Applications in Biology

Session 4

Applications in Biology

Chairs:

Richard Kerner (University Pierre et Marie Curie (Paris-VI), France)

Reidun Twarock(University of York, UK)

Titles and Abstracts

Maria Barbi (Universite Pierre et Marie Curie, France)

Title: Non-specific DNA-protein interaction: How proteins can diffuse along DNA

Abstract:The structure of DNA binding proteins (DNA-BPs) enables a strong interaction with their specific target site on DNA through direct interactions with DNA base pairs. However, recent single molecule experiment reported that proteins can diffuse on DNA. Interactions between proteins and non-specific DNA should therefore play a crucial role during the target search.

Nucleotides being negatively charged, the positive surface of DNA-BPs is expected to collapse onto DNA. This is indeed what is observed by means of Monte Carlo simulations for an oversimplified model of the system where the DNA is represented by a cylinder and the protein by a sphere.

However, the most characteristic aspect of DNA-BPs is their shape complementarity with DNA [1]. We showed that, if the concave shape of DNA-BPs is taken into account, a counter-intuitive repulsion between the two oppositely charged macromolecules exists at a nanometer range [2,3], which pushes the protein in a free energy minimum at a distance from DNA. As a consequence, a favorable path exists along which proteins can slide without interacting with the DNA bases. When a protein encounters its target, the osmotic barrier is completely counter-balanced by the local H-bond interaction, thus enabling the sequence recognition.

The implications of such a behavior on the protein 1D diffusion along DNA recently observed both in vitro and in vivo [4,5] will be the goal of future investigations.

[1] S. Jones, P. van Heyningen, H.M. Berman, and J.M. Thornton Protein-DNA interactions: a structural analysis J. Mol. Biol., 287 : 877-896, 1999.

[2]V. Dahirel, F. Paillusson, M. Jardat, M. Barbi, J-M. Victor Non-specific DNA-protein interaction: Why proteins can diffuse along DNA, Phys. Rev. Lett., 102, :228101, 2009.

[3]F. Paillusson, M. Barbi, J-M. Victor Poisson-Boltzmann for oppositely charged bodies: an explicit derivation, Molecular Physics, 107 : 1379-1391, 2009

[4] J. Gorman, and E.C. Greene, Visualizing One-dimensional Diffusion of Proteins along DNA Nature Structural and Molecular Biology15:5752-5757, 2008

[5]J. Elf, G.W. Li, and X.S. Xie. Probing Transcription Factor Dynamics at the Single-Molecule Level in a Living Cell Science, 316:1191 - 1194, 2007

Rafael Barrio (Universidad Nacional Autonoma de Mexico, Mexico)

Title:Modelling pattern growth in living organisms

Abstract: We present a generic non-linear model to treat various problems in developmental biology. The model is able not only to break the symmetry of space, but also to describe the way the system acquires a function. We shall give severa l illustrative example, form the patterning of the coats of animals, to the development of the flower meristem of plants.

Alessandra Carbone (Universite Pierre et Marie Curie, France)

Title:Combining molecular modeling and evolution to search for protein partnersAbstract:The Help Cure Muscular Dystrophy (HCMD) project investigates protein-protein interactions for more than 2,200 human proteins whose structures are known, with particular focus on those proteins that play a role in neuromuscular diseases. It screens each protein, predicts functional sites involved in binding to other proteins or ligand targets,and determines whether two proteins are potential interacting partners in the cell. The project will determine information on the structure of macromolecular complexes which is important not only for identifying functionally important partners, but also for determining how such interactions will be perturbed by natural or engineered site mutations in either of the interacting partners, or as the result of exogenous molecules, and, notably, pharmacophores. A database of such information would be of significant medical interest since, while it now becomes feasible to design a small molecule to inhibit or enhance the binding of a given macromolecule to a given partner, it is much more difficult to know how the same small molecule could directly or indirectly influence other existing interactions. HCMD is currently running its Phase 2 in World Community Grid (launch in may 2009). Phase 1 ended in June 2007 and the computation lasted about a year. I shall present some of the results coming from the analysis of the first phase of the project.

Malgorzata Dudkiewicz (WarsawUniversity of Life Science, Poland)

Title:How to identify laterally transferred genes? Mathematical and statistical approach to HGT phenomenon between Prokaryota and Eukaryota(jointly with Piotr Sliwka)

Abstract: Horizontal gene transfer (HGT) is believed to be important mechanism for the attainment of genetic plasticity in many species of bacteria and is defined to be the movement of genetic material between cells other than by descent in which information travels through the generations as the cell divides. HGT events were reported not only in bacterial species but , trough bacterial intermediation, also in animals and plants cells. It is highly desirable to distinguish genes acquired by HGT from the whole pool of genes of the given species. With the progress of genomics and bioinformatics a vast amount of sequence data is now available which makes possible analyzing the general characteristics such as Codon Usage or GC content on the genomic scale. To study heterogeneity of those characteristic one various statistical methods were used, such as factor or corresponding analysis, principal component analysis, Mahalanobis distance, L2 distance etc.

One of the group of genes suspected to be horizontally transferred are bacterial CLCA genes. CLCA were primarily characterized as calcium activated chloride channels, but after bioinformatics analysis it turned obvious that these proteins are rather related to zinc proteases. The Pfam CLCA proteins family is spread in many eukaryal species and present also in few archeal and bacterial genomes. We used database consisting of CLCA sequences and whole bacterial genomes to test known methods of HGT events identification and to propose some new approaches.

Bailin Hao (Fudan University, China)

Title:A few mathematical problems encountered in alignment-free bacterial phylogeny

Abstract: We have developed an alignment-free approach to infer phylogenetic relationships of bacteria from their complete genomes. Operationally this approach works well as shown by a comprehensive comparison with bacterial taxonomy. However, its foundation involves mathematical problems in statistics, combinatorics, graph and language theories. We shall touch on some of these problems, especially, unsolved ones.

Herve Isambert (Institut Curie, France)

Title:Causal inference analysis of the evolutionary expansion of gene families implicated in cancer and other genetic diseases

Abstract:The expansion of gene families implicated in cancer and other genetic diseases is an evolutionary oddity from a natural selection perspective. This expansion of "dangerous" gene families in vertebrates is correlated with other genomic properties such as their connectivity within protein complexes, gene divergence rates, gene expression levels, etc. Yet, many of these correlations are in fact mediated through the indirect effect of a third property and only provide partial insights on evolutionary origin of this expansion of "dangerous" gene families. To go beyond such simple statistical associations and quantify their direct and indirect effects on the expansion of "cancer" gene families, we have used the Mediation framework developped by Pearl. It demonstrates the central role of two rounds of whole genome duplication at the origin of vertebrates in their enhanced susceptibility to genetic disorders and cancers. These results are also supported by a simple population genetics model that rationalizes, from an evolutionary perspective, this expansion of gene families frequently implicated in genetic disorders and cancers.

Rubem Mondaini (Federal University of Rio de Janeiro, Brazil)

Title: Linear programming methods for the treatment of small perturbations of amide planes

Abstract: The existence of Amide Planes of Protein Structures has been confirmed recently by a Mathematical Programming Approach [1]. The proposed cost function is the expression of a dihedral angle in terms of three variables: two bond angles, and the angle corresponding to alpha-carbon geometry. The average value of this dihedral angle is calculated to be 180 degrees by exhaustive statistical analysis of dipeptide structures [2] and this was the first indirect confirmation of Pauling's insight on the existence of amide planes of Protein Structure [3]. In this work we show how the methods of Mathematical Programing can be applied to derive the same average value which we believe to be the first of a series of introductory results belonging to a new modelling process of biomolecular structure. We then consider the small perturbation of the three variables above and we introduce the expressions of the two remaining dihedral angles.

From the observation of some regularities on the distances between atom sites along a protein backbone, we start our modelling by considering 3-dimensional curves through sequences of evenly spaced atom sites, according to an Euclidean definition of distance. This will lead to the introduction of elementary Ans?tze for the coordinates of the position vectors of these evenly spaced atom sites and we make the assumption of local equilibria on the configuration of an atom site and its nearest neighbors. This assumption is enough for deriving the position of the central atom site from a generalized Fermat's problem, since it also means the minimization of the potential energy function [4]. There are two interesting previous results coming from theseAnsätzeand the equilibrium condition. The first one is that they preclude the existence of atom sites with more than 4 links to their nearest neighbors which is a known fact of protein structure. The other result is that they also imply that the curves quoted above should be right circular helices, which corresponds to another Pauling's insight - the alpha helices.

In order to summarize, it was found that from three known facts about the protein structure: evenly spaced atom sites, alpha helices and a maximum of 4 links of an atom site to its nearest neighbors, any two of them imply the third. In a first example of this modelling, we have chosen helices through the sequences of alpha-carbon, hydrogen and oxygen as well as through the sequences of nitrogen and carbonyl [4]. The results, albeit introductory, are in good agreement with the literature [1]. The study of the perturbations of the two remaining dihedral angles allows for checking the stability of Ramachandran Plots and to test its efficiency to predict new protein structures. Work along these lines is now in progress and will be presented on this talk.

References

1) R.P.Mondaini, "A Correlation between Atom Sites and Amide Planes in Protein Structures", in BIOMAT 2009 - International Symposium on Mathematical and Computational Biology, 136 -151, World Scientific Co. Pte. Ltd.

2) A.S. Edison - "Linus Pauling and the Planar Peptide Bond", Nature Structural Biology 8(3) (2001) 201 - 202.

3) C. Dale Keefe, J.K.Pearson - "Ab Initio Investigations of Dipeptide Structures, J. Mol. Structure (Theochem) 679 (2004) 65 - 72.

4) R.P.Mondaini - "The Steiner Tree Problem and its Application to the Modelling of Biomolecular Structures" in Mathematical Modelling of Biosystems - Applied Optimization Series 102 (2008) 199 -219, Springer Verlag Berlin-Heidelberg.

Piotr Sliwka(Cardinal Stefan Wyszynski University, Poland)

Title:How to identify laterally transferred genes? Mathematical and statistical approach to HGT phenomenon between Prokaryota and Eukaryota (jointly with Malgorzata Dudkiewicz)

Ileana Streinu (Smith College, USA)

Title: Periodic rigidity of crystal structures, with applications to proteins

Abstract: Recently, we initiated in silico rigidity-theoretical studies of protein crystal structures, with the goal to determine if, and how, the interactions among neighboring crystal cells affect the flexibility of the biological unit. Preliminary results, obtained using the tools available through the KINARI-Web server developed in our group, indicate that important information, correlating rigidity parameters with protein function and overlooked until now, may be captured with this kind of analysis.

In this talk, I will discuss two recent directions, one mathematical and one biological, in which this research is proceeding. The mathematical theory of periodic rigidity, recently introduced by Borcea and Streinu [Proc. Royal Society A, 2010 and Bull. London Math. Soc. 2011] is directly applicable to such investigations. It provides both rigorous treatment and substantial algorithmic advantages over previous approaches. It also leads to further challenging mathematical questions, some of which will be briefly discussed. On the applied side, I will report on recent findings from a survey of a large set of proteins analyzed with KINARI.

Michael Thorpe (Arizona State University, USA)

Title:The Flexibility and Mobility of Frameworks and Biomolecules

Abstract:Many interesting phenomena occur in material structures that arepoised between rigid and flexible. In this talk, we describe themodern theory of rigidity and show how it can be used to analyzenetworks of constraints. These results can be used as input togeometrical simulation, where the various rigid parts of a systemare moved, while maintaining all the constraints; both equalitiesand inequalities. This approach is applied to zeolites that areimportant for cracking petroleum and proteins where flexibility is oftenassociated with function.

Reidun Twarock(University of York, UK)

Title:Viruses and Geometry - Where Symmetry meets Function

Abstract:Viruses display symmetry for reasons of genetic economy: By packaging their genomic material into protein containers (capsids) that are organised with icosahedral symmetry, they maximize container volume while minimizing the portion of the genomic sequence needed to code for the capsid. From a mathematical point of view, this implies that techniques from group, graph and tiling theory can be used to predict virus architecture. We show here that via an affine extension of the icosahedral group and associated tilings new information regarding structural constraints on virus architecture can be obtained, that reveals a previously unrecognised structural correlation between different viral components. We discuss the implications of such structural features for function, i.e. for how viruses form and infect their hosts. In particular, we show that the assembly of single-stranded RNA viruses follows a set of local rules that can be understood in terms of the interactions between genomic RNA and capsid protein. We moreover present a new mathematical approach for the prediction of the structural transitions of viral capsids important for infection.

Vitaly Volpert (CNRS, University Lyon 1, France)

Title:Reaction-diffusion waves: classical theory and recent developments

Abstract:Reaction-diffusion waves arise in various applications in physics, chemistry and biology. From the mathematical point of view these are particular solutions of semilinear parabolic equations. We will present the mathematical theory of reaction-diffusion waves and will illustate it with numerous examples such as propagation of flames, tumor growth or some models in population dynamics.

Dorothy Wallace(Dartmouth College, USA)

Title:Patch SIR models on the k-regular graph

Abstract: The epidemiology of person-to-person communicable disease in large, homogeneous populations is modeled by three ordinary differential equations. These represent the susceptible, infectious and recovered individuals. For smaller populations an agent-based model can capture the inhomogeneous nature of human interactions by modeling each individual as a node in a network, or vertex in a graph. In this model we look at a set of large homogeneous populations, each modeled as a classic SIR epidemic (the patches), but which have immigration between them (the graph). It is a mathematically interesting and epidemiologically useful question to ask which aspects of disease transmission are controlled by the local properties of each SIR model, and which are controlled by the global connectivity of the graph. In this talk we will answer a piece of this question for a particular patch SIR model on any graph where each vertex has k neighbors.

Amit Zeisel(Weizmann Institute of Science, Israel)

Title: Coupled pre-mRNA and mRNA dynamics unveil operational strategies underlying transcriptional responses to stimuli.

Abstract: A major component of the response of cells to changing conditions is ashift of the transcriptome to a new state which may be more adequate forfacing the new environment. The time dependence of this shift is ofconsiderable interest and is often inferred from measurements of mRNAconcentrations.

We formulate a refined model for the dynamics of pre-mRNA and mRNAconcentrations and show that the temporal profiles of pre-mRNA are muchmore suitable than those of mRNA for reconstruction of the transcriptproduction profiles. By monitoring time-dependent changes of pre-mRNAabundance in MCF10A cells stimulated by EGF, we show that in general,production profiles exhibit different kinds of interesting andunexpected forms. In order to increase expression of specific genes tosome high desired level in a short time, cells use a strategy ofproduction overshoot for a relatively brief interval.

A genome wide view shows while these production profiles are closelyreflected by the time dependence of the pre-mRNA, the corresponding mRNAprofiles are often uncorrelated with transcript production.