workshop-2011-12-02 -- Activities of LSCP

1. The Semiflexible Fabric of Biological Matter

The mechanics of living cells is, to a great extent, determined by the cytoskeleton, a fibrillar network of biopolymers. A common feature of the basic structural elements of the cytoskeleton is their semiexibility: behavior intermediate between random coils and rigid rods. The cytoskeletal mechanics is determined by both the single polymer properties and the network-forming linking of many filaments.

In the first part of this talk, I will discuss the problem of a semiexible chain with uncorrelated quenched disorder in its arc-length-dependent spontaneous curvature. In the weakly bending approximation, we obtain analytic results for the elastic response to a stretching force applied at its end-points. I will also discuss a formally similar disordered system where a stretched filament is subject to random uncorrelated transverse forces.

In the second part of the talk, I will present a semimicroscopic theory of anisotropic amorphous solids formed by random cross-linking of semiexible polymers. In a three-dimensional model, we consider random cross-links which constrain the corresponding monomers to be parallel or antiparallel. Using the cross-link density and the polymer stiffness as control parameters, we obtain a phase diagram which contains a liquid (sol), a statistically isotropic amorphous solid (orientational glass), and a nematic gel. A two-dimensional implemen-tation of the same theoretical scheme allows us to consider cross-links which prescribe a finite angle. If the cross-linking angle is a rational fraction of 2π, we show that an amorphous solid with m-fold orientational order may emerge. Some comments will also be made on the random cross-linking of directed poly-matters.

2. Bundling in Brushes of Directed Polymers

We explore the effect of an attractive interaction between the polymers of a brush. Such an attraction could, e.g., be due to reversible cross-links. For the sake of simplicity, we assume that the brush consists of directed polymers randomly grafted on a planar surface. The preferred direction is perpendicular to the surface. We use a field-theoretic approach and treat the randomness of the grafting points as quenched disorder. In the absence of any attractive interaction, and after averaging over grafting disorder, the brush is in-plane translational symmetric. We show that an attractive interaction can cause an instability to a phase with modulated areal density, which has broken in-plane translational symmetry at a certain wavelength.


Date :	02, 05 December 2011
Place :	02, 05 December : The 5th floor lecture room, Institute of Physics, Academia Sinica, Taipei
Organized by :	National Center for Theoretical Sciences (Critical Phenomena and Complex Systems focus group) Institute of Physics, Academia Sinica (Taipei)
Contact Info. :	Miss Chia-Chi Liu (Secretary, Physics Division, NCTS) Tel:(886)-2-33665566; Fax:(886)-2-33665565; E-mail: ccliu@phys.ntu.edu.tw
Speakers :
	Dr. Ara Ghazaryan Department of Physics, National Taiwan Univ, Taiwan E-mail:
		Second-Order Susceptibility Parameters as Footprint for Discrimination of Types I and II Collagen A method for the imaging and discrimination of collagen I and II using second-order susceptibility microscopy is suggested. To obtain the collagen type-specific second-order susceptibility tensor ratios we measure second harmonic generation intensity from collagen fibers as a function of excitation polarization angle. These parameters can be obtained with single pixel resolution and by displaying them in the image format can be used as a contrast mechanism for distinguishing collagen types. To show the method in work we have imaged and discriminated type I and II collagens from rat tail tendon and trachea cartilage, respectively. The effectiveness of the proposed method was also demonstrated for detection and mapping of both types of collagen fibers in engineered cartilage tissue. With additional development, second order susceptibility microscopy may be applied to disease diagnosis and fibrogenesis research of collagen.
	Prof. Artem Novozhilov Department of Applied Mathematics, Moscow State University of Railway Engineering, Russia E-mail: anovozhilov@gmail.com
		1.On the Spread of Epidemics in a Closed Heterogeneous Population Heterogeneity is an important property of any population experiencing a disease and should be incorporated into a mathematical model whenever possible. The ways how the heterogeneity can be accounted for are manifold: from considering several different groups, to continuous distributions of the parameters, and to explicit specifying the contact structure as a network. Assuming continuous parameter distributions we can formulate some of the basic models of mathematical epidemiology in the form suitable for the methods of the theory of heterogeneous populations. An initial heterogeneous model can be reduced to a low-dimensional system of ODEs. In particular, an SIR model, when it is supposed that the population of the susceptibles is heterogeneous in susceptibility to the disease, is shown to be equivalent to a homogeneous model with nonlinear transmission function. The implications of the population heterogeneity for the disease evolution are considered. 　 References: [1] Novozhilov, A.S.: On the spread of epidemics in a closed heterogeneous population. Mathematical Biosciences, 215, 177-185 (2008),pdf. [2] Novozhilov A.S.: Heterogeneous Susceptibles–Infectives model: Mechanistic derivation of the power law transmission function. Dynamics of Continuous, Discrete and Impulsive Systems (Series A, Mathematical Analysis)., 16(S1), Suppl., 136-140 (2009), pdf. 　 2.On the Origin and Evolution of the Standard Genetic Code The standard genetic code is redundant and has a highly non-random structure. Codons for the same amino acids typically differ only by the nucleotide in the third position, whereas similar amino acids are encoded, mostly, by codon series that differ by a single base substitution in the third or the first position. As a result, the code is highly albeit not optimally robust to errors of translation. We investigate the error-minimization properties of putative primordial codes that consisted of 16 supercodons, with the third base being completely redundant. It is shown that, when the 16-supercodon table is populated with 10 putative primordial amino acids, inferred from the results of abiotic synthesis experiments and other evidence independent of the code's evolution, and with minimal assumptions used to assign the remaining supercodons, the resulting 2-letter codes are nearly optimal in terms of the error minimization level. This near-optimality could be the outcome of extensive early selection during the co-evolution of the code with the primordial, error-prone translation system, or a result of a unique, accidental event. 　 References: [1] Novozhilov, A.S., Koonin, E.V.: Exceptional error minimization in putative primordial genetic codes. Biology Direct. 4,(44) (2009), pdf. [2] Koonin, E.V., Novozhilov, A.S.: Origin and evolution of the genetic code: The universal enigma. IUBMB Life., 61(2), 99–111(2009),pdf. [3] Novozhilov, A.S., Wolf, Y.I., Koonin, E.V.: Evolution of the genetic code: partial optimization of a random code for robustness to translation error in a rugged fitness landscape. Biology Direct. 2(24) (2007), pdf.
	Prof. David B.saakian Yerevan Physics Institute, Yerevan, ARMENIA E-mail: saakian@phys.sinica.edu.tw
		Hierarchic Tree Models with Continuous Branching We Consider statistical physics model with random variables on the branches of tree. We derive new class of renormalization-group equations. We discuss the application to the financial markets.
	Dr. Jan Busa Technical University in Kosice, Slovak E-mail: anovozhilov@gmail.com
		Prediction of Financial Markets using Agent-based Modeling with Optimization driven by Statistical Evaluation of Historical Data This presentation introduces agent-based model for simple prediction of financial markets, where each agent predicts development of selected subset of assets pairs in time by separately examining the similarities between ask and bid assets histories. Agent’s fitness is proportional to the wealth accumulated by exercising long and short trading positions, with regards to predicted development of assets. Although the model is iterative and operates on equidistant price data, agents are encouraged to optimize their trading frequency to maximize simulated wealth (fitness). The model evolves by enforcing competitive behavior through optimization processes.
	Dr. Karen Petrosyan Institute of Physics, Academia Sinica, Taiwan E-mail: pkaren@phys.sinica.edu.tw
		Statistical Physics of Nonlinear Non-Equilibrium Systems: Poisson Representation Approach with Application to Biophysics Statistical physics framework will be presented for description of nonlinear non-equilibrium stochastic processes with applications to complex biophysical systems. In particular, we consider biological processes that can be modelled via master equation approach. We use the Poisson representation technique to map the master equation to the equivalent set of stochastic differential equations with exactly derived diffusion matrices. We then show how to obtain corresponding stochastic actions via the large-deviation principle. This allows, e.g., to derive fluctuation relations such as Bochkov-Kuzovlev-Jarzynski and Sagawa-Ueda equalities for arbitrary nonlinear non-equilibrium stochastic processes. We discuss possible applications for various biophysical models.
	Prof. Mai Suan Li Institute of Physics, Polish Academy of Sciences, Poland E-mail: masli@ifpan.edu.pl
		Computational Study of Diseases Associated with Protein Aggregation A number of diseases such as the Alzheimer's disease, Creutzfeldt-Jakob disease, type-2 diabetes are believed to be associated with the aggregation of proteins and amyloid peptides. In this talk I discuss general factors that govern the aggregation of polypeptide chains [1,2]. It is shown that the extent of population of an ensemble of fibril-prone structures in the spectrum of conformations of an isolated protein, is the major determinant of fibril formation rates [2,3]. Presently, available drugs help to mask symptoms, but do not treat the aggregation-associated diseases. Therefore it is vital to develop drugs to cope them. The recent progress on design of top-leads for the Alzheimer's disease will be covered focusing on compounds derived from Eastern herbs [4,5]. 　 References: [1] Mai Suan Li, D. K. Klimov, J.E. Straub, and D. Thirumalai, J. Chem. Phys. 129, 175101 (2008) [2] Mai Suan Li, N.T. Co, G. Reddy, C-K Hu and D. Thirumalai, Phys. Rev. Lett. 105, 218101 (2010). [3] H.B. Nam, M. Kouza, H. Zung, and Mai Suan Li, J. Chem. Phys. 132, 165104 (2010) [4] M.H. Viet, S.T. Ngo, N.S. Lam , and Mai Suan Li, J. Phys. Chem. B 115, 7433 (2011) [5]S. T. Ngo and Mai Suan Li, Top-leads from natural products for treatment of Alzheimer's disease: docking and molecular dynamics study (submitted for publication)
	Mr. Man Hoang Viet Institute of Physics, Polish Academy of Sciences, Poland E-mail: mhviet@ifpan.edu.pl
		Inhibitors of Aggregation of Amyloid Beta Peptides The eﬀects of beta-sheet breaker peptides KLVFF and LPFFD on the oligomerization of amyloid beta peptides were studied by all-atom simulations. It was found that LPFFD interferes the aggregation of Aβ_16-22 peptides to a greater extent than does KLVFF. Using the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method, we found that the former binds more strongly to Aβ_16-22. Therefore, by simulations, we have clariﬁed the relationship between aggregation rates and binding affinity the stronger the ligand binding, the slower the oligomerization process. The binding affinity of pentapeptides to full-length peptide Aβ_1-40 and its mature ﬁbrils has been considered using the Autodock and MM-PBSA methods. The influence of beta-sheet breaker peptides on the secondary structures of monomer Aβ_1-40 was studied in detail, and it turns out that, in their presence, the total beta-sheet content gets enhanced. However, the aggregation slows down because the beta-content is reduced in ﬁbril-prone regions. Both pentapeptides strongly bind to monomer Aβ_1-40, as well as to mature ﬁbrils, but KLVFF displays a lower binding affinity than LPFFD. Our ﬁndings are in accord with earlier experiments that both of these peptides can serve as prominent inhibitors. In addition, we predict that LPFFD inhibits/degrades the ﬁbrillogenesis of full-length amyloid peptides better than KLVFF. We have shown that, in the presence of Aβ1-40 the content of beta structure of Aβ_1-42 is reduced. This result is in agreement with the recent experiments that Aβ_1-40 inhibits aggregation of Aβ_1-42.
	Dr. Panayotis Benetatos Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, UK E-mail:pb464@cam.ac.uk
		1. The Semiflexible Fabric of Biological Matter The mechanics of living cells is, to a great extent, determined by the cytoskeleton, a fibrillar network of biopolymers. A common feature of the basic structural elements of the cytoskeleton is their semiexibility: behavior intermediate between random coils and rigid rods. The cytoskeletal mechanics is determined by both the single polymer properties and the network-forming linking of many filaments. In the first part of this talk, I will discuss the problem of a semiexible chain with uncorrelated quenched disorder in its arc-length-dependent spontaneous curvature. In the weakly bending approximation, we obtain analytic results for the elastic response to a stretching force applied at its end-points. I will also discuss a formally similar disordered system where a stretched filament is subject to random uncorrelated transverse forces. In the second part of the talk, I will present a semimicroscopic theory of anisotropic amorphous solids formed by random cross-linking of semiexible polymers. In a three-dimensional model, we consider random cross-links which constrain the corresponding monomers to be parallel or antiparallel. Using the cross-link density and the polymer stiffness as control parameters, we obtain a phase diagram which contains a liquid (sol), a statistically isotropic amorphous solid (orientational glass), and a nematic gel. A two-dimensional implemen-tation of the same theoretical scheme allows us to consider cross-links which prescribe a finite angle. If the cross-linking angle is a rational fraction of 2π, we show that an amorphous solid with m-fold orientational order may emerge. Some comments will also be made on the random cross-linking of directed poly-matters. 　 2. Bundling in Brushes of Directed Polymers We explore the effect of an attractive interaction between the polymers of a brush. Such an attraction could, e.g., be due to reversible cross-links. For the sake of simplicity, we assume that the brush consists of directed polymers randomly grafted on a planar surface. The preferred direction is perpendicular to the surface. We use a field-theoretic approach and treat the randomness of the grafting points as quenched disorder. In the absence of any attractive interaction, and after averaging over grafting disorder, the brush is in-plane translational symmetric. We show that an attractive interaction can cause an instability to a phase with modulated areal density, which has broken in-plane translational symmetry at a certain wavelength.
	Porf. Sasun G. Gevorgyan Yerevan Physics Institute, Yerevan, ARMENIA E-mail: gevorgyan@phys.sinica.edu.tw
		The Concept “Protein-Machine”. Some New Experimental Results Support this Hypothesis The most commonly asked questions in protein research are: what does a protein look like, what does it do, and how does it do it? Although a three dimensional structure at atomic resolution provides a clear answer to the first one, the latter questions concerning protein function are quite problematic. Part of the problem is describing just what is meant by “understanding protein function”. One of the existing descriptions of proteins is a concept “protein/machine”. The concept (and the term) ‘protein machine’ was proposed by Chernavsky et al. in 1967 [1]. The authors use a notion of the machine as “a device which uses energized motion to bring about transformation” [1], “a structure which displays high mobility in certain directions and rigidity in others” [2] or “a device with mechanically constrained parts predetermined to give some effects by restricting motion along one or several degrees of freedom” [2]. We address this issue by describing the key findings in the evolution of our understanding of cooperative ligand binding by a single protein, hemoglobin (Hb), the paradigm of structure–function relations in multisubunit proteins. Even though this history spans almost a century, it is quite relevant to current protein research. Our recent experimental data on temperature dependence of mechanical properties of crystals of hemoglobin show that the protein works as a machine. According to the working concept the machine can “started up” by the concentration change of oxygen. However, based on our results we believe that it may happen due to abnormal increase of elasticity of hemoglobin molecules with increasing temperature. And this may be considered as a competing concept for oxygen release process.