Luke A. BurkeDepartment of Chemistry

and Center for Computational and Integrative

BiologyRutgers UniversityCamden, NJ, USA

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Chemistry: transformation

Alchemy: Al-chimiya transmutation“Philosophically, chemistry is a branch of

science that attempts to predict and control rather than simply to observe and analyze.”

G. M. Whitesides, Science 284 89 (1999)

“The essence of chemistry is not only to discover but to invent and above all to create.”

J.M. Lehn in Supramolecular Chemistry VCH 1996

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Introduction to ComplexityExploration of the ideas on complexity published by

Ilya Prigogine, (1925-2003), 1977 Nobel Prize in Chemistry

What is the difference between the swinging of a pendulum and the beating of a heart? Between a crystal of ice and a snowflake?

Are the ‘worlds’ of physical and chemical phenomena predictable and can it be interpreted adequately based on a few fundamental interactions? Is complexity only to be found in biology?

Is chemistry the bridge between physics and biology?

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Topics of DiscussionTaken from: Exploring Complexity: An Introduction by Gregoire Nicolis and Ilya Prigogine

1. Complexity in Nature (discussed in this talk)2. The vocabulary of Complexity3. Dynamical Systems and Complexity4. Randomness and Complexity5. Toward a unified formulation of Complexity6. More examples of Complexity

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1. Complexity in Nature1.1 What is Complexity ? Definition One: Part of our everyday experience, related to

various manifestations of life, “a complicated synthesis”. Definition Two: “A complex system is one whose evolution

is very sensitive to initial conditions.” Phenomena in basic physics textbooks are “simple”, i.e. one object – one action, or a process that can be analyzed as a series of “simple” couples

1 ml of H2O, molecular chaos, but system is not “complex”, intermolecular forces of attraction are short-range

However, subject the 1ml to conditions of a snowstorm and an intricate pattern will emerge in each snowflake.

Must speak of Complex Behavior rather than complex systems

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1.2 Thermal convection as a prototype of Self-organization phenomena in Physics

Bénard, Henri. 1900. "Les Tourbillons Cellulaires dans une Nappe Liquide," Rev. General Science Pur. Appl. Vol. 11:1261-1271.

Plate at T1

H2O

Plate at T2

T2 > Tc > T1

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Fluid in Motion: time lapse view of Rayleigh-Benard cells. The picture (on left) was taken over ten seconds, so the aluminum flakes in the fluid look like long trails instead of small particles. This helps to visualize how the fluid is moving: up through the center of the cell, then spreading out and sinking at the edges of the cell.http://www.etl.noaa.gov/about/eo/science/convection/RBCells.html

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I. Te = T2 – T1 = 0 Equilibrium condition No cells If perturbation is momentarily applied, system returns to

Equilibrium after perturbation dies out. (LeChâtelier) The state is “asymptotically stable”.II. T > 0 External Constraint, energy flux, Non-equilibriumA. T > small : thermal conduction, and P differ nearly

linearly; behavior is as “simple” as at Equilibrium.

B. T > Tc Fluid shows bulk movement, Bénard cells Minute observer inside cell can now decide where he is

and where he is not by looking at the direction of the rotation of the cell. By moving along and counting the number of cells, he acquires a notion of distance in space. The emergence of space = “symmetry breaking”.

G. T > Tc > Tc’ turbulence000

12

4

X

X

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Symmetry BreakingBrings us from a Euclidean (static, geometrical) view of space to an Aristotelian view in which space is shaped or defined by the function going on in the system. ( Aristotle began his natural science with biological systems and functional classification.)

In sudden transition from simple to complex behavior, order and coherence appear in the system. This suggests existence of :

Correlations, i.e. statistically reproducible relations between distant parts of the system ( 10-3 m range compared to 10-10m).

As soon as T > Tc , cells appear, thus strict determinism; but direction of rotation in one cell is unpredictable and uncontrollable.

“Far from Equilibrium”: several solutions are possible for the same parameter values.

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Nonequilibrium

Enables system to avoid thermal disorder and transform part of the energy obtained from the environment into an ordered behavior of a new type :

Dissipative Structure:

A regime characterized by symmetry breaking, multiple choices, and correlations in the macroscopic range.

Birth of complexity (a characteristic of biological systems) as an inevitable consequence of physical laws when suitable conditions are applied.

Videtes infra

Definitions (already used)System:"A collection of interacting parts that form an

integrated and consistent whole, isolatable from its surroundings.“

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Only closed systems can be perfect and completely uncomplicated. Only closed systems can exhibit dynamic equilibrium. Open systems can never be at true equilibrium, although careful experimental design may approximate it to be closed.(Isolated system: neither energy nor matter exchanged)

H2O (liq) H2O (gas)

Each water has its x,y,z coordinates (position space)and whether its designation as liquid or gas (phase space).

Definitions cont.Linearity: "An equation or graph is linear if the graph of

an equation is a straight line.“ Implies a change in one parameter (x) causes one effect. F(x) = y = m x + b

Complexity: "The interaction of many parts, giving rise to

difficulties in linear or reductionist analysis due to the nonlinearity of circular causation and feedback effects."

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Definitions, continued (www).Chaos:"Chaos is the breakdown of predictability, or a

state of disorder." (Shador) "A distinctive area of broken terrain." (Wonka) "A dynamical system that is extremely

sensitive to its initial conditions." (Word Net) "A system whose long term behavior is

unpredictable, tiny changes in the accuracy of the starting value rapidly diverge to anywhere in its possible state space. There can, however, be a finite number of available states, so statistical prediction can still be useful. " (Calresco)04/21/23 13

Emergence (Wikipedia @ 12 Oct 2009)

"Emergence is the process of deriving some new and coherent structures, patterns and properties in a complex system.

Emergent phenomena occur due to the pattern of interactions between the elements of a system over time.

often unexpected, nontrivial results of relatively simple interactions of relatively simple components.

What distinguishes a complex system from a merely complicated one is that in a complex system, some behaviors and patterns emerge as a result of the patterns of relationship between the elements." (Wikipedia)

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Chemistry has evolved a series of approaches to treat complex systems:•reasoning by analogy•averaging•linearization•drastic approximation•pure empiricism

Very few systems are described by nonlinear equations:complex enough to be interesting but simple enough to be tractableFind methods that are predictive even if nonanalytical.

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Consider the design and synthesis of a simple organic substance.

Each step in multistep synthesis involves 1022 molecules of several types, in 1024 molecules of solvent, and ca. 10 different strategies for synthesis: (question on Organic exam)

11) Fill in the missing reagents in the synthesis of buproprion. (3pts)

HC

HN

tBu

CH3

O

Cl

"Buproprion"

CH2

CH3

O

Cl

CHBr

CH3

O

Cl

Br2

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Isomers and Emergent Structures in ChemistryAs molecular size increases, so does complexity, and emergent new properties appear. -The linear and branched isomers-Enantiomers can only be distinguished in a chiral environment.-Molecules with more than one chiral center can exist as diastereoisomers, enantiomers, or meso compounds.-Variations in dihedral angle (twisting) lead to conformational isomers, and variations in dihedral angle with time lead to rotormers and dynamic molecular structures.-Many pharmaceutical agents are small molecules (12 – 100 atoms) that are able to enter enzyme active sites or hormone receptor sites where they "mimic" – the “natural” molecules, agonise (positive effect) or antagonise (negative effect).

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Mechanistic Pathways Reaction mechanisms can be deconstructed into sequences of steps where atoms rearrange and electrons transferred, ABOR (Acid-Base,Oxidation-Reduction) steps, although it is usually more useful to consider reaction mechanisms in terms of unit mechanistic steps and sequences of unit steps, :e.g.•Complexation •Fragmentation •Substitution, Elimination, Addition •Metathesis : Pericyclic processes, Precipitation, Rearrangement

H

CH3

H CH2CH3

Br

CH2CH3 H

CH3

H CH2CH3

CH2CH3+

CH3OH H

CH3

CH2CH3

CH2CH3

CH3OH2+

H

CH3

H CH2CH3

Br

CH2CH3

H

CH3

CH2CH3

CH2CH3

CH3OH

CH3O-

E1 E2

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Physical Organic Chemistry

•Analog reasoning by linearization•Developed to provide “semiquantitative” descriptions of organic mechanisms that form the framework of organic synthesis,•Reacting species exists in solution with local and nonlocal variations in structure (substituent, steric, solvation, and electronic effects),•Method: 1) select a reaction with extensive enough data to correlate structure with reactivity, then 2) hypothesize that small changes in structure correlate with G.

1.3 Self-organization Phenomena in Chemistrybut first Equilibrium Chemistry

Chemical Equilibrium: attained only when rate of forward reaction = rate of reverse

reaction

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A + B C + Dk

k'K (Eq constant) = ---------- = ---

CC CD k

k'CA CB

k (Temp, Pres) "rate constant" ----- = k CA CB

x ydCA

dtC = concentration

X

LeChâtelier’s Principle: After a stress is applied to a system at equilibrium, the system responds by eliminating the “stressor” and producing the “stressee”.

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stress

response

+ 3 H2 (g) 2 NH3 (g)N2 (g)

stress

response

Chemical Kinetics

 

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CHAr

N

HNH

Ar'

CHAr

N

HN

H"Ar

Ar'

CHAr

N

HNH

Ar'

"Ar

"Ar

1,3 dipole iminamine

Ea

E

Erel

Reaction Coordinate

TS

Chemical Kinetics

 

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ln (k/T) = -G‡/RT + C

linear equation

ln (k/T)

(1/T)

-G /R

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1,3 dipole iminamine

Ea

E

Erel

Reaction Coordinates

TS iminamine'

Ea'

E'

TS'1,3 dipole'

"earlier"

Ea Ea'

E E'

TS'

<

>

If 1,3 dipole' 1,3 dipoledestabilized relative to

r r'

r < r'

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CH2

NZN

CH2

NZNX

H

Y

X

HY

A

BCH2

ZNCH2

ZN

WhereA1:X=Ar, Y=H, Z=HA2:X=H, Y=Ar, Z=HA3:X=H, Y=H, Z=Ar

HX

Y HY

CCH2

NO

CH2

NOH

X

Y HY

DCH2

OCH2

OHX

Y HY

EN CH2

NZN

HN CH2

NZNH

X

CCH2

NZN

Y

FCCH2

HN

ZN

YHX

X

X

X

X

X

Quantitative Structure Activity Relationships (QSAR)

"A QSAR [project] attempts to find consistent [linear] relationships between the variations in the values of molecular properties and the biological activity for a series of compounds, so that these rules can be used to evaluate new chemical entities". From Introduction to QSAR Methodology on the Network Science site.

Finding a linear relationships between molecular structure and pharmaceutical activity are the highest goals of drug discovery research presently.

Conclusion:Linearities exist in “pharmacology space” in terms of

dose-response and structure-activity. “Response = Fn(structure)”

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What This MeansChemical Systems Chemistry consists of multiple systems which

together explore and define chemistry space. Consider the term "explore":G “Free Energy” goes to zero, i.e. system goes to

EquilibriumG = H – T S H enthalpy heat transfer S “entropy” measure of available states to the

system

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Chemical species are quantum objects that vibrate, rotate, translate (move), and can undergo electronic transitions. An array of mathematical tools – based on quantum mechanics and kinetic theory (statistical thermodynamics) – is available. The techniques involved are covered by undergraduate level physical chemistry courses in first and third years, and applications in graduate school.

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The equilibrium distribution of species in a system with two states, i & j, and where i is higher in energy than j, is modeled by the Boltzmann relationship:

where:n is the number of particles (mole fraction) in the states ni and njE is the energy of the states Ei and Ejk is Boltzmann's constant, 1.38066 x 10-23J.K-1

T the thermodynamic (Kelvin) temperature

At higher temperatures, the fraction of molecules with Ea is greater than at low T.

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Consider the statement: "chemistry consists of multiple systems": Each of the following is "a system":An atomThe periodic tableA closed thermodynamic systemKinetic theoryThe gas lawsA closed, half-filled jar of waterButane and its conformersA Bunsen burner flameA gas chromatographThe manufacture of methyl tertiary butyl ether, MTBEInorganic chemistryMechanistic theory

Etc., etc., etc...Chemical systems explore their local environments and in total, define the expanding boundary of chemistry space. At university, chemistry is always taught on a topic-by-topic (system-by-system) basis.

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The ergodic hypothesis states that the time averaged behavior of microscopic quantities – atoms & molecules – gives the same result as the macroscopic "ensemble" average, where the "ensemble" is a collection of all the possible states that than an assembly of molecules would reach in an infinite amount of time.

Only closed systems can be perfect and completely uncomplicated. Only closed systems can exhibit dynamic equilibrium. Open systems can never be at true equilibrium, although careful experimental design may approximate it to be closed.Isolated systems exchange neither matter nor energy with surroundings.

It is better to regard any phenomena that can be described in terms of a chemical equation as representing change in phase space.

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Linear Chemistry: Summing UpThe linear regions of behavior in chemistry space are

so incredibility important to science, technology/engineering and education that practitioners tend to concentrate on the linear regions. The effect is that chemistry space appears to be more linear and predictable than it actually is.

Scientists and philosophers of science are interested in linear behavior because linear data can be converted to models, theories and laws, and this profound knowledge is used to help explain the world we inhabit.

Engineers and technologists are always looking to exploit regions where behavior is stable and predictable. Bridges are seldom designed to be on point of collapse, and likewise, chemical engineers develop processes which maximize yield and minimize the risk of explosion.

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The linearities are associated with the pattern recognition logic of molecular biology. These linearities are emergent. Chemistry is evolving away from the manipulation of individual molecules to describing systems of molecules: components of living cells and of “materials”.

Nobels in Chemistry:2009 "for studies of the structure and function of the ribosome“2008 "for the discovery and development of the green fluorescent protein, GFP“2006 "for his studies of the molecular basis of eukaryotic transcription“2004 "for the discovery of ubiquitin-mediated protein degradation“2003 "for discoveries concerning channels in cell membranes“2002 "for the development of methods for identification and structure analyses of biological macromolecules"

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Gases, Liquids, Solids and the Phase Interaction Matrix

We learned about the gaseous, liquid & solid states of matter during in our very first science classes.

Later, we learned, perhaps, that at high concentrations – close to 1:1 molar ratios – classic homogeneous

systems like methanol and water are actually considerably more complicated than may be assumed.At high concentrations, activity and fugacity "fudge

factors" have to be employed.Linear behavior is rare. Most phase interactions are

non-linear, inherently complex and emergence abounds.04/21/23 36

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"When a simple alcohol such as methanol or ethanol is mixed with water, the entropy of the system increases far less than expected for an ideal solution of randomly mixed molecules. Our data indicate that most of the water molecules exist as small hydrogen bonded strings and clusters in a 'fluid' of close packed methyl groups, with water clusters bridging to neighbouring methanol -OH functions through hydrogen bonding. "Molecular Segregation Observed in Concentrated Alcohol-Water Solution by Dixit et. al., Nature, 416, 829-832 (2002)

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Isolated system, T = 0

S = R ln(Vf inal / Vinit) > 0

Gas expansion

T1 = T2

1 2

21

T1 = T2

Thermal diffusion

Production of entropyin steady statebut more order!

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deS = dH/T

diS = Heat transfer, Chem. reactions,

Dif fusions

Irreversible mechanisms diS > 0 or 0 @ Eq

dS = diS + deS

dS = 0 @ Stationary State and diS = - deS (negentropy)

Entropy production = diS/dt = J . X > 0J = f lux of irreversible process (rate of chem reaction, heat transfer)X = force (T gradient, G)

J-M Andre, Chaos and chemistry: Simple models to understand chaos in chemistry, in Computational Materials Science, J. Leszczynski, p. 1-29, Elsevier (2004).

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Coupled acid-base and oxidation-reduction reaction steps,the beginning of our journey to the exploration of Dissipative structures,Bifurcations, Chaos,Strange Attractors, … Life

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