Response analysis in biochemical chain reactions with negative feedforward and feedbackward loops

Finite difference equations can be used to study the responses of biochemical chain reactions at any step of the chain to an external stimulus. In this study, we developed mathematical models for two hypothetical chain reactions involving loops to study the responses in the chain as the length of the chain gets longer, so called transient and steady state responses. The first model is for a chain with a negative feedforward loop, and the second one is for a chain that has a negative feedback loop. Although both of the models have the same steady state equations and values, we showed that the chain with negative feedforward and negative feedback loops can produce significantly different behaviors. The former can bring the chain into oscillations with various periods and eventually chaos when the feedback is strong enough as the length of the reaction chain increases, whereas the latter is not capable of producing oscillations and more complicated dynamics.     

N-烷基化聚对苯二甲酰对苯二胺梳状高分子中烷基侧链对刚性主链堆积行为的影响

基于聚对苯二甲酰对苯二胺(PPTA), 采用N-烷基化方法制备了系列PPTACns(烷基侧链碳原子数n=8, 10, 12, 14, 16, 18)刚性主链梳状高分子, 利用DSC, XRD和FTIR等方法研究了其主链堆积行为、 分子链构象及热性能等与烷基侧链长度及结晶特性之间的关系. XRD和DSC结果表明, 当烷基侧链碳原子数达到14时, 烷基侧链发生结晶. XRD结果显示, PPTACns具有层状结构, 烷基侧链长度对主链层间距影响显著. FTIR研究发现, 烷基侧链的聚集状态对PPTACns分子链的构象产生较大影响, 伴随着烷基侧链结晶的熔融, PPTACns的分子链构象发生显著改变. 烷基侧链处于熔融状态的PPTACns的ν_C=O和γ_C-H谱带峰位与烷基侧链不结晶的PPTACn接近.     

Role of chain stiffness on the conformation of single polyelectrolytes in salt solutions

Conformation of single polyelectrolytes in tetravalent salt solutions is investigated under the framework of a coarse-grained model, using Langevin dynamics simulations. The chain size, studied by the radius of gyration, shows three different variational behaviors with salt concentration, depending on the chain stiffness. According to the size variations, polyelectrolytes of fixed chain length are classified into three categories: (1) flexible chain, for which the variation shows a curve similar to a tilted L, (2) semiflexible chain, whose curve resembles U, and (3) rigid chain, for which the curve is a straight line. The wormlike chain model with persistence length predicted by the Odijk-Skolnick-Fixman theory is found to be able to qualitatively describe the end-to-end distance at low salt concentration not only for semiflexible and rigid chains but also for flexible chain. In a low salt region, a flexible polyelectrolyte extends more significantly than a semiflexible chain, in reference of the size of their uncharged counterparts, and in a high salt region, regardless of chain stiffness, a chain attains a dimension comparable to that of its neutral polymer. The chain stiffness influences both the local and the global chain structures. A flexible chain exhibits a zigzagged local structure in the presence of salt ions, and the condensed structure is a disordered, random globule. A semiflexible chain is locally smooth, and the condensed structure is orderly packed, taking a form such as hairpin or toroid. Moreover, the chain stiffness can also affect the nature of the coil-globule transition. The transition occurred in a discrete manner for semiflexible chain, whereas it occurred in a continuous way for flexible chain. This discrete feature happened not only at low salt concentration when a semiflexible chain collapsed but also at high salt concentration when the collapsed chain is reexpanded. At the end, the effects of chain stiffness and salt concentration on the conformation of single polyelectrolytes are summarized in a schematic state diagram.     

Studies on Single Chain Structure of Konjac Glucomannan

1INTRODUCTION The single chain structure of KGM is the ele-mentary acting unit of its biological function and viscoelasticity of mechanical properties.The re-search method of saccharide chain and the com-plexity of its structure have restricted the study on structure-activity relationship.Therefore,the studies concerning KGM both at home and abroad mainly focus on its application,whereas less on its structure.Previous researches were only related to the determination and distribution as…     

Mesoscopic dynamic Monte Carlo simulations of the adsorption of proteinlike HP chains within laterally constricted spaces

Two-dimensional dynamic Monte Carlo simulations are applied to the protein-like HP chain model to investigate the influence of lateral confinement of the adsorbed chain on adsorption thermodynamics and the ensemble of accessible chain conformations. The structure of the model makes it possible to enumerate all possible chain conformations and thereby define with precision the relation between adsorption thermodynamics and changes in accessible chain conformations resulting from the adsorption process. Lateral confinement of the adsorbed chain is shown to dramatically reduce the number of accessible energy states and unique chain conformations such that, under certain conditions, adsorption is predicted to actually stabilize the chain against denaturation. Lateral confinement preferentially eliminates expanded conformations of the adsorbed chain, shifting the equilibrium from the unfolded state toward the native state. As a result, the conformational entropy of the adsorbed chain is predicted to be lower than that of the chain free in solution. The protein-like HP chain responds to an increase in the hydrophobicity of the sorbent surface by strongly favoring those conformations that minimize the overall internal energy of the system. As a result, adsorption severely destabilizes the native-state conformation. The ability of our simulation results to provide insights into underlying mechanisms for nonspecific protein adsorption is illustrated through qualitative comparison with activity data for hen egg-white lysozyme adsorbed on silica at different surface concentrations.     

Formation of Salt Bonds in Polyampholyte Chains

In this paper we study the influence of the formation of intrachain ion pairs (salt bonds) and the distribution of counterions on the behavior of single polyampholyte chains in a dilute solution. It has been shown that neutral polyampholyte chains can undergo jump‐like collapse transition from the swollen state to the globular state with the formation of ion pairs between oppositely charged ions of the chain. A polyampholyte chain with an excess charge shows the behavior of a conventional polyelectrolyte chain and counterions play an important role in the chain behavior. We distinguish three possible states of counterions: free counterions inside and outside the macromolecule, and a bound state of counterions forming ion pairs with the corresponding ions of the polymer chain. We found a non‐monotonous behavior of the chain upon increasing the excess charge on the chain: the chain swells from a compact state to elongated conformation and shrinks again to the compact state when the excess charge of the chain is increased.     

Molecular dynamics simulation study on adsorption and diffusion processes of a hydrophilic chain on a hydrophobic surface

Molecular dynamics simulations are applied to investigate the adsorption and diffusion processes of a single hydrophilic poly(vinyl alcohol) (PVA) chain with different chain lengths on a hydrophobic graphite surface. It is expected that the chain and the surface "dislike" each other because one is hydrophilic and the other is hydrophobic. But surprisingly, a short PVA chain is well adsorbed on the surface, accompanied by large changes in the chain configuration. With increasing degree of polymerization (N), the chain turns gradually from two-dimensional adsorption to possessing certain height in the direction perpendicular to the surface. Moreover, the adsorption energy increases and the diffusion coefficient decreases with increasing N. In particular, for N = 20 in equilibrium, the hydroxyls of this short chain are close to the graphite surface in the stable adsorption configuration. In addition, we change the effective dielectric constant to 76.0 to mimic good solvent condition. The chain configurations and the diffusion coefficients both vary in contrast to the foregoing results.     

THE SPATIAL DISTRIBUTION AND MOMENTS OF CIRCULAR FREELY JOINTED CHAIN

The spatial distribution function and second moments of circular freely jointed chain are derived based on an analytical method. The circular Gauss chain, which is simple for long chains, is compared with the circular freely jointed chain, which is exact for short chains. It is shown that the Gauss chain model predicts a more compact configurational distribution than the exact freely jointed chain. The two chain models, however, become closer to each other when the chain length increases. It is found that the difference of the mean square radius of gyration calculated with these two chain models is a constant, independent of the chain length.     

Catalytic synthesis of styryl‐capped isotactic polypropylenes

Bis‐styrenic molecules, 1,4‐divinylbenzene (DVB) and 1,2‐bis(4‐vinylphenyl)ethane (BVPE), were successfully combined with hydrogen (H₂) to form consecutive chain transfer complexes in propylene polymerization mediated by an isospecific metallocene catalyst (i.e., rac‐dimethylsilylbis(2‐methyl‐4‐phenylindenyl)zirconium dichloride, I ) activated with methylaluminoxane (MAO), rendering a catalytic access to styryl‐capped isotactic polypropylenes (i‐PP). The chain transfer reaction took place in a unique way where prior to the ultimate chain transfer DVB/H₂ or BVPE/H₂ caused a copolymerization‐like reaction leading to the formation of main chain benzene rings. A preemptive polymer chain reinsertion was deduced after the consecutive actions of DVB/H₂ or BVPE/H₂, which gave the styryl‐terminated polymer chain alongside a metal‐hydride active species. It was confirmed that the chain reinsertion occurred in a regio‐irregular 1,2‐fashion, which contrasted with a normal 2,1‐insertion of styrene monomer and ensured subsequent continuous propylene insertions, directing the polymerization to repeated DVB or BVPE incorporations inside polymer chain. Only as a competitive reaction, the insertion of propylene into metal‐hydride site broke the chain propagation resumption process while completed the chain transfer process by releasing the styryl‐terminated polymer chain. BVPE was found with much higher chain transfer efficiency than DVB, which was attributed to its non‐conjugated structure with much divided styrene moieties resulting in higher polymerization reactivity but lower chain reinsertion tendency. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3709–3713, 2010     

Computer Simulation of High-Frequency Heating of a Protonated Poly(ethylene oxide) Chain in a Vacuum

Heating of an isolated protonated poly(ethylene oxide) chain by high-frequency electric field was simulated using molecular dynamics. Simulations were performed at the field strength of about 10⁸ V/m and frequencies from 1 to 100 GHz. At initial temperature (500 K), the chain is a globule. Absorption of the field energy heats the chain and leads to a growth in its size. In some frequency ranges, the field causes the chain to rotate as a whole. The rotation leads to a sharp increase in the heating rate and the rate of stretching the chain. The rotating chain has larger size than its non rotating counterpart at the same temperature. Contrary to the non rotating chain, this chain can be in a two-phase state in which the globular and the stretched microphases coexist. The absorption spectrum of the chain is temperature dependent and, at high temperatures, contains two distinctly expressed peaks. In the vicinity of these peaks, the chain rotates with a frequency equal to the field frequency or about half the field frequency. The results obtained are explained using the model of a spatial damped oscillator in which, together with the usual resonance, the subharmonic resonances typical for nonlinear systems arise.     

An exact enumeration study on adsorption transition of a tethered chain at an adsorbing surface

<正>The number of configurations,c(n,m),of a single chain with length n attached to a flat surface with m monomers contacting the surface is exactly enumerated.A function of c(n,m) about m and n is obtained.From the function,a scaling law for mean energy of chain is derived,and we estimate the critical pointε_c = 0.276 and the crossover exponentφ= 0.5.The free energy difference between tethered chain and free chain in dilute solution is also studied,which shows the critical adsorption point is about 0.272 for infinite long chain with φ= 0.5.     

A Monte Carlo simulation study of the effect of chain length on the hydrolysis of poly(lactic acid)

Abstract The intrinsic relationship between molecular chain length and the probability of chain reaction during poly(lactic acid)(PLA)hydrolysis was investigated by Monte Carlo simulation.The chain reaction rate was calculated by introducing a power function of different molecular chain lengths.The hydrolysis of both amorphous and extended-chain crystal PLA was selected as the model system.It is found that,the chain reaction probability was proportional to the chain length with a power of 0.4 for amorphous PLA and 0.7 1 for extended-chain crystal PLA,respectively.These results indicate that PLA with longer chain length usually exhibits larger reaction rate than that with shorter length.Comparing the hydrolysis of the two kinds of PLA,the competition between longer and shorter chains in the different condensed structures is different.     

Mean field theory for the intermolecular and intramolecular conformational transitions of a single flexible polyelectrolyte chain

The diMarzio theory has been extended to elucidate the intermolecular and intramolecular phase segregations of a single flexible chain polyelectrolyte in dilute salt-free solutions. At the long chain limit, this theory yields the formalism obtained from the more sophisticated Edward Hamiltonian for polyelectrolyte problems. The calculated phase diagram exhibits the features of a first-order phase transition, with continuous and discontinuous transitions separated by a critical point. Under the discontinuous transition, the polyelectrolyte chain exhibits coexistent expanded and collapsed conformational states, same as intermolecular phase segregation. For a limiting long chain, the mean chain size at critical point is roughly 90% of the size of an ideal chain. Such a result implies that partial contraction within a chain molecule is required to collapse a flexible polyelectrolyte chain. Moreover, the theory predicts that for a longer chain, intramolecular segregated conformations differ significantly from intermolecular segregated conformations, but the difference becomes small for shorter chains. Besides, the charge needed to induce intramolecular segregation is smaller than that of intermolecular segregation for a given chain length. These findings are consistent with previous literature results.     

液晶离聚物--分子设计与热性能

综述了液晶离聚物的分子设计与液晶热性能的关系,一般主链液晶,离子在链中浓度增加,玻璃化温度（Ｔｇ）和熔点（Ｔｍ）下降,离子在端基,对Ｔｇ和Ｔｍ影响不大;离子对侧链淮晶的影响,取决于主链的柔顺性和离子在链中的位置等。一般情况下,无论对主链还是侧链液晶离聚物,随着离子在链中浓度增加,液晶相向各向同性液体转化温度（Ｔｉ）降低。     

聚乙烯链构象熵的研究

采用旋转异构态模型，考虑近程二级相互作用和远程自回避相互作用，在金钢石格点上模拟聚乙烯链，用完全计算法研究了它的构象熵。我们得到聚乙烯链的我象熵现温度及链长的函数关系式。发现在约２００Ｋ温度以上，聚乙烯链的构象的熵随温度沽小不明显，在约２００Ｋ以下，构象熵随温度迅速减小，约在４２Ｋ的构象熵为零。我们还以现，该链的构象熵近似地与链长成正比。     

Importance of chirality and reduced flexibility of protein side chains: a study with square and tetrahedral lattice models

Side chains of amino acid residues are the determining factor that distinguishes proteins from other unstable chain polymers. In simple models they are often represented implicitly (e.g., by spin states) or simplified as one atom. Here we study side chain effects using two-dimensional square lattice and three-dimensional tetrahedral lattice models, with explicitly constructed side chains formed by two atoms of different chirality and flexibility. We distinguish effects due to chirality and effects due to side chain flexibilities, since residues in proteins are L residues, and their side chains adopt different rotameric states. For short chains, we enumerate exhaustively all possible conformations. For long chains, we sample effectively rare events such as compact conformations and obtain complete pictures of ensemble properties of conformations of these models at all compactness region. This is made possible by using sequential Monte Carlo techniques based on chain growth method. Our results show that both chirality and reduced side chain flexibility lower the folding entropy significantly for globally compact conformations, suggesting that they are important properties of residues to ensure fast folding and stable native structure. This corresponds well with our finding that natural amino acid residues have reduced effective flexibility, as evidenced by statistical analysis of rotamer libraries and side chain rotatable bonds. We further develop a method calculating the exact side chain entropy for a given backbone structure. We show that simple rotamer counting underestimates side chain entropy significantly for both extended and near maximally compact conformations. We find that side chain entropy does not always correlate well with main chain packing. With explicit side chains, extended backbones do not have the largest side chain entropy. Among compact backbones with maximum side chain entropy, helical structures emerge as the dominating configurations. Our results suggest that side chain entropy may be an important factor contributing to the formation of alpha helices for compact conformations.     

Anionic synthesis of well-defined polymer blends by controlled chain-transfer reactions

The scope and limitations of controlled chain transfer reactions in living anionic polymerization have been investigated. In contrast to the random nature of normal chain transfer reactions, this procedure first effects controlled living anionic polymerization followed by addition of a stoichiometric amount of suitable chain transfer agent when the monomer has been completely consumed. The resulting anionic species is then used to initiated polymerization of a second monomer charge with the same monomer or with a different monomer. A variety of hydrocarbon acids and amine compounds with pKa values in the range of 30–40 have been evaluated as chain transfer agents in the presence and absence of coordinating ligands. Efficient chain transfer to poly(styryl)lithium has been observed using 1,1-diphenylpropane. Reinitiation efficiency to both styrene and butadiene monomer was quantitative and controlled blends of different molecular weight polystyrenes or blends of polystyrene with polybutadiene have been prepared. The use of these chain transfer reactions to prepare functionalized polymers has also been investigated.     

Nascent crystallization of a growing chain on a catalyst surface: a nonequilibrium molecular dynamics simulation study

The growing chain molecular dynamics (GCMD) simulation method, a new nonequilibrium molecular dynamics code, is proposed to simulate the polymer chain aggregation behavior during polymerization on a catalyst surface. We found that the growing chain crystallizes on the surface in two stages: the nucleation stage and the crystal growth stage. In the first part of the nucleation period, the short polymerizing chain first absorbs on the surface and can be in either an ordered or disordered structure. Still in the nucleation period, when the chain reaches a degree of polymerization, about 100 bonds, the chain folds into a stable nucleus on the substrate with 3-5 stems. In the crystal growth stage where the polymerization also proceeds, we observed a stem elongation process in combination with a chain folding process. In the stem elongation step, the number of stems in the nucleus remains constant, and all the stems expand together to a length of ca. 5-25 ns. In the subsequent chain folding step, the stem length decreases about 20 bonds within a period of ca. 0.1-0.5 ns. During chain growth, the elongation process and the folding process occur in an alternating and repeated fashion. The crystallization mechanism of the polymerizing chain was discussed.     

偏氟乙烯/三氟氯乙烯交替共聚物在TATB表面吸附的分子动力学模拟

采用COMPASS力场和NVT正则系综的动力学模拟方法, 搭建了聚合度分别为10, 50和100的偏氟乙烯(VDF)/三氟氯乙烯(CTFE)交替共聚物, 对交替共聚物在1,3,5-三氨基-2,4,6-三硝基苯(TATB)的(0,0,1)晶面上的吸附和结构进行了分子动力学(MD)模拟. 结果表明, 在300～320 K温区, 聚合度为100的VDF/CTFE交替共聚物链对TATB晶体有理想的表面活性和吸附能力, 以train型构象平铺于TATB表面. 通过对聚合度为10的交替共聚物的多链体系在TATB表面吸附的MD模拟, 表明了VDF/CTFE交替共聚物具有非凝聚吸附的高表面活性特征. 对搭建的乙酸乙酯溶剂化的聚合度为50的VDF/CTFE交替共聚物在TATB晶体表面吸附的模拟, 实验证明了溶剂小分子能够降低共聚物链的吸附能力, 且链以tail型构象吸附于TATB表面.     

The influence of the polymer chain stiffness on tracer diffusion in polymeric matrices

The diffusion of penetrants in polymers is of technological importance in many areas including chromatography and fuel cell membranes. In this work, the effect of chain conformations on tracer diffusion is studied using molecular simulations and a percolation theory. The polymeric matrix is composed of tangent hard sphere chains that are fixed in space; conformations are changed by tuning the stiffness of the chains. The tracer diffusion coefficient is relatively insensitive to the chain stiffness when polymer chains are frozen as in polymer glasses with the local chain dynamics switched off. An analysis of the matrix using percolation theory shows that the polymer volume fraction at the free volume percolation threshold is also relatively insensitive to the chain stiffness, consistent with the diffusion results. This is surprising because the site‐site intermolecular pair correlation functions in the matrix are quite sensitive to the chain stiffness. In contrast, the tracer diffusion coefficient in a melt of mobile chains decreases significantly as the chain stiffness is increased. We conclude that tracer diffusion is only weakly correlated with the chain conformations and local chain dynamics plays an important role. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011