. Itwould certainly be interesting andinsightful to unravel the connection between our story and these a priori unrelated physical interpretations of Taubes’ result.

2

References

1. S. Donaldson, \Polynomial Invariants For Smooth Four-Manifolds,” Topology 29(1990)257.

2. E. Witten, \Topological Quantum Field Theory,”Commun. Math. Phys. 117(1988)353.

3. N. Seiberg and E. Witten, “Monopole Condensation, And Confinement In N = 2 Supersymmetric Yang-Mills Theory,”

[arXiv:hep-th/9407087];Nucl.Phys.B426 (1994)19; “Monopoles, Duality and Chiral SymmetryBreaking in N=2 Supersymmetric QCD,”[arXiv:hep-th/9408099];Nucl.Phys.B431 (1994)484.

4. E. Witten, \Monopoles and Four-Manifolds”, Math.Res.Lett. 1:769-796,1994.

[arXiv:hep-th/9411102].

5. G. Moore and E. Witten, \Integration Over the u-plane in Donaldson Theory”,

Adv.Theor.Math.Phys. 1:298-387,1998. [arXiv:hep-th/9709193].

6. E. Witten, \Supersymmetric Yang-Mills Theory On A Four-Manifold”,

J.Math.Phys. 35:5101-5135,1994. [arXiv:hep-th/9403195].

7. P.B. Kronheimer and T.S. Mrowka, \Embedded Surfaces and the Structure of Donald-son’s Polynomial Invariants”, J. Differential Geom. Vol. 41, No. 3(1995),573-734.

8. P.B. Kronheimer and T.S. Mrowka, \Recurrence relations and asymptotics for four-manifold invariants”, Bull. Amer. Math. Soc. (N.S.) 30(1994)215-221.

9. P.B.KronheimerandT.S.Mrowka,“GaugeTheory for Embedded Surfaces: I”, Topology Vol. 32 (1993).

10. P.B. Kronheimer and T.S. Mrowka, “Gauge theory for embedded surfaces: II”, Topology 34 (1995)37-97.

11. S. Gukov and E. Witten, “Gauge Theory, Ramification, And The Geometric Lang-lands Program”, Current Developments in Mathematics Volume 2006 (2008), 35-180.

[arXiv:hep-th/0612073].

12. A. Beilinson and V. Drinfeld, “QuantizationOf Hitchin’s Integrable System And HeckeEigensheaves,”preprint(ca.1995),

http://www.math.uchicago.edu/arinkin/langlands/.

13. M.C. Tan, Integration Over The u-Plane In Donaldson Theory With Surface Operators, [arXiv:0912.4261].

14. M.C. Tan, “Supersymmetric Surface Operators And Four-Manifold Theory”, to appear.

15. P. Ozsváth, Z. Szabó, “The Symplectic Thom Conjecture”, Ann. of Math. (2) 151 (2000), no. 1, 93-124.[arXiv:math/9811087].

16. P. Ozsváth and Z. Szabó, “Higher Type Adjunction Inequalities in Seiberg-Witten Theory”, J. Di_erential Geom. Volume 55, Number 3(2000),385-440.[arXiv:math/0005268].

17. C.H. Taubes, “Seiberg-Witten And GromovInvariants For Symplectic 4-Manifolds”, International Press.

18. D. Tong, “Quantum Vortex Strings: A Review”,[arXiv:0809.5060].

19. J.Pawelczyk,“FromSeiberg-WittenInvariantsToTopological Green-Schwarz String”, Phys.Lett. B 415(1997)358-362,[arXiv:hep-th/9706134]

20. E. Witten, “From Superconductors And Four-Manifolds To Weak Interactions”, Bull. Amer. Math. Soc.44(2007),361-391.7

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Charge Transport and Rectification in SAM-Based Junctions Dr Christian A. Nijhuis,Department of Chemistry

Introduction

Molecular electronics originally promised that molecule(s) bridging two or more electrodes would generate electronic function, and overcome the scaling limits of conventional semiconductor

technology.1 So far, there have been no commercially successful electronic devices employing small molecules as the active element. The main reason for the lack of success of such devices in everyday life is that simple, reliable fabrication techniques are lacking. Most fabrication techniques involve the direct deposition of metal top-contacts on self-assembled monolayers (SAMs) on bottom-electrodes.2 During the deposition process of the top-contact, the incoming metal atoms and small clusters can react with, or (partially) penetrate, the SAMs.3 Other methods have been reported that use other approaches to introduce top-contacts, but these methods suffer from other inherent limitations.2 Consequently, physical-organic studies are lacking and the mechanisms of charge transport across molecular tunneling junctions are poorly understood. Indeed, many phenomena reported for molecular junctions were caused by properties independent on the chemical stuctrures inside the junctions due, for instance, metal filaments, or the presence of layers of metal oxides.4

Simple Test-Beds: Junctions with Liquid Metal Top-Electrodes

A test-bed for measuring charge transport across SAMs must full fill three criteria. i) The fabrication of the junctions must be easy and reliable, i.e., high yields, and stable, good quality of the junctions. ii)

Statistically large numbers of data must be generated to account for defects (all SAM-based junctions have defects due to impurities, surface roughness of the electrodes, defects in the SAMs, etc.). iii) Physical-organic studies must be possible, i.e., the fabrication technique must be compatible with a wide range of molecular structures. To avoid the problems associated with direct metal deposition, Whitesides et al. developed techniques to contact SAMs on Au or Ag bottom-electrodes with liquid metal top-electrodes,i.e.,Hgoreutecticgalliumindium(EGaIn,mp.15.7ºC).5,6 EGaIn has three characteristics that makes it an attractive material to form top-contacts with. EGaIn is i) a low-toxicity material and is commercially available, ii) electrically conductive (the resistivity and work function are similar to that of Ag),andiii)moldable,thatis,EGaIncanbemolded,unlikeHg,intonon-sphericalshapes.

Figure 1 shows that cone-shaped tips of EGaIn suspended from a syringe can be fabricated by simply pulling out a syringe of a drop of EGaIn. In a second step, this tip of EGaIn can be used to contact a metal substrate with a SAM to complete the tunneling junction. The whole process takes about 60 s. These junctionsarestable forhours,givehighyieldsofworkingdevices (70-90%),andareuseful tocollect large numbers of data obtained from large numbers of junctions. Typically, to collect 100 – 1000 current-voltage curves from 40 – 50 junctions prepared with SAMs formed on 5 – 10 substrates takes one day.

Dr Christian A. Nijhuis

Academic Profile:Dr. Christian A. Nijhuis received his Masters degree in Chemistry from the University of Groningen in 2002, and Ph.D. degree from University of Twente in 2006 with “Cum Laude” (top 5%). Under the direction of Professor David N. Reinhoudt, his doctoral thesis included studies on the surface chemistry of supramolecular assemblies and their use in bottom-up nano-fabrication. He receivedthe Simon Stevin Research award from the Netherlands Organization for Scientific Research (NWO) in 2006 to conduct overseas research. In the group of Professor George M. Whitesides, as a postdoctoral research fellow, he developed a platform for measurements of charge transport across layers that are one molecule thick. In 2010, he received the NRF research fellowship and he joined the Department of Chemistry at the NUS asanAssistantProfessor.Hecurrentlyuses bottom-up nanofabrication techniques to construct self-assembled nano-electronic devices to open up and to solve key problems in physics.

Research Interests:

• Molecularelectronics

• Bottom-upnano-fabrication

• Surfacechemistry

• Supramolecularchemistry

• Electrochemistry

• Synthesis

Contact Details:Department of ChemistryNational University of SingaporeBlockS7,level4,room9,3 Science Drive 3,Singapore 117543

Telephone : (65) 6516 2667Email : chmnca@nus.edu.sg

Figure 1: A series of photographs of the formation of a conical tip of EGaIn. From left to right: A micromanipulator 1) brings a drop of EGaIn suspended from the needle of a syringe into contact with the bare, reflective surface of an Ag film, and 2) raises the syringe until the EGaIn separates into a conical tip (which remains attached to the needle of the syringe) and a drop on the Ag surface. The pictures are sequential and show the formation of a single tip; the time spanned by this sequence is less than 5 s.

8

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

These junctions, with the EGaIn-tip suspended from a syringe, do not make it possible to conduct measurements as a function of temperature. Such measurements are required to obtain information about the mechanisms of charge transport across SAMs. Figure 2 shows optical micrographs of arrays of tunneling junctions with EGaIn top-electrodes stabilized in micro-channels in a transparent polymer (polydimethylsiloxane, PDMS).7 Figure 2 also shows a schematic presentation of an ideal junction, but in reality these junctions will have defects. These devices, with working junctions in 70-90%yield,arestableforweeks,withstandeverydayhandlinginthelab,andaresuitableforconductingmeasurementsatlowtemperatures,andto do so with statistically large numbers of data (N = 100 – 1000) to account for the defects inside them.

New Physics: Organometallic Molecular Rectification

Tunneling junctionswith SAMs of S(CH2)11Fc (Fc = ferrocene) rectified current, that is, they acted like diodes and only passed current in one directionofbias,butjunctionswithSAMofS(CH2)n-1CH3 (n = 12, 14, 16, or 18) did not rectify (Fig. 3). Thus, these junctions are molecular rectifiers

with a rectification ratio (|J(-1.0 V)|/|J(1.0 V)| where |J(V)| is the absolute value of current density as a function of voltage, V) of 128 (determined using 997J(V)-curves) with a log-standard deviation of 3.3, and with a yield of 87% in working junctions. The rectification is caused by the molecules inside the junctions and not by any other asymmetries of the junctions.6

These devices make it possible to conduct temperature dependent measurements and to perform detailed physical-organic studies.8 These studies revealed that the observed large rectification ratios (> 1.0 × 102) originate from a change in the mechanism of charge transport that is dependent on the applied bias (Fig. 3). Theoretical studies, however, claimed that molecules can not rectify with rectification ratios larger than ~20.9 In addition, in 1974AviramandRatner10 proposed molecular rectifiers for the first time, and since then, a large number of attempts have been made to fabricate devices with these proposed molecular rectifiers. To date, it could not be shown unambiguously that the rectification in those studies (often with rectification ratios less than 10) was molecular in origin, statistically significantly different from 1 (no rectification), and/or followed the mechanism as proposed by Aviram and Ratner.11 Thus, these SAM-based tunneling junctions resolved the longstanding question whether molecules can rectify currents and that the Aviram-Ratner mechanism is not required to achieve rectification.

Figure 2: A and B) Optical micrographs of the arrays of metal–SAM//EGaIn junctions. A micro-channel in PDMS is aligned perpendicularly to the Ag electrodes. Filling the channel with EGaIn, by applying vacuum at the outlet while a drop of EGaIn is present at the inlet, completes the fabrication of the SAM-based junctions. C) An idealized schematic representation of a junction with a SAM of SC11Fc. In reality, these junctions will have defects due to surface roughness of the electrodes, defects in the SAM, etc.

Figure 3: A) Average traces of the absolute value of the current density, |J|, plotted vs. applied voltage for all AgTS-SC11Fc//Ga2O3/EGaIn junctions (53 junctions, 977 traces), and AgTS-SC11//Ga2O3/EGaIn junctions (23 junctions, 415 traces); B) Histograms of R for AgTS-SC11Fc//Ga2O3/EGaIn junctions (53 junctions and 997 traces, R = J(-1V)/J(+1V)), and AgTS-SC10CH3//Ga2O3/EGaIn junctions (23 junctions and 415 traces); C) four J(V) curves of a AgTS-SC13CH3//EGaIn junction measured at four different temperatures (T = 110, 190, 250, and 293 K) in vacuum (1 × 10-6 bar). The J(V) curves do not depend on the temperature which is consistent with tunneling as the mechanism of charge transport; D) three J(V) curves of a AgTS-SC11Fc//EGaIn junction measured at three different temperatures in vacuum (1 × 10-6 bar). The J(V) curves only change at negative bias, but not at positive bias. This chance indicates that hopping dominates the mechanism of charge transport only at negative bias, while tunneling dominates at positive bias.

9

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Conclusions and OutlookThe two methods described here for the fabrication and characterization of SAM-based junctions solve many of the issues in molecular electronics and come close to the goal of developing a test-bed for studying charge transport across SAMs. Such test-beds are necessary to discriminate artifact from real data and to obtain the mechanisms of charge transport across SAMs. These techniques are potentially useful to measure the electronic properties of a much wider range of nanostructures, e.g., nanaparticles, thin polymer films, biomolecules, etc. The fact that these molecular diodes change the mechanism of charge transport in a two-terminal device in only one direction of bias, but not in the other, could also be useful in the design of other molecular-based devices.

References

1. Collier,C.P.;Wong,E.W.;Belohradsky,M.;Raymo,F.M.;Stoddart,J.F.;Kuekes,P.J.;Williams,R.S.;Heath,J.R.Science 1999,285,391.

2. Akkerman,H.B.;deBoer,B.J. Phys.: Condens. Matter 2008, 20, 013001.

3. Fisher,G.L.;Walker,A.V.;Hooper,A.E.;Tighe,T.B.;Bahnck,K.B.;Skriba,H.T.;Reinard,M.D.;Haynie,B.C.;Opila,R.L.;Winograd,N.;Allara,D.L.J. Am. Chem. Soc. 2002, 124, 5528.

4. Beebe, J. M.; Kushmerick, J. G. Appl. Phys. Lett. 2007, 90, 083117.

5. Chiechi, R. C.; Weiss, E. A.; Dickey, M. D.; Whitesides, G. M. Angew. Chem. Int. Ed. 2008, 47, 142.

6. Nijhuis, C. A.; Reus, W. F.; Whitesides, G. M. J. Am. Chem. Soc. 2009, 131, 17814.

7. Siegel,A.C.;Tang,S.K.Y.;Nijhuis,C.A.;Hashimoto,M.;Phillips,S.T.;Dickey,M.D.;Whitesides,G.M.Acc. Chem. Res. 2010, 43, 518.

8. Nijhuis, C. A.; Reus, W. F.; Barber, J.; Dickey, M. D.; Whitesides, G. M. submitted.

9. Stadler,R.;Geskin,V.;Cornil,J.J. Phys.: Condens. Matter. 2008, 20, 374105.

10. Aviram, A.; Ratner, M. A. Chem. Phys. Lett. 1974, 29, 277.

11. Metzger, R. M. Chem. Rev. 2003, 103, 3803.

10

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Nuclear Mechanics and Genome RegulationAssociate Professor G.V.Shivashankar,Department of Biological Sciences

promoter sequences, within the 3D architecture of the cell nucleus, to bring about changes in gene expression program. Although the location of promoter sequences on 1D DNA polymer is known from genome sequencing, its 3D location when folded into chromatin via histone and non-histone proteins within the nucleus is largely unknown. Further a number of essential post-translational modifications of histone proteins result in specificity and accessibility of promoter sequences to initiate gene transcription3.

Sorting of physico-chemical cues to alter gene expression programs would therefore depend on the genome assembly within the nucleus and the regulation of post-translational modifications of histone proteins. Recent work in the literature has shown that the genome organization is non-random and perhaps cell-type specific4. Work from several labs including ours, is beginning to show that chromosomes are highly plastic in stem-cells and gene-rich chromosomes in differentiated cells are spatially clustered and are highly correlated with transcriptome network of the cell. In addition, the process of gene transcription requires transcription machinery, which is found to be enriched in dynamic compartments within the eukaryotic cell nucleus5. The spatio-temporal recruitment of transcription apparatus onto promoter sites, bound with the appropriate transcription initiation signals derived through cell-mechanics cues, would finally result in the desired genetic outputs. However, it remainsto be seen how such spatially coded maps of chromosome positioning in the nucleus and dynamic transcription machines enable efficient sorting of mechanical signals and initiate gene transcription in a highly regulated manner.

In conclusion we are just at the beginning of understanding the impact of cellular geometry on nuclear mechanics and genome regulation6. In addition, the mechanical integrity of the cell nucleus and nuclear mechanical signalling are found to profoundly influence cellular homeostatic controls: either driving cells towards differentiation, proliferation or apoptosis. Further diseases such as Cancer are conjectured to originate at a single-cell level in its local mechanical environment, within the tissue contexts, when gene expression patterns are altered. Therefore understanding the mechanical control of gene function in living cells has become a central theme in modern cell biology and biophysics. With the advent of new methods described in the literature7, there exists now a promising future in this research area. In this context, our laboratory’s approach is one that of modular8, than molecular, in probing design principles underlying these cellular mechanical systems.

Nuclear Mechanics and Genome Regulation

Mechanical signals from the extracellular matrix impinge on cellular geometry

resulting in altered functional nuclear landscape and gene function. These alterations regulate diverse biological processes including stem-cell differentiation, developmental genetic programs and cellular homeostatic control systems. Howsuch signals are integrated to the 3D spatio-temporal organization of the cell nucleus to elicit differential gene expression patterns are poorly understood. Using a multi-disciplinary approach, combining high resolution live-cell imaging and mechanics experiments, our laboratory investigates the biophysical principles underlying the coupling between cellular geometric cues to the nucleus and its impact on gene regulation.

Biological cells are mechanical in origin and sense their local microenvironment using cell-surface receptors. For example integrin receptors bind to extra-cellular matrix proteins such as fibronectin thus adapting their morphology to local geometric cues. A variety of molecular intermediates at the focal adhesion complexes have been explored in recent years describing cell-matrix interactions and the remodelling of cytoskeletal networks1. While the cytoskeleton is a well appreciated critical component of cellular morphology, emerging evidence suggests that it may also have important consequences for maintenance of nuclear architecture and its mechanical properties. Work from a number of laboratories including ours is beginning to suggest an elaborate physico-chemical network of protein assemblies coupling the cytoskeleton to the nucleus2. This coupling results in a prestressed nuclear organization in living cells: balancing contractile and tensile forces of the cytoskeleton, the entropic forces of DNA polymer and the chromatin condensation forces. In addition the prestressed nuclear architecture perhaps could serve as substrates for transduction of mechanical signals to the nucleus.

Regulation of gene expression in response to cellular geometric cues requires mechanisms that act at a distance. A number of canonical signalling pathways are activated in response to mechanical signals converging on transcription factors - such as NFkB that translocate to the nucleus upon activation. While these soluble factors translocate via diffusive processes, recent evidence also highlight the physical transmission of active stresses via the cytoplasmic-nucleus connections to remodel chromatin assembly. In addition the physico-chemical signals that arrive at the nucleus have to be sorted to appropriate

Academic Profile:Shivashankar joined the Department of Biological Sciences and the Research Centre for Excellence in Mechanobiology at the National University of Singapore as a Tenured AssociateProfessorinNov2009.Priorto this he was at the National Centre for Biological Sciences (NCBS), Tata Institute of Fundamental Research (TIFR)-Bangalore, India. With a background in experimental physics, his research interests turned to biological systems during the course of his PhD work at The Rockefeller University. His long-term interestsin information control has led him to explore the link between cellular geometry and genome assembly and its implications to mechanoregulation of genetic information within the nucleusoflivingcells.Hewasawardedthe BM Birla Science Prize (2006) and the Swarnajayanthi Fellowship (2007).Hewasrecentlyelectedtothefellowship of the Indian Academy of Sciences in 2010.

Research Interests:MechanoBiology, Bioimaging & Biophysics of Gene Regulation

Contact Details:Department of Biological Sciences,NUS Centre for Bioimaging Sciencesand Research Centre for Excellence in Mechanobiology, National University of Singapore, Singapore 117543

E-mail: dbsgvs@nus.edu.sg or shiva.gvs@gmail.com

G.V.Shivashankar

11

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Figure: Single fibroblast cells are attached to micro-patterned fibronectin surfaces to emulate distinct shapes and mechanical signals they experience in physiology. These methods are beginning to provide us with an approach to control cellular geometry and explore its impact on nuclear mechanics and genome regulation. (pattern area: 2000 mm2, blue-DNA, green-actin, red-microtubules). Schematic of our current understanding of how mechanical forces may impinge on gene function is also shown. Cellular geometric cues influence both physical coupling between the cytoskeleton and nucleus as well as chemical coupling through signaling intermediates. These physico-chemical signals will then have to be integrated with the spatio-temporal architecture of genome assembly, its plasticity and the transcription compartment (factory) dynamics to regulate gene expression.

References

1. CaiY,SheetzMP,CurrOpinCellBiol,21,47-50,2009

2. WangN,TytellJD,IngberDE,NatRevMolCellBiol,10,75-82,2009

3. RuthenbergAJ,LiH,PatelDJ,AllisCD,NatRevMolCellBiol,8,983-994,2007

4. Misteli T, Cell, 12, 787-800, 2007

5. SutherlandH,BickmoreWA,NatRevGenet,10,457-466,2009

6. Shivashankar GV, Ann Rev Biophy (2010 - 11)

7. Shivashankar GV (Editor), Nuclear Mechanics & Genome Regulation, Methods in Cell Biology series, Academic Press (2010-in press)

8. HartwellLH,HopfieldJJ,LeiblerS,MurrayAW,Nature,402,C47-52,1999

12

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

2) The pressure is strictly controlled by the viscosity term plus some lower order perturbation [2]. Once we know this relationship, we knowthat in a numerical algorithm pressure can be treated explicitly. The stability of the algorithm will not be jeopardized, yet we gain efficiency as we break a bigger system for ( u, p ) together into two smaller systems for u and p separately. Moreover, the above pressure equation is related to the commutator between Laplace and Leray projection operators. This new understanding leads to a systematic way of designing high order andstableschemes[3].

One thing that makes fluid mechanics fascinating is that related experiments are performed in front of your eyes at every single moment and every single day, and your questions never end. From my previous example, we know how to solve the system if velocity on the whole boundary is prescribed. But then every time when I open a faucet, I see the limitation of this condition. Because if I open several faucets at the same time, I have no way to prescribe a priori the outflux for each faucet. Mathematically, any pre-assumed mass-preserving outflux leads to a well-defined system.Howcanwesingleoutthephysicalonethat we have observed?

From elasticity, we know that a typical free boundary condition is traction-free. So, it is very natural to set the pseudo-traction of the fluid to equal to the ambient pressure along the outflow boundary: where is the outflow boundary and pa is the ambient pressure. This turns out to be already known. What is new is now we can obtain a pressure Poisson equation with a Dirichlet type pressure boundary condition on :

Numerical Methods for Incompressible Viscous Fluid and Fluid Structure InteractionDr Liu Jie, Department of Mathematics

Three years ago, mathematicians all over the world are celebrating the 300th anniversary

of Leonhard Euler’s birth. So the Euler equations that describe the motion of an ideal gas have been known for hundreds of years (255 years). The equations for viscous gas were laid down by Claude-Louis Navier 188 years ago. As fluids are so intimately related to our lives, over the past two hundred years, those equations have been studied by enormous people and have inspired many scientific streams.

However,in1946,JohnvonNeumannnoticed[1]“Our present analytical methods seem unsuitable for the solution of the important problems arising in connection with nonlinear partial differential equations .... The truth of this statement is particularly striking in the field of fluid dynamics….The advance of analysis is, at this moment, stagnant along the entire front of nonlinear problems. That this problem is not of a transient nature but that we are up against an important conceptual difficulty …. yet no decisive progress has been made against them ....”

Indeed, von Neumann had already made the decisive progress and found (founded) the new tool. That is the computer. He finished the First Draft of a Report on the EDVAC in the same year. The rest half century witnessed an everlasting flourish of numerical methods for fluid dynamics and other differential equations.

After so many years’ development, some people (in particular engineers) think computational fluid dynamics is fully developed and the job has been completely taken over by engineering people. Why a mathematician nowadays should still be interested in developing new algorithms for such an old problem? Well, in the Moscow State University, the mathematics and the mechanics are in the same department. That indicates the strong and permanent connection between mathematics and mechanics. Indeed some existing algorithm takes time to digest and leaves rooms for further development. In my cases, mathematics gives qualitative estimation of the interaction between different quantities. That in return tells us how to treat different quantities economically but in a way that they deserve.

Here are the some examples. Consider theincompressible Navier-Stokes equations

Academic Profile:Dr. Liu Jie received the B.S. degree in applied mathematics from the Tsinghua University, Beiing in 2000.He obtained the Ph.D. degree inapplied mathematics and scientific computation from the University of Maryland, College Park in 2006. After spending 3 years in the University of California, Irvine as a visiting assistant professor, he joined NUS, department ofmathematicsin2009asanassistantprofessor.

Research Interests:

• Computationalfluidmechanics

• Fluidstructureinteraction

• Speechprocessing

Contact Details:Department of MathematicsNational University of SingaporeBlock S17 (SOC1), Room 08-1510, Lower Kent Ridge RoadSingapore119076

Telephone: (65)65162798Email : matlj@nus.edu.sg

Liu Jie

We assume no-slip boundary condition on the boundary Γ. u is the velocity and p is the pressure. Constant v is the kinematic viscosity. The density is taken to be constant. The above equation describes the motion of an incompressible viscous Newtonian fluid like water or low speed gas. Many people consider

pressure as the Lagrange multiplier associated with the divergence free constraint. That leads to discretizations using inf-sup stable finite elements and one has to solve a large system that couples u and p together. Further studies reveal that the pressure is a slave variable in the sense that (1) It is solely determined by velocity atthesameinstant[7]

13

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Onceagainwecanshowthattheresultingpressureiscontrolledbytheviscosityterm.Hencefirstordersemi-implicitschemefortheNavier-StokesequationsusingthenewpressurePoissonformulation isunconditionallystable [4].Thenumerical resultof flowinabifurcatedtube isshowninFigure 1.

0 0.5 1 1.5 2 2.5 3 3.5 4−0.5

0

0.5

Figure 1: Streamline plot of flow in a bifurcated tube.

Figure 2: Vorticity contour plots of flow around an elastic bar attached to a rigid cylinder. Bar is of St. Venant-Kirchhoff type. Inflow from the left channel gradually starts before reaching a constant parabolic profile.

Figure 3: Final trajectory (displacement) of the middle point in the right bottom of the bar. It is not symmetric because there is gravity and the position of the cylinder slightly deviates from the middle of the channel.

0 0.2 0.4 0.6 0.80

0.2

0.4

1

0 0.2 0.4 0.6 0.80

0.2

0.4

3

0 0.2 0.4 0.6 0.80

0.2

0.4

4

0 0.2 0.4 0.6 0.80

0.2

0.4

5

0 0.2 0.4 0.6 0.80

0.2

0.4

6

0 0.2 0.4 0.6 0.80

0.2

0.4

8

−6 −4 −2 0

x 10−3

−0.04

−0.03

−0.02

−0.01

0

0.01

0.02

0.03

0.04References

1. H. Goldstine and J. von Neumann, On the principles of large-scale computingmachines,JohnvonNeumann,Works,V,2,(1946)

2. J.-G. Liu, J. Liu and R. Pego, Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate, Comm. Pure Appl. Math. 60 (2007) 1443--1487.

3. J.-G. Liu, J. Liu and R. Pego, Stable and accurate pressure approximation for unsteady incompressible viscous flow. J. Comput. Phys. (to appear)

4. J. Liu, Open and traction boundary conditions for the incompressible Navier-Stokes equations, J. Comput. Phys. 228(2009)7250--7267.

5. J. Liu, Simple seamless arbitrary Lagrangian Eulerian methods up to 5th order accuracy in time, In preparation.

6. J. Liu, A numerical method for fluid structure interaction using domain decomposition, In preparation.

7. S. A. Orszag, M. Israeli and M. Deville, Boundary conditions for incompressible flows. J. Sci. Comput. 1,(1986)75--111.

8. C. Truesdell and W. Noll, The non-linear field theories of mechanics, 3rd edition. Edited by S. S. Antman, Springer-Verlag, Berlin (2004).

We do see phenomena related to fluid mechanics every day, but if we are more careful, most of them are related to the coupling between a fluid and its surrounding or enclosed solids (rigid or deformable). So, studying fluid structure interaction becomes natural. The first thing we should address ishowtosolvethefluidequationsonatimevaryingdomain.TheideacomesfromTruesdell[8]whichIbelieveisasimplificationorextensionofthestandard arbitrary Lagrangian Eulerian method. I have obtained a class of efficient and rather simple semi-implicit schemes for the time dependent Navier-Stokesequationsinatimevaryingdomain.Methodsalongthislineareprovabletobestableandaccurateupto5thorderintime[5].NowIam ready to address fluid structure interaction. Using a domain decomposition approach, the iteration that enforces the continuity of velocity and tractionalongtheinterfaceisprovedtoconvergegeometrically[6].SeeFigures2and3forthebenchmarktestsoffluidstructureinteraction.

14

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Notes

15

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Facu

lty o

f Sci

ence

Res

earc

h N

ewsl

ette

r

Notes