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Schedule for Original Research Presentations

Apr 29, Tue May 1, Thu

1:30-1:45 Alex Wertheim Yang Liu

1:45-2:00 Avinash Mamidanna Brett Toronto

2:00-2:15 Derek Wibben Barbara Turdo

2:15-2:30 Emily Sutton Brett Yost

2:30-2:45 Helme Castro Charles John

2:45-3:00 Indrani Deshpande Elizabeth Herold

3:00-3:15 Nasser Hamdan Michael Tanner

3:15-3:30 Ishita Jain Nicholas Wagner

3:30-3:45 Santosh Vemula Tyler Kunce

3:45-4:00 Ting Yang Michael Waddington

O. R. P.

• Not only about writing, more about thinking:– Creativity

– attitude to scientific research

– uptake of essence of the bioinspired material engineering

– logic and systematic

– Background knowledge (from previous and recent study)

– Include References for any cited papers, books, or websites!

• A nice outline is half-way to the success.

• Some help for you to get a higher score for this course…

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O. R. P.

• Scope:

1. Problem to address: avoid too big and genetic (Example: cancer and Aids, photosynthesis and phototropism)

2. Solutions: be specific and practical

“This research proposal aims to … for …, allowing us to….”i. A new material

ii. A new design (assembly, structure, material system)

iii. A new function

iv. A new solution (using existing material)

• Background:

1. Significance – why care?

2. Research status and previous reported work, & remaining problem/challenges

• “Methodology” and “Research Plan”

• “Bioinspiation”

• Title: A good title should convey the essential message of the research idea and the unique novelty and contribution.

Please upload

your Lit Rev Presentations

to google drive or directly copy to me

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MSE 598/494 Bio-inspired Materials and BiomaterialsMSE 598/494 Bio-inspired Materials and Biomaterials

Instructor: Ximin He

TA: Xiying Chen Email: xchen128@asu.edu

2014-04-22

Lecture 19-20

Self-assembly IIPrinciples of Cooperativity

What you will learn in the next 75 minutes

Cooperativity

in Bioinspired Self-assembling Systems

1. Why care?

2. Three basic types of cooperativity mechanisms

3. Statistical Factors in Self-assembly

4. Master Equation

5. Stability of the Self-assembly

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What is the Governing Principle?

enzyme catalysis

membrane transport

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What is the Governing Principle?

multiple molecular recognition

self-assembly

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Cooperativity and its Importance

• Cooperativity: A regulation mechanism for a large variety of processes

– multiple molecular recognition,

– enzyme catalysis,

– membrane transport,

– self-assembly

• Implementing cooperativity in artificial systems– better understanding the mechanisms involved in the natural processes

– preparing functional materials and devices that benefit from such an efficient regulation

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Assessment of Cooperativity

• Multiple binding events may be cooperative, rather than independent, meaning that binding at one site may influence the binding at another positively or negatively for the binding strength

• Following a 3-step procedure:(1) evaluation of the isolated binding events;

(2) development of a model (the noncooperative model) where each binding event of the system behaves as if it were isolated from the others;

(3) testing of the behavior of the real system against that predicted by the noncooperative model

multiple molecular recognition

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Basic types of cooperativity mechanisms

1. Allosteric cooperativity

arising from the interplay of intermolecular binding events

2. Chelate cooperativity

due to the mere presence of one or more intramolecularbinding interactions

3. Interannular cooperativity

occurring when intramolecular binding events are not independent of other

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Statistical factors in self-assembly

• An accurate and consistent evaluation of statistical factors in self-assembly processes is crucial to predict the expected stability constant in the absence of cooperative effects and, therefore, to spotlight the emergence of cooperativity.

• The evaluation methods:– symmetry number method

– direct count method

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Statistical factors - symmetry number method

Kobs: observed equilibrium constant of a generic equilibrium

The product of a microscopic or “chemical” constant K and a statistical factor, Kσ

symmetry number, σ = σext * σint

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Statistical factors - symmetry number method

σext: the number of different but indistinguishable atomic arrangements that can be obtained by rotating a given molecule as a whole, i.e. multiplying the order of the independent simple rotational axes of the point group to which the molecule belongsσint: the number of different but indistinguishable atomic arrangements that can be obtained by internal rotations around single bonds, or, in the case of fluxional molecules, by inversion, pseudorotation, or other intramolecular processes

symmetry number, σ = σext * σint

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I. ALLOSTERIC COOPERATIVITY

• Allosteric: being a change in the shape and activity of a protein (as an enzyme) that results from combination with another substance at a point other than the chemically active site

• Allosteric cooperativity:

Arises from the interplay of intermolecular binding interactions

Depending on a multivalent receptor binds to the same or different types of ligands- homotropic, e.g. oxygen to hemoglobin

- heterotropic

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I. ALLOSTERIC COOPERATIVITY

For the interaction of an n-valent receptor with a monovalent ligand,• The statistical factor, σ for the ith stepwise equilibrium = (n − i + 1)/i(divalent: unbound receptor has σ = 2, half-bound receptor has σ = 1, the fully bound receptor has σ = 2)

• To quantify allosteric cooperativity is to evaluate the cooperativity factor α

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Stepwise binding of a monovalent ligand B to a divalent receptor AA:

Useful method to assess cooperativity, only for intermolecular binding events

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Effective Molarity (EM)

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EM: the limit concentration of the chain A–B below which intramolecular processes are more favored than intermolecular processes (Unit: mol/L)

intramolecular (Kintra)

intermolecular EM [A-B]

intramolecularintermolecular

Under the condition that [A–B] = EM,

intramolecular constant Kintra = apparent intermolecular constant K[A–B] = K·EM

EM = Kintra/K

K - representing the inherent chemical reactivity of end groups

EM - representing a connection factor that accounts for the fact that the two reactive groups

are connected to each other

Effective Molarity (EM)

EM = EMH * EMS

EM has both an enthalpic (H) and an entropic (S) component

• EMH only depends on the strain energy of the ring, so EMH < 1 unless a strainless ring is formed, in which case, EMH = 1

• For a strainless ring, EM=EMS

When the number of rotatable bonds of the chain connecting the end groups ↑

internal rotations become more restricted upon ring closure

EMS ↓So, when the end groups are connected by a rigid structure, preorganized to form a strainlessring, EMmax value is reached.

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No. of rotors in the linking chain

EM value for covalent & noncovalentcyclization processes

Effective Molarity (EM)

• The formation of weaker bonds such as hydrogen bonds and metal–ligand bonds, often encountered in self-assembling systems, involves a smaller entropy change (about −40 J K−1 mol−1 at a standard state of 1 mol L−1) that makes intermolecular reaction equilibria unfavorable.

• These changes do not occur in intramolecular reactions and thus 108 mol L−1 and 102

mol L−1 are the maximum EM values that can be found for intramolecular processes involving the formation of tight and loose bonds, respectively.

For a r-meric chain (> 25-30 skeletal bonds),

EM r −3/2

Physical sense of EM:the molar concentration of one chain end experienced by the other end of the same chain

log EMS ≈ 10 − 3/2 log r

II. CHELATE COOPERATIVITY

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• Chelate a class of coordination or complex compounds consisting of a central metal

atom attached to a large molecule (ligand), in a cyclic or ring structure. Example of a chelate ring: ethylenediamine-cadmium complex

• Chelate cooperativityarises from the presence of one or more intramolecular binding interactions, that is, as a consequence of the chelate effect, also called multivalency.

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Chelate Cooperativity

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The binding of a divalent ligand BB to a divalent receptor AA:

intramolecular binding constant

• 1/2 - the statistical factor for the cyclization process,

• K - the microscopic intermolecular• constant expressing the strength of

the binding interaction, • EM - the microscopic effective molarity

Chelate Cooperativity

• Chelate cooperativity, in contrast with allosteric cooperativity, depends on ligand concentration

• Four states for the receptor: 1. free AA,

2. the partially bound 1:1 open complex o-AA·BB,

3. the fully bound 1:1 cyclic complex c-AA·BB,

4. the 1:2 complex AA·(BB)2

• Positive cooperativity is characterized by a low concentration of partially bound species.

• The presence of the chelate interaction leads to a low concentration of the partially bound intermediate complex o-AA·BB favoring the fully bound cyclic complex c-AA·BB

K · EM = 50.

o-AA·BBAA·(BB)2

c-AA·BB

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Chelate Cooperativity

• EM is the threshold concentration of ligand binding groups above which the intramolecular process loses the competition with the intermolecular one

• The advantage provided by the chelate interaction is dissipated at high ligand concentrations

equilibrium constant

III. INTERANNULAR COOPERATIVITY

Equilibrium constants are expressed in terms of: a statistical factor, a microscopic intermolecular constant K, and the microscopic effective molarities EM1 and EM2

• The initially free internal rotation of the receptor is restricted by the binding of the first ligand molecule.

• Thus, part of the free energy of binding is spent to compensate for the corresponding entropy loss.

• Binding of the second ligand molecule is stronger because the entropic cost for the freezing of internal rotation has already been paid by the first ligand molecule.

This type of cooperativity is not due to an increase of the affinity of the binding sites of the receptor, but to an increase of the EM of the second ring with respect to that of the first ring.

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Interannular cooperativity: arises from the interplay of two or more intramolecular interactions

Binding of a divalent ligand BB to a tetravalent receptor 4A with a free internal rotation, assuming [BB]0 >> [4A]0 and α = 1

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Interannular Cooperativity – an example

• Hydrogen bonding by the first ligand molecule suppresses internal rotation of the double-wheel receptor, making the binding of successive ligand molecules easier

• Freezing of torsional motion is just one of the possible mechanisms of interannularcooperativity; other mechanisms can involve either attractive or repulsive interligandinteractions

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Two porphyrin “wheels,” each of which bears four pyridinyl binding sites; the two wheels are connected by a cerium “axle,” so that they can rotate relative to each other.

STABILITY OF AN ASSEMBLY

• α and γ are cooperativity factors accounting for overall allosteric and interannularcooperativity, respectively

• Kσ is the statistical factor of the assembly process, easily evaluated on the basis of the symmetry numbers of the assembly and of its constituent building blocks;

• K measuring the strength of the single binding interaction and EM, in the case of a cyclic or multicyclic assembly, measuring the ease of formation of the reference cyclic structure;

• b is the number of binding interactions joining the building blocks together;

• c is the degree of cyclicity of the assembly, c = b − i + 1 (i = No. of building blocks)

• Depending on the values of the parameters α, γ , and c, several models can result.

Ksa = α γ Kσ Kb EMc

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Self-assembly consists of the spontaneous generation of ordered supramoleculararchitectures from a given set of components under thermodynamic equilibration.

The overall equilibrium constant for the formation of an assembly, Ksa, depends on a plurality of intermolecular and intramolecular interactions

A master equation for the stability of an assembly:

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STABILITY OF AN ASSEMBLY

Depending on the values of the parameters α, γ , and c, several models can result :

1. The Noncooperative Model. (α = γ = 1, c = 0).applies to assemblies involving only intermolecular interactions without any allosteric effect

2. The Allosteric Cooperative Model. (α = 1, γ = 1, c = 0).cooperative systems involving only intermolecular interactions such as hemoglobin

3. The Chelate Cooperative Model. (α = γ = 1, c>0).applies to cyclic and multicyclic assemblies in which the constituent cyclic units are identical

4. The Allosteric–Chelate Cooperative Model. (α = 1, γ = 1, c>0).both allosteric and chelate cooperativity are taken into account

5. The Interannular–Chelate Cooperative Model. (α = 1, γ = 1, c>0).both interannular and chelate cooperativity

6. The Allosteric–Interannular–Chelate Cooperative Model. (α = 1, γ = 1, c>0).all the possible types of cooperativity are taken into account

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STABILITY OF AN ASSEMBLY

6. The Allosteric–Interannular–Chelate Cooperative Model. (α = 1, γ = 1, c>0). • The most general model (all possible types of cooperativity taken in account)• To separate the product αγ into its components, the factor α must be evaluated

separately by studying the interaction of the receptor with a monovalent ligand.• So far, no clear-cut examples in which all three types of cooperativity have been

evidenced and quantified

the double stranded copper(I) trihelicate 1

illustrate the application of the master Eq.to the helicate 1 that can be considered the archetypal bioinspired self-assembling system

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Summary

Self-assembly II – principle of cooperativity

• Three types of cooperativity that should be considered:

1. allosteric cooperativity (α)

2. chelate cooperativity (β)

3. interannular cooperativity (γ )

• The presence of chelate cooperativity is immediately evident on the basis of the cyclic or multicyclic nature of the assembly, while allosteric and interannular cooperativity need reference models or traditional plots to be spotted (binding isotherm, Scatchard plot, and Hill plot).

• In any case, Ksa = α γ Kσ Kb EMc provides the conceptual framework to quantitatively assess cooperativity in self-assembly.

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Reading Resources

Theoretic Studies:

• Ercolani, G.; Schiaffino, L. Angew. Chem. Int. Ed. 2011, 50, 2.

• J. -C. G.; Ercolani, G.; Piguet, C. Chem. Eur. J . 2008, 14, 2994;

• Dalla Favera, N.; Guenee, L.; Bernardinelli, G.; Piguet, C. Dalton Trans. 2009, 7625;

• Riis-Johannessen, T.; Dalla Favera, N.; Todorova, T.; Huber, S. M.; Gagliardi, L.; Piguet, C. Chem. Eur. J . 2009, 15, 12702;

• Dalla Favera, N.; Kiehne, U.; Bunzen, J.; Hytteballe, S.; L¨utzen, A.; Piguet, C. Angew. Chem. Int. Ed. 2010, 49, 125;

• Lemonnier, J.-F.; Guenee, L.; Bernardinelli, G.; Vigier, J.-F.; Bocquet, B.; Piguet, C. Inorg. Chem. 2010, 49, 1252.

Self-assembled Monolayers, DNA Origami and Block-copolymers

for electronics, drug delivery, and many other applications

(Option for Lit Rev Presentation and Original Research)

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Homework for Lect 19-20

1. Please state what is the allosteric, chelate and interannularcooperativity, respectively.

2. What are the symmetry factors of ethane and ammonia, respectively? Please provide the full derivation and justification of calculation.

• Due by Apr 24th

• Please hand in the hard copy to the TA, Xiying Chen on the class of Apr 24th

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