The Structure and Function of Living Organisms

Abstract

The systemic approach adopted in this work focuses on generic biological phenomena. The goal is to explain the strategies employed by biological systems by invoking fundamental concepts in physics, chemistry, and information theory. Structure and function is the first of five chapters which make up the book.

In biology, structure and function are tightly interwoven. This phenomenon is closely associated with the principles of evolution. Evolutionary development has produced structures which enable organisms to develop and maintain its architecture, perform actions, and store the resources needed to survive. For this reason we introduce a distinction between support structures (which are akin to construction materials), function-related structures (fulfilling the role of tools and machines), and storage structures (needed to store important substances, achieving a compromise between tight packing and ease of access).

Arguably the most important property of biological structures is their capacity for self-organization. Ongoing evolution has led to the emergence of biological constructs capable of exploiting basic physico-chemical interactions in support of directed organization processes, limiting in this way the quantity of the encoded information needed to perform their function. Examples of self-organization include the spontaneous folding in water of polypeptide chains and creation of cellular membranes.

In biology, structure dictates function.

• 1. Role and importance of polymers in biology

• 2. What is meant by “autonomous operation” and how is it achieved?

• 3. Reasons behind the diversity of intra- and extracellular scaffold structures

• 4. Role of the cellular membrane as the boundary between the cell and its environment

• 5. How is the cellular membrane stabilized?

• 6. Role of polysaccharides in biology—reasons behind the observed diversity

• 7. Tools and machines in biology—what are the advantages of constructing machines?

• 8. What does the Michaelis-Menten equation tell us about the properties of enzymes?

• 9. Mechanism of action of enzyme inhibitors (versus drugs)

• 10. Types of proteins—structural characteristics and relationship between structure and function

• 11. How is energy stored in biological systems?

• 12. Self-organization—its properties and importance in biology

• 13. How is information stored in biological systems?

The mechanisms described in this chapter can be experimented with using two web applications we provide for the reader’s convenience.

HPHOB online tool provides the ability to compute FOD model parameters for arbitrary protein structures. The tool is available at https://hphob.sano.science.

The reliance of nature on self-regulation and self-organization implies a certain specificity in interactions. At the same time, evolutionary pressure acts to eliminate burdensome and disadvantageous structures. Tight coupling between structure and function is therefore ubiquitous in biology. Analysis of the available information points to strategies for creation and exploitation of structures which facilitate certain processes in living organisms.

1.1 General Physiochemical Properties of Biological Structures

1.1.1 Small-Molecule Structures and Polymers

Biology makes an extensive use of small-molecule structures and polymers. The physical properties of polymer chains make them a key building block in biological structures. There are several reasons as to why polymers are indispensable in nature:

• A. Polymers enable multipoint surface contact, which strengthens reactions and yields strong complexes held together with noncovalent bonds. The structure of a polymer makes noncovalent bonding (which is far more common than its covalent counterpart) a meaningful mode of interaction, sufficient to stabilize compounds which could not otherwise be constructed from monomers.

  Figure 1.1 depicts the interaction of monomeric units and polymers in a model system.

• B. They enable the use of globular polymer structures as carriers of atypical environmental conditions, particularly apolar microenvironments, isolated from water by a polymer layer. This phenomenon gives rise to active protein compounds, which—owing to the apolar nature of their environment—catalyze many reactions otherwise unattainable in water (Fig. 1.2).

• C. The multifocality of interactions involving polymers provides for the emergence of structures unique in terms of their surface shape and orientation (Fig. 1.3). In this way polymers can be used to encode information.

• D. Creation of complexes using noncovalent bonds enables reversible and controllable reactions which are fundamentally important in biological systems.

Fig. 1.1

The effect of noncovalent interaction on the properties of small-molecule compounds and polymers. Noncovalent bonding of (a) monomeric units (kinetic energy exceeds compound stabilization energy—compound not formed), (b) polymers (noncovalent bonding energy exceeds the kinetic energy of individual interacting compounds (aggregate formed))

Fig. 1.2

Distribution of apolar amino acids in a myoglobin molecule (wireframe model). Apolar amino acids are represented as colored spheres. The globin molecules with (left) and without (right) heme were put together to expose the active region (data obtained from the Protein Data Bank)

Fig. 1.3

Active group of immunoglobulin with an attached ligand (polypeptide chain in space-filling model) and a planar cross-section of the same complex (data obtained from the Protein Data Bank)

1.1.2 The Biological Purpose of Cellular and Organism Structures

In general terms, biological structures can be divided into three groups, each serving a different purpose:

• 1. Supporting structures, not directly involved in processes which constitute life, but providing a framework and foundation for such processes. These structures perform shielding, reinforcing, and dividing functions, which roughly equate to the role of architecture in our macroscopic world.

• 2. Structures directly involved in the functioning of living organisms, i.e., those that facilitate metabolism and motion. If we accept the proposition that biological functions are inseparably tied to regulatory processes and that all functional structures belong to regulatory loops, these structures can be further subdivided into receptors, effectors, and information conduits.

• 3. Storage structures, i.e., structures used to store information and energy. Their goal is to fit as much energy (or information) into as small a volume as possible, as well as to enable rapid access to both.

The presented classification acknowledges the divergence of structural elements which form living organisms. The properties of structures belonging to each group are a clear consequence of their evolutionary goals. Similar models exist in many non-biological systems where individual objects interact to perform a common task. An example of such a system is depicted in Fig. 1.4.

Fig. 1.4

The factory as an autonomous entity with subunits which fulfill (a) supporting, (b) functional, and (c) storage tasks

It can be noted that the challenges that need to be overcome when, e.g., erecting buildings (such as factories) are substantially different from those involving machines and tools. Furthermore, any production process (and particularly one that is subject to fluctuations in the supply of raw resources and demand for finished goods) must take into account storage capabilities: the shape of manufactured goods should enable efficient storage and easy access.

Figure 1.5 summarizes the properties of the presented structures and the reasons behind introducing this classification.

Fig. 1.5

Task-oriented properties of biological structures

1.1.3 Supporting Structures

The purpose of these structures is to provide shielding and support and also—owing to their physical properties—ensure sufficient rigidity and elasticity of biological entities. Supporting elements are, by their nature, one- or two-dimensional: they include fibers, membranes, and walls.

As conditions and processes which take place inside a cell differ significantly from those encountered outside, supporting structures must be suitably differentiated to suit both. Thus, each cell and each organism make use of many different types of supporting structures.

1.1.3.1 Cellular Supporting Structures

Cells owe their existence to fibers forming the so-called cytoskeletons. The cytoskeleton can best be described as an aggregation of structures which provide the cell with rigidity while also ensuring certain elasticity, similar to the scaffold of a tent. However, unlike a manmade scaffold, the cytoskeleton must allow for changes associated with the biological function of the cell (relative motion of cellular organelles; motion of the entire cell). Motion is sustained by maintaining a dynamic balance between formation and decomposition of fibers. In addition to directed motion, the supporting structure must also enable expansion and contraction of the cell.

As explained above, motion is facilitated by fibrillar structures which consist of globular subcomponents, attached and detached to one another in a steady process of synthesis and decomposition. Typical fibrillar structures which fulfill these criteria include microtubules and microfilaments (Fig. 1.6 A and B).

Fig. 1.6

Basic components of cytoskeletons: (A) microtubules, (B) microfilaments, and (C) intermediate filaments: (a) dimeric forms, (b) tetrameric forms, and (c) final form of the fiber

Microtubules are pipe-like structures (Fig. 1.6 A) characterized by significant rigidity and ability to withstand mechanical forces. In terms of their structural properties, they can best be compared to a factory smokestack (Fig. 1.7).

Fig. 1.7

Smokestack (a) and rope (b) as physical models of supporting structures shaping the mechanical properties of cytoskeletons

The chain-like microfibrils (Fig. 1.6 B) also consist of globular units. Their elasticity is far greater than that of microtubules. In a way, they resemble ropes, although their tensile strength is not as great (a consequence of the fact that, just like microtubules, they are also composed of globular units).

In contrast, structures formed from fibrillar compounds are far stronger and capable of resisting significant longitudinal forces. The most distinctive cellular supporting structure is the so-called intermediate filament—another type of fiber which contributes to the scaffolding of a cell. Intermediate filaments differ significantly from the structures mentioned above. Their monomeric elements are fibrillar, unlike microtubules and microfilaments which consist of globular units (Fig. 1.6 C). They assume the form of parallel dimers (Fig. 1.6C.a) forming a structure which can be compared to roof tiling (Fig. 1.6C.b) Together, these units constitute the final form of the intermediate filament (Fig. 1.6C.c). Intermediate filaments resemble ropes with respect to their physical properties (Fig. 1.7).

Unlike microtubules and microfilaments, intermediate filaments are apolar. Their dimers are bound in a counter-parallel fashion, such that their terminal carboxyl and amine domains enter a 1:1 relation with one another. Moreover, it seems that intermediate filaments are not autonomous in determining their direction of expansion within a cell and that they are assisted in this respect by microtubules. Research suggests that intermediate filaments do not degrade in the same way as microtubules: instead of yielding a substrate which can be further used to construct supramolecular structures, they are instead digested and broken down into fragments. Owing to these properties, intermediate filaments are more closely related to extracellular supporting structures. They are not restricted to acting within the boundaries of a cell; instead, they may permeate the cellular membrane (at points where desmosomes are located) and attach themselves to the cytoskeletons of neighboring cells. They stabilize multicellular complexes in epithelial tissues and organs.

Elongation of intermediate filaments is made possible by specific interactions of globular fragments positioned at the ends of monomeric fibrils (Fig. 1.6C). In addition to elongation, the filaments are also capable of growing in thickness. The fibrous nature of their monomeric components grants them physical resilience and supports their biological function as supporting structures, although their relative lack of autonomous direction and low renewal rate make them the most static component of the cellular cytoskeleton.

Intermediate filaments are nonuniform in nature, though they all share a similar basic structure. Their lack of uniformity is a result of specific adaptation to the requirements of various types of cells.

As structures, microfilaments and microtubules are not strictly limited to facilitating motion: their rigidity and elasticity enable them to play an important role in reinforcing the structure of the cell.

It appears that microfilaments concentrated near the boundaries of the cell are responsible for maintaining proper tension of its membrane, while microtubules provide the cell with appropriate rigidity (Fig. 1.8).

Fig. 1.8

The tent as a support model, comprising elements with varying rigidity and elasticity (poles and guy ropes), which together ensure proper shape of the finished structure

Observing the dynamic changes in the length of microfilaments and microtubules as well as the motion patterns effected by interaction with motor proteins enables us to classify such cytoskeletal structures as functional in nature. This association of supporting structures with motion is quite peculiar and unlike most manmade objects. In search for suitable macroscopic equivalents, we can refer to escalators, rotating stages, and drawbridges, which—depending on the situation—may serve as barriers or roads (Fig. 1.9).

Fig. 1.9

Painting of a drawbridge by Vincent van Gogh

1.1.3.2 Cellular Shielding Structures

The second class of cellular supporting structures comprises of shielding structures—specifically, cellular membranes (consisting of phospholipids) and extracellular membranes (e.g., the basal membrane, composed of fibrillar protein and glycoprotein aggregates). Phospholipid cellular membranes also include glycolipids, cholesterol, and various proteins. While all integrated proteins contribute to the stability of their membranes, only some of them (such as spectrin) are clearly supportive in nature, serving as a scaffold for the membrane itself.

The cohesiveness and rigidity of membranes are important in determining their function. Phospholipid solutions act as liquid crystals: in water they form a planar (non-spherical) micelle capable of performing the functions of a membrane. Such interlocking panel-like arrangement is made possible by minimizing repulsive forces through mutual cancellation of positive (choline) and negative (phosphoric acid) charges in the polar fragments of phospholipid molecules (Fig. 1.10).

Fig. 1.10

Close internal and external placement of positive and negative charges in the polar layer of the phospholipid membrane facilitates interlocking arrangement of molecules, resulting in the formation of a planar micelle (neutralization of charges eliminates repulsive forces)

The lipotropic and liquid crystal properties of membranes enable them to retain some characteristics of a liquid. At normal body temperatures, cellular membranes have the approximate thickness of tar. The elasticity of the membrane can be increased or decreased without affecting ambient temperature, by altering the ratio of saturated and unsaturated fatty acids (Fig. 1.11).

Fig. 1.11

The impact of double bonds and cis- and trans-isomers on the area of adhesion and range of potential molecular interactions in the lipid layer of a cellular membrane

The presence of a double bond and the resulting divergence of cis- and trans-configurations reduce adhesion and inhibit molecule interactions, thus lowering the overall rigidity of the system. On the other hand, the increased adhesion of saturated molecules results in increased rigidity, more closely resembling that of a solid. An identical phenomenon occurs in margarine production where the viscosity of vegetable oils is increased via reduction reactions.

Another important mechanism which contributes to the rigidity of cellular membranes is cholesterol intercalation.

Cellular membranes (both cytoplasmic and nuclear) may be further stabilized by a two-dimensional lattice consisting of fibrillar proteins parallel to the membrane. Such a scaffold is formed, e.g., by spectrin molecules in the membranes of erythrocytes and other types of cells. Spectrin is a protein-based fibrillar complex made up of a coiled pair of giant polypeptide chains designated α and β. Both chains consist of periodic sequences of repeating protein domains, each in the shape of a helix, separated by hinge fragments. Together with microfibrils, they create a lattice attached to the underside of the membrane. This structure is particularly important in erythrocytes which lack the skeleton present in eukaryotic cells and therefore require special membrane stabilization mechanisms.

1.1.3.3 Extracellular Supporting Structures

Similar to intermediate filaments, protein microfilaments present in extracellular supporting structures are not directly involved in motion; thus they may be fibrillar, with relatively limited exchange dynamics. Examples of such structures include collagen and elastin. Just like in intermediate filaments, their fibrillar nature is primarily due to the lack of variability in their amino acid composition (repeating GLY-PRO-X sequences in collagen and PRO-GLY-VAL-GLY in elastin).

Contrary to amino acid sequences which give rise to fibrillar structures, the globular nature of functional proteins is determined by high variability of amino acid chains, in particular the uneven distribution of hydrophobic residues.

The abundance of proline and glycine in collagen chains determines their structure (although it should be noted that collagen owes its fibrillar nature chiefly to the repeatability of amino acid sequences). A high number of proline and glycine units impose specific torsion on the resulting spiral, while their relatively small volumes (particularly in the case of glycine) provide the resulting strands with high cohesiveness which translates into increased rigidity.

Elastin is a special protein responsible for the elasticity of tissues. The very notion of elasticity is somewhat unusual as the material in question must be capable of fluid noncooperative transition from a folded to a stretched state, yet retain the tendency to return to the initial folded state (much like rubber). Such properties are not found in secondary and tertiary structures of polypeptide chains, which—being cooperative—tend to unfold in an abrupt manner, kinetically equivalent to the phase transition observed in denaturation (Fig. 1.12).

Fig. 1.12

Transitions in a cooperative (solid line) and noncooperative (dashed line) system as a response to destabilizing forces

The elasticity of elastin results from shearing hydrogen bonds. In this respect, it may be compared to mechanically induced melting. The fluid nature of this process proves that the structure of elastin peptide chains is highly random (Fig. 1.13).

Fig. 1.13

A hypothetical model explaining the elasticity and noncooperative melting of elastin. The diagram in the top right-hand corner presents the symbol and structure of desmosine. Darkened areas indicate potential hydrogen bonding sites

Owing to the rotational freedom of glycine in polypeptide chains and the fact that glycine constitutes 50% of elastin, the resulting protein may assume a practically unlimited number of folding configurations. The force which induces folding is most likely associated with hydrogen bonds stabilizing the so-called β-turns, wherever proline and glycine are directly adjacent. In addition, the hydrophobic nature of elastin (a consequence of valine abundance) protects hydrogen bonds from coming into contact with water, thus facilitating smooth refolding with many intermediate states and high structural randomness. Covalent binding of peptide chains with desmosine bridges ensures continuity of the resulting material, enabling it to assume one-, two-, and even three-dimensional shapes. This type of structure is functionally equivalent to a spring mattress, whose individual components are capable of contraction yet bound together in a stable configuration (Fig. 1.14).

Fig. 1.14

Fragment of a spring mattress—a mechanical model functionally analogous to elastin

The polypeptide chains of collagen are mostly polar and therefore unable to fold in a random fashion. Here, water-isolated hydrogen bonds can exist only between separate chains; hence collagen stabilizes in the form of tightly fused triple-chain conglomerates (Fig. 1.15). The tight fusing of collagen fibrils, made possible by their high glycine content, increases their rigidity and enables them to mechanically stabilize connective tissue.

Fig. 1.15

Structure of collagen, showing the location of water-isolated hydrogen bonds which link individual strands

Keratins are another family of fibrillar proteins, distinguished by their purpose and function. They act as intermediate filaments and are essentially intracellular in nature, although they may occasionally traverse cellular boundaries. Synthesized inside living cells, they persist through cell death, forming a solid, insoluble mass, expressed, e.g., as fingernails and hair.

Keratins include repeating seven amino acid sequences (a property common in intermediate filaments). This repeatability determines their fibrillar nature, while low polarity and high numbers of disulfide bonds linking individual chains contribute to the mechanical resilience of structures composed of keratin fibers.

1.1.3.4 Polysaccharides as Supporting Structures

A special class of supporting structures consists of polysaccharides. These substances are characterized by high rigidity, which is due to the stabilizing influence of β-glycosidic bonds (Figs. 1.16 and 1.17).

Fig. 1.16

The branching helical structure of α-type polysaccharide chains reduces the potential for inter-chain contact and limits their packing density

Fig. 1.17

The simple, nonhelical structure of β-type polysaccharide chains facilitates easy inter-chain contact and ensures good mechanical resilience of the resulting complexes

Contrary to storage sugars, i.e., α-type polysaccharides which exhibit the tendency to form helical structures, the presence of β-glycosidic bonds results in threadlike strands which interact with one another in a highly specific fashion. Good contact between individual fibrils, particularly the high number of point-to-point interactions observed in β-type polysaccharide chains, makes the resulting complexes highly resistant to mechanical damage and thus useful in supporting structures. The relatively low diversity of monomeric units observed in hydrocarbon polymers (compared to proteins) results in similarly low diversity among their derivative structures.

It should be noted that the general diversity of proteins is a direct consequence of the enormous variability in both the number and ordering (sequence) of amino acids, giving rise to a wide array of function-specific structures. By the same token, polysaccharides consisting of a single type of monomer cannot adapt to diverse functions and are therefore better suited to providing structural support.

Cellulose is a conglomerate of long fibrils, each comprising hundreds of glucose molecules. The most frequently observed unit of cellulose is a packet consisting of approximately 60–80 fused threadlike polymer strands. Further packing yields a clustered, uniform mass.

Polysaccharide frameworks are ubiquitous in the realm of plants and among primitive animals such as insects. In the latter group, the most frequently occurring polysaccharide is chitin—an interesting example of how nature reinforces polypeptide structures by increasing the number of inter-chain interactions. In the case of chitin, this function is performed by amide clusters, which easily form hydrogen bonds and therefore increase the overall tensile strength of the framework. On the other hand, rigidity can also be reduced via uniform polarization of individual monomers comprising the polymer chain, which increases their electrostatic repulsion and lowers the tensile strength of the resulting material (Fig. 1.18).

Fig. 1.18

Fragments of polysaccharides with differing levels of polarity: (a) chitin, (b) cellulose, (c) hyaluronate, (d) keratan sulfate, (e) chondroitin sulfate, and (f) heparin

Polar polysaccharides, such as keratan sulfate or chondroitin sulfate, are encountered in tissues as chains. Together with specific proteins and (optionally) hyaluronic acid, they can form giant, branching, treelike structures which play an important role in binding water molecules. Their interaction with collagen fibers (with which they form complexes) gives the connective tissue the required rigidity and turgor as a filler (Fig. 1.19).

Fig. 1.19

The characteristic branching structure of proteoglycans: (A) hyaluronic acid, (B) glycoprotein chains, and (C) bound water molecules (shaded areas)

Glycosaminoglycans are a good example of how polar polysaccharides can be employed in the connective tissue (Fig. 1.19).

In summary, we can state that—contrary to the cellular cytoskeleton—extracellular polymer structures (both protein- and carbohydrate-based) play a strictly passive and supportive role in living organisms.

1.1.4 Structures Associated with Biological Functions

The term “functional structures” denotes structures which facilitate metabolism and motion (respectively—changes in the properties of matter and changes in location).

Reversible creation of specific complexes enables biological functions.

The seemingly endless diversity of biological functions frustrates all but the most persistent attempts at classification. For the purpose of this handbook, we assume that each function can be associated either with a single cell or with a living organism. In both cases, biological functions are strictly subordinate to automatic regulation, based—in a stable state—on negative feedback loops, and in processes associated with change (for instance, in embryonic development)—on automatic execution of predetermined biological programs. Individual components of a cell cannot perform regulatory functions on their own (just like a thermometer or heat pump extracted from a refrigerator). Thus, each element involved in the biological activity of a cell or organism must necessarily participate in a regulatory loop based on processing information.

In light of this assumption, we can divide all functional structures into the following categories:

• 1. Receptor structures

• 2. Effector structures

• 3. Information carriers

• 4. Structures which are subject to regulation (regulated process components)

The detector function of a receptor and the action of an effector may be facilitated by simple proteins or by complexes consisting of many protein molecules. Proteins are among the most basic active biological structures. Most of the well-known proteins studied thus far perform effector functions: this group includes enzymes, transport proteins, certain immune system components (complement factors), and myofibrils. Their purpose is to maintain biological systems in a steady state. Our knowledge of receptor structures is somewhat poorer, mostly due to their tight integration with cellular membranes, making them difficult to extract and isolate in a crystalline form.

Involvement in a given function may be either active or passive. Active involvement occurs in proteins and certain forms of RNA. The term “active form” typically denotes the form genetically programmed to create a specific complex and fulfill a specific biological purpose. This form is also responsible for ensuring that the resulting complex is well suited to its function and that it undergoes structural changes while performing that function. Biological functions are usually mediated by proteins. On the other hand, passive involvement in biological mechanisms is characteristic of reaction substrates and products, as well as various messenger molecules such as hormones and DNA.

Contrary to supporting structures, the proteins which participate in functional aspects of life are almost invariably globular.

Receptor and effector structures may be either simple or complex. The need for complex receptors emerges when signals become unclear and difficult to classify. A similar process occurs in effectors, where certain tasks require advanced and well-organized systems. For instance, most enzymatic effectors can be divided into distinct stages (catalysis of complex reactions often involves many separate steps). Such multienzyme effectors assist, e.g., in glycolysis, synthesis of purines and pyrimidines, as well as synthesis and degradation of fatty acids.

Simple structures, including individual enzymes and components of multienzyme systems, can be treated as “tools” available to the cell, while advanced systems, consisting of many mechanically linked tools, resemble machines. The rationale behind constructing machines is obvious: certain processes cannot take place without the aid of complex mechanical devices. Combined action of tools enables efficient processing of materials while reducing the need for immediate access to information. In a machine model, individual elements (tools) perform work under the supervision of integrating mechanisms (Fig. 1.20) such as conveyor belts, chains, gears, etc. In a cell the role of conveyor belts is fulfilled by special protein structures acting as booms or servos. Other more advanced structures can be distinguished as well, facilitating the conversion of energy into structural changes. Such mechanisms are often thermally powered, i.e., their action is determined by the laws of Brownian motion.

Fig. 1.20

A simple tool (shovel) (a) and an advanced snow collector, consisting of linked shovels (b) (four stages of operation depicted for machine b)

Machine-like mechanisms are readily encountered in living cells. A classic example is fatty acid synthesis, performed by dedicated machines called synthases. The process is similar to β-oxidation; however synthesizing a fatty acid molecule carries a net increase in the structural ordering of the product. This property implies the need for energy as well as a source of information which is implicitly contained in the structure of synthase, enabling its enzymes to collaborate on a common task. In contrast, enzymes charged with degradation of fatty acids require no such information and do not need to form machines as their final product is more chaotic than the substrate they break down.

Fatty acid synthase is a homodimer consisting of two identical (260-kd) subunits which perform enzymatic actions related to the synthesis of palmitic acid. Both structures are cross-linked with loose hinge fragments, enabling relatively unrestricted motion—an important property required for good contact between the enzyme and the chain undergoing synthesis. Owing to the apolarity of the substrate, synthesis occurs in dedicated hydrophobic gaps in which the active moieties are concentrated. The boom-like structure which aligns the substrate with active sites of the complex is called ACP (acyl carrier protein). It includes a long, flexible chain, structurally similar to coenzyme A. High flexibility of the whole complex, and particularly of ACP, creates suitable conditions for alignment of the substrate with moieties required at each stage of the synthesis process. Both halves of the machine come into play at certain stages, while their cross-linked nature is primarily a stabilizing factor (Fig. 1.21).

Fig. 1.21

Schematic model of fatty acid synthase, showing clustered enzymatic domains and servos (ACP). Small black circles represent SH (sulfhydryl) groups, while brackets indicate moieties responsible for specific stages of the synthesis process

Another example of a biological machine is the pyruvate carboxylase enzyme which consists of two enzymatic domains (biotin carboxylase domain and carboxyl transferase domain) in addition to a biotin-binding domain (Fig. 1.22). Multiunit structures acting as machines can be encountered wherever complex biochemical processes need to be performed in an efficient manner.

Fig. 1.22

Functional model of a simple machine (pyruvate carboxylase). The colored section indicates the biotin-binding domain

As mentioned above, the simplest biological machines employ long, flexible booms and servos with thermally determined motion patterns (Fig. 1.23). More advanced molecular machinery draws the energy for coordination and mechanical action from high-energy bonds. A good example is the ribosome which acts as a shifting matrix for the synthesis of polypeptide chains.

Fig. 1.23

Examples of exterior area structures: (a) biotin-binding domain, (b) lipoamide, and (c) ACP

If the purpose of a machine is to generate motion, then a thermally powered machine can accurately be called a motor. This type of action is observed, e.g., in myocytes, where transmission involves reordering of protein structures using the energy generated by hydrolysis of high-energy bonds.

Some production tasks are performed by the entire “factory chains,” i.e., structures integrated in cellular membranes in an ordered fashion. This mode of operation is applied in synthesis and distribution of certain proteins (Fig. 1.24). The nucleus of the cell, acting as a “design department,” issues blueprints via the “conveyor belt” structure of endoplasmic reticulum. The resulting products enter the Golgi apparatus while undergoing stepwise changes. Inside the apparatus they are “packaged” and cleared for “export” (i.e., expression outside the cell). The “wrapping paper” is actually a special protein called clathrin, whose associations assume the form of vesicles, encapsulating the synthesized “payload” proteins.

Fig. 1.24

Cellular structures involved in protein synthesis. Individual machine parts are integrated in membranes in an ordered fashion

In biology, function is generally understood as specific physiochemical action, almost universally mediated by proteins. Most such actions are reversible which means that a single protein molecule may perform its function many times. Functional proteins are usually globular in shape and contain similar types of active sites—pockets or clefts characterized by concentration of exposed hydrophobic residues and appropriate (for a given substrate) arrangement of polar amino acid groups or non-protein-based aggregates, enabling the site to attach to specific types of ligands. In addition, enzymatic active sites include a catalytic element (Fig. 1.25).

Fig. 1.25

Schematic diagram of the active site of trypsin. The exposed serine oxygen is the catalytic element responsible for attacking the Cα carbon of the amino acid involved in the peptide bond

This element is directly responsible for catalysis, i.e., for action which affects a specific bond in the substrate and converts it to an intermediate state where it can spontaneously reassemble into the final product. Catalysis can be performed by a special amino acid group, a metal ion, or a coenzyme (Fig. 1.26).

Fig. 1.26

Schematic diagram of a protein active site with a coenzyme (thiamine pyrophosphate) as the catalytic element of pyruvate decarboxylase

The intermediate state is an unstable form of the substrate, highly susceptible to environmental stimuli. This instability typically hinges on a single molecular bond also. Substrates can enter intermediate states as a result of mechanical stress resulting from local incompatibilities between a tightly bound substrate molecule and the active moiety of the enzyme. A good example is lysozyme whose active moiety strongly binds to polysaccharide fragments consisting of six monomers, one of which is sterically unaligned. The resulting change in the structure of the substrate deprives the glycosidic bond of its stability and eventually leads to hydrolysis.

In general terms, we can state that enzymes accelerate reactions by lowering activation energies for processes which would otherwise occur very slowly or not at all.

Hydrophobic component is required for the formation of stable ligand complexes in aqueous environments, irrespective of structural considerations. This is due to the fact that electrostatic interactions and hydrogen bonds are strongly selected against in physiological saline solutions, as water itself is a good donor and acceptor of protons, while salt ions act as shields. Thus, saline environments limit surface interactions and prevent native proteins from aggregating even at high concentrations (for instance, in blood plasma or egg white). Since spontaneous noncovalent surface interactions are very infrequent, the shape and structure of active sites—with high concentrations of hydrophobic residues—make them the preferred area of interaction between functional proteins and their ligands. They alone provide the appropriate conditions for the formation of hydrogen bonds; moreover, their structure may determine the specific nature of interaction. The functional bond between a protein and a ligand is usually noncovalent and therefore reversible. Covalent bonds formed in certain catalytic processes are usually short-lived and do not contribute to the stability of the product). In addition to providing a suitable area for reactions, hydrophobic environments also play an important role in determining the orientation of substrates. Any polar moiety in a predominantly hydrophobic area (i.e., the active site) stands out like a beacon and may determine the alignment of the substrate (Fig. 1.27).

Fig. 1.27

The role of background conditions in exposing the object of interest. Candlelight is clearly visible in a dark background (a) but becomes hard to discern when the background is well lit (b)

Chemical affinity of complexes may be expressed in terms of their dissociation constant K, where k₁ and k₂ indicate the rate of formation and degradation of the complex:

$$ K={k}_2/{k}_1 $$

The dissociation constant determines the state of equilibrium in antibodies, receptors, transport proteins, and other protein-ligand complexes. For enzymes, the equation is supplemented by a third variable indicating the rate at which the complex converts into its final product (k₃):

$$ K=\left(\ {k}_2+{k}_3\right)/{k}_1 $$

In enzymatic reactions K is also called the Michaelis–Menten constant (K_M) in honor of Leonor Michaelis and Maud Menten who discovered the relation between reaction rate v and substrate concentration S, showing that the equation

$$ v={V_{\mathrm{M}\mathrm{AX}}}^{\ast}\left[S\right]/\left({K}_{\mathrm{M}}+\left[S\right]\right) $$

determines the so-called saturation curve and that further concentration of the substrate beyond its maximum value for a given concentration of the enzyme does not result in an increased reaction rate. This observation yielded two important parameters of enzymatic reactions (K_M and V_MAX) and contributed to many important discoveries involving enzymes.

The activity of enzymes goes beyond synthesizing a specific protein-ligand complex (as in the case of antibodies or receptors) and involves an independent catalytic attack on a selected bond within the ligand, precipitating its conversion into the final product. The relative independence of both processes (binding of the ligand in the active site and catalysis) is evidenced by the phenomenon of noncompetitive inhibition, where the Michaelis-Menten constant remains unchanged despite a cessation of enzymatic activity in the presence of an inhibitor. This proves that the process of catalysis (dependent on coordinated action of numerous amino acids and, optionally, a coenzyme) is orthogonal to the enzyme’s capability to bind the ligand. Kinetic studies of enzymes have provided valuable insight into the properties of enzymatic inhibitors—an important field of study in medicine and drug research. Some inhibitors, particularly competitive ones (i.e., inhibitors which outcompete substrates for access to the enzyme), are now commonly used as drugs.

While proteins are among the most basic structures whose involvement in biological processes may be described as active and in spite of the fact that nearly all biological activity is protein-based, it should be noted that some biological processes occur on the RNA level. Ribozymes (which perform a handful of biological functions) appear to be among the most primordial active structures in biology.

Proteins are capable of functioning both as receptors and effectors. They may also actively transmit biological signals (e.g., kinases), although the role of passive carriers usually falls to non-protein structures (peptides, steroids, etc.) The distinction between receptor and effector proteins is the basic premise of this handbook. It applies to all functional proteins, irrespective of their location and task. Effector structures include enzymes, ion pumps and channels, proteins involved in transcription of genetic material, proteins which regulate muscle contraction, etc.

With respect to the locations and properties of proteins, we can generally distinguish the following groups (see Table 1.1):

• 1. Cellular proteins

• 2. Proteins belonging to the organism level

Table 1.1 General properties of proteins originating from cells and the organism

Since cells and organisms exist as distinguishable (though interrelated) biological entities, their respective proteins serve different purposes and can therefore be treated as separate groups. Cellular proteins are found inside cells and in cellular membranes, while organism’s proteins are present in interstitial cavities and in blood.

Cellular functional proteins are usually globular and often associated with enzymatic or regulatory functions, although in certain types of cells (such as myocytes) proteins governing contraction and relaxation may have a fibrillar structure. Another important subgroup consists of cytoskeletal proteins.

Membrane proteins also tend to be globular; however they are clearly distinct from intracellular proteins with respect to their structure and task. Unlike water-soluble proteins, they expose hydrophobic residues on their surface. This property is required for integration with cellular membranes. Membrane proteins responsible for interfacing with the external environment include receptors, pumps, and structures which facilitate cell adhesion and interaction.

Interstitial structures are apart from polysaccharides mostly composed of support proteins. A wholly distinct group of proteins can be found in blood. Their task is to mediate organ-to-organ communication, ensure homeostasis, and perform a wide array of protective functions, e.g., immune response, blood coagulation, inhibition of proteolytic enzymes, etc.

1.1.5 Energy and Information Storage Structures

Sequestration of resources is subject to two seemingly contradictory criteria:

• 1. Maximize storage density.

• 2. Perform sequestration in such a way as to allow easy access to resources.

In order for any system to gracefully tolerate variations in the availability of raw resources and demand for products, storage capabilities are required. Such capabilities augment the system’s autonomy, permitting continued operation even when crucial resources are temporarily lacking or products cannot be disseminated. In most biological systems, storage applies to energy and information. Other types of resources are only occasionally stored (this includes, e.g., iron, which is consumed in large amounts yet infrequently available—sequestration of iron is mediated by a dedicated protein called ferritin).

Energy is stored primarily in the form of saccharides and lipids. Saccharides are derivatives of glucose, rendered insoluble (and thus easy to store) via polymerization. Their polymerized forms, stabilized with α-glycosidic bonds, include glycogen (in animals) and starch (in plantlife). An important side effect of this type of bonding is the formation of twisted polymer chains, limiting packing density but enabling easy access. Glycosidic links are usually of type 1–4 (sometimes 1–6), giving rise to branching, treelike structures which can be readily manipulated by enzymes due to the multitude of potential points of contact (see Fig. 1.16).

It should be noted that the somewhat loose packing of polysaccharides, compounded by the presence of partially oxygenated carbons and relatively high degrees of hydration, makes them unsuitable for storing large amounts of energy. In a typical human organism, only ca. 600 kcal of energy is stored in the form of glycogen, while (under normal conditions) more than 100,000 kcal exists as lipids. Lipid deposits usually assume the form of triglycerides (triacylglycerols). Their properties can be traced to the similarities between fatty acids and hydrocarbons. Storage efficiency (i.e., the amount of energy stored per unit of mass) is twice that of polysaccharides, while access remains adequate owing to the relatively large surface area and high volume of lipids in the organism.

Most living organisms store information in the form of tightly packed DNA strands. Once neutralized with histones (in eukaryotic organisms), DNA can be wound on a protein scaffold, as depicted in Fig. 1.28.

Fig. 1.28

Hypothetical packing of DNA strands into chromosomes. The figure depicts consecutive stages of DNA coiling. Relative dimensions of elements are distorted in order to emphasize packing strategies

The principles of efficient packing and easy access apply here as well, precluding the simplest possible packing of DNA—multilayered coiling (akin to winding a thread on a spool). Similarly, all forms of solid-like aggregations are inefficient and therefore unusable. The most effective form of DNA packing involves looping the strand and winding it around a chromosomal scaffold so that each loop can be accessed separately and each fragment uncoiled without unwinding the entire chain. This model can roughly be compared to the arrangement of books on library shelves, enabling unobstructed access to each book (Fig. 1.29).

Fig. 1.29

The library as an information storage model, allowing easy access to books. Similar strategies can be observed in DNA packing

DNA packing begins by arranging it on histones. However, final packing consists of several stages. Histone-centered loops can be further coiled, creating a tight spiral with a microscopic thickness of 30 nm. In such a coiled thread, each loop is independently attached to a protein scaffold which forms the backbone of the chromosome. The final rate of compression (compared to the length of the uncoiled strand) is approximately 10,000-fold. It should be noted that only a small percentage of DNA (about few %) conveys biologically relevant information. The purpose of the remaining ballast is to enable suitable packing and exposure of these important fragments. If all DNA were to consist of useful code, it would be nearly impossible to devise a packing strategy guaranteeing access to all of the stored information.

1.2 Self-Organization

All complex cellular structures are the result of self-organization. In this process, simple elements spontaneously generate complex structures by connecting to one another in a predetermined way, usually with noncovalent bonds. The function of the cell is limited to synthesis of startup elements for self-organization. Figure 1.30 depicts this phenomenon by comparing the concept of self-organization with deliberate ordering.

Fig. 1.30

Organization and self-organization in the creation of coherent structures (schematic depiction). Construction of a scaffold via (a) deliberate activity and (b) spontaneous process. In the latter case, chaotically arranged elements with appropriate latches spontaneously assemble into a coherent structure

Controlled self-organization applies only to evolved structures oriented on association, e.g., water-soluble structural components which are thermodynamically unstable (metastable) and try to maximize their relative stability by reaching a global energy minimum. For obvious reasons, this process usually applies to partly polar structures immersed in aqueous solutions; however it may also be observed in fully polar structures where tight packing eliminates the possibility of interaction with water (note that the presence of water tends to inhibit noncovalent interactions between separate units). The cooperative interaction may be the driving force facilitating removal of water, e.g., folding of α-helical polypeptide chains stabilized by hydrogen bonds.

The structure of the aggregate depends on the structure of its components. Self-association yielding coherent structures can be viewed as a type of self-organization. Examples of self-association include the growth of planar phospholipid micelles and folding of polypeptide chains. In general, self-organization is most often based on noncovalent interactions where the associable domain elements achieve (through random collisions) the most energetically stable form for a given set of environmental conditions. Fibrillar supporting structures are intrinsically passive, and their aggregation is a consequence of relatively large contact surfaces. On the opposite end of the activity spectrum, cells guide the process of self-organization by altering the concentrations of substrates and the order in which they are exposed; however, they are usually unable to directly affect the process itself (with certain exceptions where the cell synthesizes structures capable of interfering with self-organization—such as chaperones).

Self-organization may also occur as a result of specific interactions such as the contact between proteins and ligands in active sites.

Fibrillar molecules tend to form parallel clusters. If special structures (e.g., planar or three-dimensional forms) are required or if atypical separation between parallel monomers becomes necessary, the cell may synthesize fibrillar units with attached globular fragments. Such fragments condition the emergence of specific aggregates (a similar process can be observed in the development of intermediate filaments). In most cases, however, the final form of the product is a result of the function of independent globular proteins, sometimes called accessory proteins (Fig. 1.31).

Fig. 1.31

Arrangement of microfilaments enforced by accessory proteins: (a) fimbrin, (b) α-actinin, and (c) filamin

Cellular synthesis of accessory proteins determines, to a large extent, the outcome of self-organization processes. This is similar to the final assembly of furniture or pipe segments using connectors in order to achieve the required configurations (Fig. 1.32).

Fig. 1.32

The role of accessory elements in construction tasks

1.3 Hypothesis

1.3.1 Protein Folding Simulation Hypothesis: Late-Stage Intermediate—Role of Water

The In Silico Protein Folding Process

In biology, function is enabled by proteins. Interestingly, only the primary structure of a protein—its polypeptide sequence—is genetically encoded; however, function can only be expressed when the resulting polypeptide chain adopts a specific 3D conformation through folding. Protein folding is a spontaneous process, guided mainly by changes in entropy: ΔG = ΔH – TΔS. It is mediated by interactions between amino acid residues (of varying polarity) and the environment, which is usually represented by water (highly polar) or the surface of a cellular membrane (nonpolar), which anchors some proteins. In addition, folding may be affected by local contact with other proteins or non-protein structures, such as polysaccharides. Finally, the structure of the protein may depend on the sequence of events accompanying its synthesis process. Secondary structure may begin emerging even before the chain has been fully synthesized and released by the ribosome, resulting in a different conformation than ab initio folding of a fully synthesized chain. The presence of a polar solvent promotes the formation of a hydrophobic core, which consists of hydrophobic residues encapsulated by a polar surface. However, the primary sequence does not always enable such arrangement of residues in the 3D protein body. In native proteins, certain deviations from the “ideal” distribution (which consists of a centralized hydrophobic core and a uniform hydrophilic shell) are evolutionarily conditioned and directly related to the protein’s function: they correspond to its active sites.

Proteins which share functional characteristics, such as immunoglobulins, albumin, or hemoglobin, usually go through similar folding stages. This enables us to predict their conformation based on the crystal structure of a sample polypeptide. Such techniques tell us how proteins fold, but do not provide knowledge of the underlying process. In contrast, here we try to answer a different question: why do proteins adopt certain conformations?

• 1. Protein Folding

The “oil drop” model is a long-standing abstraction of protein structure, originally proposed by W. Kauzmann [lit]. It treats the protein molecule as a two-layer construct consisting of a polar surface layer and a strongly hydrophobic center (the “core”). According to this model, tertiary structure is stabilized—in addition to disulfide bonds—by a specific distribution of hydrophobicity. The model we propose, referred to as the fuzzy oil drop model, modifies this discrete binary structure by introducing a continuous hydrophobicity gradient, mathematically expressed as a 3D Gaussian superimposed onto the target molecule. This gradient peaks at the center of the ellipsoid and decreases along with distance from the center, reaching near-zero values at a distance of 3σ (this is known as the three-sigma rule). The corresponding abstraction reflects structural similarities between bipolar molecules, i.e., substances, which form micellar structures in an aqueous solvent (such as soap). Notably, amino acids are also bipolar (with varying levels of polarity), and the presence of water plays a major role in the folding process. The polar solvent promotes exposure of polar residues on the surface and directs hydrophobic residues toward the center of the emerging structure, ensuring entropically advantageous conditions at the protein/water interface. Note, however, that the protein usually cannot form a perfect “micelle-like” structure due to the presence of covalent bonds between amino acids, restricting their mobility—this is why perfect micellar order is rarely observed in native proteins (note also that this would render the protein incapable of interacting with any molecules other than water or solvated ions). Some classes of proteins produce near-perfect micellar structures; these include downhill, fast-folding, ultra-fast-folding, or type III antifreeze proteins—all indicative that the presence of water is a crucial aspect of the folding process and is also sufficient for the protein to develop a hydrophobic core along with a hydrophilic shell. Figure 1.33 illustrates proteins in which the distribution of hydrophobicity is consistent with the Gaussian form (linear and 2D presentation).

Fig. 1.33

Idealized distribution of hydrophobicity consistent with the Gaussian distribution: (a) 2D presentation (shades of gray correspond to increasing levels of hydrophobicity) and (b) linear presentation (simple Gaussian)

How Function Is Encoded as Distribution of Hydrophobicity

The presence of an idealized micelle-like distribution (matching a 3D Gaussian form)—as remarked above—promotes high solubility but also prevents the protein from interacting with other specific molecules, which is a condition of biological activity. This is why, in addition to fragments which exhibit a micellar order, in vivo proteins also include discordant fragments where the observed distribution of hydrophobicity deviates from the theoretical pattern. This situation can be quantitatively modeled using Kullback-Leibler’s divergence entropy model, which quantifies the contribution of accordant and discordant fragments to the protein’s overall distribution of hydrophobicity (consisting of a hydrophobic core and a polar shell).

Divergence entropy, sometimes also referred to as distance entropy, expresses the difference between the target distribution (in our case—the 3D Gaussian) and the distribution actually observed in the given structure (which, in proteins, depends on hydrophobic interactions between amino acid residues).

Figure 1.34 illustrates a discordant distribution of hydrophobicity, where strongly hydrophobic residues are not concentrated at the center of the protein body.

Fig. 1.34

Example distribution with a displaced hydrophobic core. (a) 2D presentation (shades of gray correspond to increasing levels of hydrophobicity) and (b) linear presentation (skewed Gaussian)

• 2. Local Excess of Hydrophobicity on the Protein Surface

Another deviation from the theoretical model, known to be associated with biological activity, involves exposure of hydrophobicity on the protein surface. Proteins which follow this structural pattern tend to associate with other molecules, including other proteins, forming quaternary structures (Fig. 1.35) which can be regarded as containing a single, shared hydrophobic core. Exposed hydrophobicity may therefore indicate a potential complexation site, capable of attracting a partner protein which also exposes hydrophobic residues on its own surface.

Fig. 1.35

Discordant distribution of hydrophobicity—exposure of hydrophobicity on the protein surface. (a) 2D presentation (shades of gray correspond to increasing levels of hydrophobicity); the black line corresponds to the cross-section depicted on the right-hand side. (b) Linear presentation (two distorted Gaussians, which together form a centralized hydrophobic core for the dimeric structure)

• 3. Local Deficit of Hydrophobicity

Another type of discordance involves a local deficit of hydrophobicity, typically associated with the presence of a binding cavity (Fig. 1.36).

Fig. 1.36

Distribution of hydrophobicity showing a local deficit compared with the theoretical 3D Gaussian. (a) 2D presentation (shades of gray correspond to increasing levels of hydrophobicity); the black line corresponds to the cross-section depicted on the right-hand side. (b) Linear presentation (truncated Gaussian associated with the presence of a cavity)

Hydrophobicity distribution analysis (Figs. 1.34 and 1.35) reveals that a large portion of the protein body follows a distribution which approximates the 3D Gaussian, thus ensuring that the protein remains soluble (i.e., exposes a polar surface to its environment).

• 4. Effect of Non-aqueous Environments on the Folding Process

An entirely different situation is observed in the case of membrane proteins, surrounded by a strongly hydrophobic layer of hydrocarbons, which is part of the cell membrane. In order to achieve stability, a protein anchored in this manner (e.g., rhodopsin) must expose hydrophobic residues on its surface. Additionally, if the protein is meant to interact with a ligand, its central part must include a suitable polar cavity. Such deficit of hydrophobicity in the protein’s interior is particularly noteworthy in light of the presented model, which suggests a concentration of hydrophobicity in the core. Figure 1.37 shows a sample system with these properties.

Fig. 1.37

Hydrophobicity distribution in a membrane protein. (a) 2D presentation, showing excess hydrophobicity on the surface (where the protein contacts the membrane). (b) Linear presentation, illustrating differences between the observed (black) and theoretical (blue) distribution

Taken together, these properties result in a distribution of hydrophobicity which deviates from the 3D Gaussian and may even be its polar opposite. An example is provided by ion transport proteins, which expose hydrophobic residues in order to anchor themselves in the cell membrane and also contain polar cores, with a central cavity surrounded by hydrophilic residues. This is schematically depicted in Fig. 1.38.

Fig. 1.38

Distribution of hydrophobicity in an ion transport protein. (a) 2D presentation (shades of gray correspond to increasing levels of hydrophobicity). (b) Linear presentation, revealing differences between a centralized hydrophobic core (blue) and the observed distribution in proteins which act as ion transport channels (black)

• 5. Complex Structure of Ion Transport Proteins

Such proteins are composed of multiple chains, each of which includes a transmembrane domain as well as a terminal domain (or domains) exposed to the aqueous environment. In the latter case, the central part is hydrophobically deficient (due to the presence of a channel and its polar surroundings, enabling contact with the solvent). Figure 1.39 illustrates an idealized distribution of hydrophobicity in a terminal domain.

Fig. 1.39

Idealized distribution of hydrophobicity in the terminal domain of an ion transport protein. (a) 2D presentation (shades of gray correspond to increasing levels of hydrophobicity)—the black horizontal line corresponds to the cross-section illustrated on the right-hand side. (b) Linear presentation, revealing differences between the idealized 3D Gaussian (blue) and the modified distribution (black)

• 6. Hydrophobicity Distribution Parameters

So far we’ve focused on visual interpretations of the presence of the aqueous solvent and its effect on the folding process. In mathematical terms, the presented model can be described as follows.

As already suggested, W. Kauzmann’s original oil drop model has been extended into what we refer to as the fuzzy oil drop (FOD) model. In FOD, the discrete distribution of hydrophobicity gives way to a continuous distribution, mathematically expressed as a 3D Gaussian form. This Gaussian corresponds to the idealized distribution of hydrophobicity in the protein body. It enables us to assign a specific value of hydrophobicity to each effective atom (i.e., to averaged-out coordinates of all atoms which comprise a given residue). The resulting idealized micellar distribution is denoted T and described by the following function (Eq. 1.1):

$$ {H}_i^T=\frac{1}{H_{\mathrm{sum}}^T}\exp \left(\frac{-{\left({x}_i-\overline{x}\right)}^2}{2{\sigma}_x^2}\right)\exp \left(\frac{-{\left({y}_i-\overline{y}\right)}^2}{2{\sigma}_y^2}\right)\exp \left(\frac{-{\left({z}_i-\overline{z}\right)}^2}{2{\sigma}_z^2}\right) $$

(1.1)

The observed distribution (denoted O) may differ from T since it depends on the interactions between residues (or, more specifically, between their representative effective atoms). Such interactions depend, among others, on the separation between residues as well as on their intrinsic hydrophobicity. Specific values of O_i are given by M. Levitt’s formula [lit] (Eq. 1.2):

$$ {H}_i^o=\frac{1}{H_{\mathrm{sum}}^O}\sum \limits_j\Big\{{\displaystyle \begin{array}{l}\left({H}_i^r+{H}_j^r\right)\left(1-\frac{1}{2}\left(7{\left(\frac{r_{ij}}{c}\right)}^2-9{\left(\frac{r_{ij}}{c}\right)}^4+5{\left(\frac{r_{ij}}{c}\right)}^6-{\left(\frac{r_{ij}}{c}\right)}^8\right)\right),\kern1em \mathrm{for}\kern0.5em {r}_{ij}\le c\\ {}0,\kern1em \mathrm{for}\kern0.5em {r}_{ij}>c\end{array}} $$

(1.2)

Here, r_ij is the separation between effective atoms, C is the cutoff distance (assumed to equal 9 Å), and H^r is the intrinsic hydrophobicity. Both distributions (T and O) may be quantitatively compared following normalization. This comparison relies on the concept of divergence entropy, originally proposed by Kullback and Leibler [lit] (Eq. 1.3):

$$ {D}_{KL}\left(P|Q\right)=\sum \limits_{i=1}^N{P}_i{\log}_2\frac{P_i}{Q_i} $$

(1.3)

In the presented model, the distribution subject to analysis (P_i) corresponds to O_i, while the reference distribution (Q_i) is supplied by T_i.

Given the nature of the analyzed quantity (entropy), the need for another reference distribution emerges. This distribution, denoted R, is regarded as opposite to T, as it ascribes the same value to each residue in the chain (R_i = 1/N, N being the total number of residues). Under such conditions, hydrophobicity is uniformly distributed throughout the protein body, and no hydrophobic core is present. As a result, the status of a given protein may be described using a pair of D_KL values:

$$ {D}_{\mathrm{KL}}\left(O\left|T\right.\right)=\sum \limits_{i=1}^N{O}_i{\log}_2\left({O}_i/{T}_i\right) $$

(1.4)

for the O|T relationship, and

$$ {D}_{\mathrm{KL}}\left(O\left|R\right.\right)=\sum \limits_{i=1}^N{O}_i{\log}_2\left({O}_i/{R}_i\right) $$

(1.5)

for the O|R relationship.

In some respects, the R distribution may be regarded as analogous to “vacuum conditions,” emerging in the absence of any external factors which might influence the distribution of hydrophobicity in a protein chain.

The overall status of the protein depends on the relation between DKL values computed for the O|T and O|R configurations, respectively. If the former value is lower, the protein is said to possess a centralized hydrophobic core. This is schematically depicted in Fig. 1.40.

Fig. 1.40

Visualization of distributions used to determine the status of the given protein. (a) Idealized Gaussian distribution (T)—reduced to a single dimension for clarity. (b) Observed distribution (O), conditioned by mutual interactions between residues (i.e., between their effective atoms). (c) Linear distribution (R) where each residue is assigned the same value of hydrophobicity. (d) RD scale (where 0 corresponds to T, while 1 corresponds to R). The red line indicates the value of RD calculated for the observed distribution (see item B above); in this case RD = 0.700

In order to avoid having to deal with two separate coefficients for a single object, we introduce the RD (relative distance) parameter, which is expressed as follows:

$$ \mathrm{RD}=\frac{D_{\mathrm{KL}}\left(O|T\right)}{D_{\mathrm{KL}}\left(O|T\right)+{D}_{\mathrm{KL}}\left(O|R\right)} $$

(1.6)

When RD < 0.5, the protein is assumed to contain a well-defined hydrophobic core and a polar shell—unlike the structure illustrated in Fig. 1.40.

This abstraction enables us to quantitatively assess the similarities and differences between different distributions—whether local (Figs. 1.34, 1.35, and 1.36) or global (Figs. 1.37, 1.38, and 1.39).

• 7. Involvement of Environmental Hydrophobic Factors in Shaping the Protein’s Structure

As noted above, global mismatch between the observed distribution of hydrophobicity and the idealized Gaussian is often due to active involvement of the environment, which guides the folding process depending on its own properties. In such cases, the environment contains a hydrophobic factor, which can be recognized in the fuzzy oil drop model as a function complementary to the original Gaussian, denoted M_i (where 3DG corresponds to the T distribution):

$$ {M}_i={\left[1\hbox{--} 3{\mathrm{DG}}_i\right]}_n $$

(1.7)

It turns out, however, that even membrane proteins do not follow the distribution described by Eq. (1.7). The presence of water is ubiquitous, and therefore—in addition to any hydrophobic factors—the aqueous solvent must be acknowledged in our calculations. Thus, our description of the external force field is extended as follows:

$$ {M}_i={\left[3{\mathrm{DG}}_i+{\left(1\hbox{--} 3{\mathrm{DG}}_i\right)}_n\right]}_n $$

(1.8)

In practice, the M distribution is calculated by substituting T_MAX for “1.” Furthermore, we introduce the K parameter, which reflects the varying proportions of the aqueous and hydrophobic environments. This yields the final equation:

$$ {M}_i={\left[3{\mathrm{DG}}_i+\mathbf{K}{\left({T}_{\mathrm{MAX}}\hbox{--} {T}_i\right)}_n\right]}_n $$

(1.9)

(The n index corresponds to normalization of the distribution.)

Analysis of various proteins reported in literature indicates that K = 0 is observed in structures listed at the beginning of this subsection, downhill, fast-folding, ultra-fast-folding, and type III antifreeze proteins—all of which contain well-defined hydrophobic cores, encapsulated by polar shells. This condition is also fulfilled by the nearly all protein domains (when analyzed as standalone units).

For the vast majority of proteins, particularly single-chain proteins, 0 < K < 0.5. This group also includes some enzymes and small proteins which have a quaternary structure (mainly homodimers), as shown in Figs. 1.34, 1.35, and 1.36.

Figure 1.41 illustrates the role of the K coefficient. The idealized distribution (T), where the aqueous solvent directs all hydrophobic residues toward the center of the protein body while exposing polar residues on its surface, is not a good match for the observed distribution (O). Modifying T with K = 0.5 results in a target distribution which more closely reflects the observed values (brown curve). This suggests that the protein in question may have folded in an environment which, in addition to water, includes a so-called chaotropic factor [lit], whose involvement is mathematically expressed by the value of K = 0.5.

Fig. 1.41

Distribution shown in Fig. 1.40 superimposed onto a profile which satisfies K = 0.5 (teal curve). The T and O distributions are plotted in blue and brown, respectively

For membrane proteins, K may adopt values greater than 0.5 or even greater than 1.0. Examples of such proteins (where, in some cases, K > 3) include bacterial efflux pumps.

Analysis of a large group of proteins using RD and K parameters shows that the fuzzy oil drop model, in its modified form (FOD-M), is a useful tool in the study of protein structures. It also suggests that protein structure prediction tools which rely on numerical algorithms should acknowledge the variability of the external environment along the lines proposed above. In each case, the environment contributes a force field which plays an active role in shaping the structure of the emerging protein and affects its biological properties.

The notion that “sequence determines the 3D structure of a protein” reflects the structural encoding of functional properties. In fact, we can more accurately state that “sequence determines the scope and degree of the inability to generate a perfect micellar structure.” The values of RD and K determine the specific properties of the given conformation, which may only be capable of biological activity in the presence of external factors other than water—for example, the cellular membrane.

Misfolding

Our discussion of protein structure analysis should also acknowledge the pathological phenomenon known as misfolding. This is something that occurs in living organisms on an ongoing basis; however, organisms have evolved methods to eliminate incorrectly folded proteins—for example, through the so-called unfolded protein response (UPR) mechanism [lit].

Misfolding is particularly notable as the causative factor promoting formation of amyloid plaque. In general, globular proteins tend to follow the Gaussian distribution (Fig. 1.42a), whereas amyloid fibrils consist of unit chains, each of which is planar rather than globular. It is, in fact, possible to assess the presence of a hydrophobic core in each of these planar units—however, such cores are two-dimensional and therefore modeled by a 2D Gaussian (Fig. 1.42b). As a result, the unit chain only exposes polarity at the edges of its “disc,” whereas both sides contain unshielded hydrophobic residues (Fig. 1.42c), which, in turn, promotes complexation with other similarly shaped chains. This is why amyloid fibrils tend to exhibit unbounded growth.

Fig. 1.42

Distribution of hydrophobicity (denotes by shades of gray) in (a) globular protein roughly consistent with the 3D Gaussian (high K). (b) Individual unit chain of an amyloid fibril, consistent with the 2D Gaussian (low K). (c) Larger fragment of an amyloid fibril, where the clustering of individual unit chains produces a distribution of hydrophobicity roughly consistent with the 3D Gaussian (low K). (d) Regularly shaped protein following redistribution of hydrophobicity (low K). (e) Transformation results in a distribution which differs from theoretical values (high K). (f) Ultimately, the entire fibril deviates from the 3D Gaussian distribution (high K)—this is assumed to result from the presence of chaotropic agents

The description of the external force field proposed in FOD and FOD-M models can be applied to any type of environment, as well as to any input chain with specific chemical properties.

Based on the FOD-M model, we may propose an amyloid transformation mechanism, which turns out to be variable in scope. The transformation of the native protein into its amyloid form can be accompanied by a decrease or an increase in the value of K. The specific mode of transformation may be assessed by comparing WT structures and their amyloid counterparts. Two distinct modes can be distinguished:

Amyloid transformation accompanied by a decrease in the value of K occurs, e.g., in the case of alpha-synuclein. The native protein deviates significantly from a globule, and its value of K is very high. Its structure has been determined in complex with a micelle mimicking the axon terminals of presynaptic neurons with which alpha-synuclein associates in vivo. The amyloid structure listed in Protein Data Bank, however, shows a low value of K and reveals the presence of a hydrophobic core. This scenario can be interpreted as follows:

The high value of K results from the presence of a target, which alters the properties of the surrounding environment and forces the protein to adopt a non-globular conformation. Once this external factor is removed, alpha-synuclein can produce a micellar structure, which comprises a centralized hydrophobic core along with a hydrophilic shell—the latter formed by loose, unstructured fragments of the chain (residues 1–30 and 100–140). Therefore, the amyloid structure of alpha-synuclein emerges as a result of interaction with the aqueous solvent in conditions where free protein molecules (detached from the scaffold) are abundant (see Fig. 1.43a and b).

Fig. 1.43

Variable modes of amyloid transformation: (a) Alpha-synuclein in its native form, in complex with axon terminals of presynaptic neurons (experimentally simulated by a micelle)—high value of K. (b) Alpha-synuclein in its amyloid form (K < 0.5, which represents dominant influence of the aqueous environment). (c) VL domain of immunoglobulin G—low value of K; globular structure. (d) VL domain of immunoglobulin G in its amyloid conformation—high value of K caused by external factors

The opposite process—i.e., amyloid transformation accompanied by a major increase in K—is observed for the L domain of the IgG light chain. Here, too, the external environment plays a crucial role, although in this particular case amyloid transformation is caused by introduction of nonstandard external factors (Fig. 1.43c and d).

We can conclude that in both cases the environment is an important driver of amyloid transformation. With regard to alpha-synuclein, it acts as a scaffold, maintaining a high value of K and ensuring proper biological activity of the protein. In other cases high K may be caused by the unusual external factors—for example, shaking, which is known to promote amyloid transformation in experimental studies. Shaking causes aeration of the solvent and greatly increases the surface area of the water-air interface. Under these conditions water loses its ability to properly guide the folding process of solvated polypeptide chains. On the other hand, in the case of alpha-synuclein, water appears to cause the protein to adopt a non-native conformation which is typical for globular proteins. This is schematically depicted in Fig. 1.43.

Fragments marked in red participate in formation of the amyloid fibril.

• 1. Universality of the FOD Model and Its Modified Form (FOD-M)

When summarizing the outcomes of applying the modified fuzzy oil drop (FOD-M) model, we can conclude the following:

• 1. The protein is effectively an “intelligent micelle,” in which local deviations from the 3D Gaussian distribution of hydrophobicity correspond to biological activity.

• 2. The widely repeated notion that the protein’s 3D structure is determined by the sequence may be extended by noting that the sequence also determines the type and scope of deviations from a perfect micellar structure. Such targeted deviations correspond to sites which mediate biological activity—for example, local deficiencies of hydrophobicity are often associated with binding cavities, capable of interacting with a specific ligand, while excess hydrophobicity on the protein surface may indicate a complexation site which gives rise to quaternary structures.

• 3. Applying the FOD-M model to fully folded proteins reveals factors which stabilize the protein’s native structure, ensuring biological function. In particular, the K parameter expresses the involvement of external hydrophobic factors (other than the polar aqueous environment).

• 4. The K parameter is also useful in folding simulations—it would, after all, be impossible to explain the extreme structural diversity of in vivo proteins with a mechanism which does not acknowledge the influence of the external environment. The biological properties of a protein must reflect the properties of the environment in which that protein is expected to express its function.

• 5. In addition to characterizing the protein’s structure (discordance vs. a globular conformation which includes a centralized hydrophobic core), the K parameter also conveys the involvement of external “chaotropic” factors which disrupt the natural structure of the aqueous solvent. High values of K indicate that water no longer plays a key role in guiding local processes.

• 6. Another phenomenon worth taking into account is the structure of amyloid fibrils, dominated by inter-chain hydrogen bonds. In such systems, each residue enters into two hydrogen bonds with adjacent chains, and this process is repeated across nearly the entire chain. The presence of a “chaotropic” factor likely promotes formation of hydrogen bonds.

Amyloid Transformation

Under certain conditions, the globular structure of a soluble protein may yield an entirely different distribution of hydrophobicity, leading to planar conformations, mathematically described by a 2D Gaussian. The properties of the underlying mechanism remain an open question; it can, however, be assumed, that the globular structure emerges as a result of a favorable change in ΔS, guided by the polar environment which promotes exposure of hydrophobicity on the surface and concealment of hydrophobic residues within the core. On the other hand, amyloid fibrils are primarily stabilized by hydrogen bonds, which involve all N–H and C=O groups of a given peptide. Such significant involvement of hydrogen bonds suggests that the process is instead driven by ΔH. The causes of such a change remain unclear; however, in later chapters we propose some mechanisms which might explain the amyloid transformation process.

As already mentioned, all known amyloid structures consist of planar unit chains. In this sense, amyloid transformation may be compared with migrating from a 3D to a 2D Gaussian. This is particularly evident in cases where the central part of the cross-section (perpendicular to the fibril’s axis) is occupied by hydrophobic residues.

Conformational changes which accompany amyloid transformation require further analysis; however, amyloids are generally dominated by beta folds, separated by short loops. Hydrogen bonds—a characteristic feature of beta structures—link atoms belonging to adjacent chains. In this case, the conformational changes occurring in helical segments appear obvious; however, it is more difficult to explain the transformation between beta folds in native proteins and different beta folds in their amyloid counterparts.

Referring again to the 3D and 2D Gaussian forms, it should be noted that the helix is clearly an example of a 3D structure, given the presence of side chains which radiate outward from the central “hub” in a spiral fashion. Planar structures may therefore only emerge on the basis of beta folds.

Amyloid transformation may also be studied by comparing the differences between dihedral angles (Phi and Psi) in the native form and its amyloid counterpart. While in helices and native beta folds the distribution of these angles is relatively broad, amyloid structures are limited to a very narrow range of angles—for instance, in the case of transthyretin (native structure, 1DVQ; amyloid form, 6SDZ), as evidenced by Ramachandran plots (Fig. 1.44).

Fig. 1.44

Distribution of Phi and Psi angles (blue dots) on Ramachandran plots in transthyretin. (a and b) Amyloid structure and (c and d) native structure. (a and c) Ramachandran plot indicating zones which correspond to curvature radii for a given pair of Phi and Psi angles. (b and d) Ramachandran plot indicating zones which correspond to twist angles between adjacent peptide bond planes in a polypeptide chain. Calculation of these parameters is also described in Sect. 3.7.1. See also Protein Folding In Silico—Woodhead Publishing currently Elsevier 2012, Ed: Irena Roterman-Konieczna Oxford, Cambridge, Philadelphia, New Dehli 2012

In helical fragments, the values of angles are always limited to very narrow range which roughly corresponds to an “idealized” helix. On the other hand, when looking at beta folds, we can see that in amyloids these angles occupy a much smaller range than in native proteins. It is also worth noting that the data points are distributed along a specific line (the diagonal).

When confronting the distribution of Phi and Psi angles with geometric parameters (curvature radius and twist angle between planes of adjacent peptide bonds), we can notice that values of V = 0 and V-180 are preferred. Hydrogen bonds tend to produce parallel structures, without any twist, as seen in all beta and beta-barrel structures (Fig. 1.44a). This perfectly parallel arrangement of hydrogen bonds is only possible when V becomes equal to 0 or 180° (Fig. 1.44b). In contrast, the distribution of Phi and Psi angles suggests that in native proteins the curvature radii may vary even when it comes too beta sheets. This dispersion of curvature radii produces tertiary structural artifacts, as seen, e.g., in wild-type transthyretin, where V values which deviate from 0 or 180 give rise to an arched form, seen in proteins which contain secondary or supersecondary beta fragments.

Structural changes are evident when comparing the three fragments. In the native form, the beta sheet is twisted due to changes in orientation of adjacent peptide bond planes (where V is close to, but not exactly equal to, 180°—as seen in Fig. 1.44c). In the amyloid structure, V becomes equal to 180. One of the fragments becomes a loop, but the remaining two run parallel to each other, enabling the formation of hydrogen bonds. It is also notable that a beta sheet consists of fragments contributed by the same polypeptide chain, whereas in an amyloid there is contact between beta folds belonging to independent chains. This process involves transformation from a 3D to a 2D structure.

Our analysis may also be applied to loops responsible for creating the 3D structure. It should be noted that the set of points on the Ramachandran plot which represents the native structure (Fig. 1.45a and b) corresponds to the helical fragment, whereas in its amyloid counterpart, the same points belong to loops which do not adopt a helical conformation.

Fig. 1.45

Structure of individual fragments, highlighting the beta sheet. The fragment which does not retain beta conformation in the amyloid is marked in red. (a) Amyloid (6SDZ) and (b) native protein (1DVQ)

The range of values plotted for the amyloid conformation of transthyretin is restricted to the maximum curvature radius—i.e., linear structures, where V = 180°. This results in a planar arrangement of unit chains, which promotes formation of hydrogen bonds between parallel polypeptides.

Comparing the native and amyloid structures of transthyretin further highlights the conformational changes which accompany amyloid transformation. Here, the relevant question is: what factor contributes to parallel alignment of adjacent polypeptide planes (V = 0 or 180°), enabling hydrogen bonds to form? Some clues might be provided by studying the structural properties of water in its natural state, in physiological saline solutions, as well as in the presence of distorting factors. The presented hypothesis assumes that such factors promote formation of 2D structures while disrupting 3D structures. In particular, it might be interesting to look at the relation between the structural properties of the solvent and the planar and highly symmetrical nature of the hydrogen bond network. Tracing the progressive changes in Phi and Psi angles, as well as the resulting geometric rearrangements, may shed new light on the amyloid transformation process.

The role of environment shall be linked with the issue of information. The information carried by amino acids is not sufficient to cover the information amount necessary to point the Phi and Psi angles for 3D structure determination. The information deficiency is covered by information the source of which is the specificity of external force field which is delivered by the surrounding for folding process. The detailed presentation of hypothesis of amyloid transformation can be found in: From globular proteins to amyloids. Ed: Irena Roterman-Konieczna, Elsevier, Amsterdam, Netherlands, Oxford OX5 3GB UK, Cambridge MA 02139, USA 2020 available on line [https://www.google.pl/books/edition/From_Globular_Proteins_to_Amyloids/7K9uEAAAQBAJ?hl=pl&gbpv=1&dq=Roterman-Konieczna+From+globular+proteins+elsevier&printsec=frontcover].

The essential progress in studies concerning protein structure largely contributes to the improvement of drug design techniques including techniques of drug distribution in the organism in particular these allowing focusing of drug activity in the target as, for example, technique represented by immunotargeting In: Self-Assembled Molecules—New Kind of Protein Ligands Ed: Irena Roterman and Leszek Konieczny; Springer Open 20188. Available on-line [https://link.springer.com/book/10.1007/978-3-319-65639-7].