Biochemistry: Comprehensive Guide to Protein Composition and Structure

Fundamental Properties and Functional Versatility of Proteins

• Polymeric Architecture:

  • Proteins are linear polymers built from monomeric units called amino acids, linked end-to-end.

  • Natural proteins typically consist of sequences ranging from $50$ to $2000$ amino acid residues.

• Chemical Versatility:

  • Contain a broad array of functional groups, including alcohols, thiols, thioethers, carboxylic acids, carboxamides, and basic groups.

  • These reactive functional groups dictate enzymatic catalysis and biological activity.

• Complex Protein Assemblies:

  • Proteins interact specifically with one another and with other biological macromolecules (such as nucleic acids) to form intricate structural and functional assemblies.

  • Examples include DNA sliding clamps that encircle double-stranded DNA to promote processive replication, and organized myofibril networks within muscle cells.

  • Myofibrils in muscle cells consist of repeating structural units called sarcomeres, composed of interdigitating thick filaments and thin filaments bounded by Z-discs.

• Conformational Flexibility:

  • Proteins display varying degrees of rigidity or flexibility depending on biological function.

  • Rigid structures serve as structural components, whereas flexible proteins undergo marked conformational changes upon ligand binding.

  • A key example is periplasmic iron-binding protein, which undergoes a large hinge-like structural shift upon binding a single iron atom.

Amino Acid Architecture and Chirality

• General Structure of $\alpha$-Amino Acids:

  • An $\alpha$-amino acid consists of a central tetrahedral $\alpha$-carbon ($C_\alpha$) linked to four distinct covalent groups:

  • An amino group ($-NH_3^+$).

  • A carboxylic acid group ($-COO^-$).

  • A hydrogen atom ($H$).

  • A distinctive side chain ($R$ group).

• Chirality and Stereochemistry:

  • Because four different chemical groups are attached to the central $C_\alpha$, $\alpha$-amino acids (with the exception of glycine) are chiral.

  • Chiral amino acids exist as two non-superimposable mirror-image stereoisomers designated as the L isomer and the D isomer.

  • Ribosomal protein synthesis exclusively incorporates L amino acids into proteins.

• Ionization State as a Function of pH:

  • At physiological/neutral pH (\text{pH} \n\n\approx 7.4), free amino acids exist in aqueous solution as dipolar ions, also known as zwitterions.

  • In the zwitterionic state, the amino group is protonated ($-NH_3^+$) bearing a positive charge, and the carboxyl group is deprotonated ($-COO^-$) bearing a negative charge.

  • At strongly acidic pH ($\text{pH} < 2$), both functional groups are protonated ($-NH_3^+$ and $-COOH$), giving the molecule a net positive charge.

  • As pH increases past $pK_1 \approx 2$, the carboxyl group loses its proton to yield the zwitterion.

  • At strongly basic pH ($\text{pH} > 9$), the amino group loses its proton ($-NH_2$ and $-COO^-$), giving the molecule a net negative charge as pH surpasses $pK_2 \approx 9.5$

Classification and Properties of the 20 Amino Acids

• Functional Group Categorization:

  • The 20 standard amino acids are classified into four structural categories based on side-chain properties: Hydrophobic, Polar, Positively Charged, and Negatively Charged.

• 1. Hydrophobic Amino Acids (Nonpolar Side Chains):

  • Glycine (Gly, G): The simplest amino acid ($R = -H$); achiral, enabling unusual spatial flexibility in peptide backbones.

  • Alanine (Ala, A): Side chain is a compact methyl group ($-CH_3$).

  • Valine (Val, V): Branched aliphatic hydrocarbon side chain ($-CH(CH_3)_2$).

  • Leucine (Leu, L): Branched aliphatic side chain ($-CH_2CH(CH_3)_2$).

  • Isoleucine (Ile, I): Aliphatic hydrocarbon side chain ($-CH(CH_3)CH_2CH_3$) containing a second chiral center at the $\beta$-carbon atom.

  • Proline (Pro, P): Aliphatic side chain folded back onto its own amino group to form a five-membered pyrrolidine ring, imposing severe conformational rigidity on the protein backbone.

  • Methionine (Met, M): Aliphatic side chain containing a hydrophobic thioether linkage ($-CH_2-CH_2-S-CH_3$).

  • Phenylalanine (Phe, F): Contains a bulky aromatic phenyl ring attached to a methylene group ($-CH_2-C_6H_5$).

  • Tryptophan (Trp, W): Bulkiest hydrophobic amino acid; features an aromatic indole ring joined to a methylene group ($-CH_2-\text{indole}$).

• 2. Polar Amino Acids (Uncharged Neutral Side Chains):

  • Serine (Ser, S): Contains a polar, hydrophilic hydroxyl group attached to a methylene carbon ($-CH_2OH$).

  • Threonine (Thr, T): Contains a hydroxyl group and a second chiral center at its $\beta$-carbon atom ($-CH(OH)CH_3$).

  • Tyrosine (Tyr, Y): Aromatic ring containing a polar phenolic hydroxyl group ($-CH_2-C_6H_4-OH$).

  • Asparagine (Asn, N): Contains a polar carboxamide functional group ($-CH_2-CONH_2$).

  • Glutamine (Gln, Q): Contains an extended polar carboxamide side chain ($-CH_2-CH_2-CONH_2$).

  • Cysteine (Cys, C): Contains a highly reactive sulfhydryl or thiol group ($-CH_2-SH$); pairs of cysteine sulfhydryl groups oxidize to form covalent disulfide bonds.

  • Histidine (His, H): Contains an aromatic imidazole ring that can readily gain or lose a proton at near-physiological pH values.

• Proton Accumulation and Release by Histidine:

  • The imidazole ring of histidine has a typical $pKa$ value near $6.0$.

  • Because this $pKa$ is close to physiological pH ($\text{pH} \approx 7.4$), small local pH shifts dictate whether histidine exists in its neutral or positively charged (protonated) form.

  • This dual availability allows histidine to function as a proton donor or proton acceptor in enzymatic active sites.

• 3. Positively Charged Amino Acids (Basic Side Chains):

  • Lysine (Lys, K): Features a flexible aliphatic chain terminated by a primary amino group ($-CH_2-CH_2-CH_2-CH_2-NH_3^+$) that carries a positive charge at neutral pH.

  • Arginine (Arg, R): Terminated by a strongly basic guanidinium group ($-CH_2-CH_2-CH_2-NH-C(NH_2)_2^+$), which remains fully protonated and positively charged across physiological conditions.

• 4. Negatively Charged Amino Acids (Acidic Side Chains):

  • Aspartate / Aspartic Acid (Asp, D): Carboxyl side chain ($-CH_2-COO^-$) that loses its proton at physiological pH, acquiring a full negative charge.

  • Glutamate / Glutamic Acid (Glu, E): Longer carboxyl side chain ($-CH_2-CH_2-COO^-$) carrying a net negative charge at physiological pH.

Quantitative Ionization Constants and Nomenclature

• Ionizable Groups and Typical $pKa$ Values in Proteins:

  • Seven of the 20 standard amino acids possess ionizable side chains capable of proton exchange.

• Summary of Typical Ionization Constants (Table 2.1):

  • Terminal $\alpha$-carboxyl group: $pKa = 3.1$

  • Aspartic acid / Glutamic acid side-chain carboxyl groups: $pKa = 4.1$

  • Histidine imidazole side chain: $pKa = 6.0$

  • Terminal $\alpha$-amino group: $pKa = 8.0$

  • Cysteine sulfhydryl side chain: $pKa = 8.3$

  • Tyrosine phenolic hydroxyl group: $pKa = 10.0$

  • Lysine $\epsilon$-amino side chain: $pKa = 10.4$

  • Arginine guanidinium side chain: $pKa = 12.5$

• Amino Acid Abbreviations and Single-Letter Codes (Table 2.2):

  • Alanine: Ala, A

  • Arginine: Arg, R

  • Asparagine: Asn, N

  • Aspartic acid: Asp, D

  • Cysteine: Cys, C

  • Glutamine: Gln, Q

  • Glutamic acid: Glu, E

  • Glycine: Gly, G

  • Histidine: His, H

  • Isoleucine: Ile, I

  • Leucine: Leu, L

  • Lysine: Lys, K

  • Methionine: Met, M

  • Phenylalanine: Phe, F

  • Proline: Pro, P

  • Serine: Ser, S

  • Threonine: Thr, T

  • Tryptophan: Trp, W

  • Tyrosine: Tyr, Y

  • Valine: Val, V

  • Ambiguity designation Asx (B): Indicates Asparagine or Aspartic acid.

  • Ambiguity designation Glx (Z): Indicates Glutamine or Glutamic acid.

• Evolutionary Selection of the Standard 20 Amino Acids:

  • The choice of these specific 20 amino acids provides optimal chemical versatility.

  • These molecules were available through prebiotic chemical synthesis pathways.

  • Alternative potential amino acid structures were likely excluded due to high reactivity or instability.

Primary Structure and Peptide Bond Geometry

• The Peptide Bond:

  • Polypeptide chains are formed by linking the $\alpha$-carboxyl group of one amino acid to the $\alpha$-amino group of another via an amide link (peptide bond).

  • The reaction is a condensation process involving the elimination of a molecule of water ($H_2O$).

• Polypeptide Chain Directionality:

  • Polypeptide chains possess defined polarity and directionality.

  • By convention, the amino-terminal (N-terminal) residue is designated as the beginning of the chain.

  • The carboxyl-terminal (C-terminal) residue marks the termination of the chain.

  • Example pentapeptide structure: Tyr-Gly-Gly-Phe-Leu ($\text{Y-G-G-F-L}$).

• Polypeptide Backbone Architecture:

  • A polypeptide chain consists of a repeating main chain (backbone) and variable amino acid side chains ($R$ groups).

  • The main chain exhibits hydrogen-bonding potential: carbonyl groups ($C=O$) act as hydrogen-bond acceptors, whereas amino groups ($N-H$) act as hydrogen-bond donors.

• Molecular Mass Metrics:

  • Small peptide polymers are termed oligopeptides or peptides.

  • The mean molecular mass of an amino acid residue in a protein is approximately $110\,g\,mol^{-1}$ (daltons or Da).

  • Mass unit definition: $1\text{ dalton} = 1\text{ atomic mass unit}$.

• Disulfide Bonds:

  • Polypeptide chains can be intramolecularly or intermolecularly cross-linked by covalent disulfide bonds.

  • Disulfide bonds form via oxidation of the sulfhydryl ($-SH$) groups of two cysteine residues.

  • The resulting oxidized dimer of two linked cysteines is called cystine.

• Primary Sequence Determination of Insulin:

  • In 1953, Frederick Sanger elucidated the amino acid sequence of bovine insulin, a peptide hormone.

  • Sanger's work proved that proteins possess defined amino acid sequences composed of L amino acids linked exclusively by peptide bonds.

  • Insulin consists of an A chain ($21$ residues) and a B chain ($30$ residues) held together by interchain and intrachain disulfide cross-links.

• Planar Geometry of the Peptide Bond:

  • Resonance structures give the peptide bond partial double-bond character, preventing free rotation around the $C-N$ axis.

  • Six atoms lie in a single geometric plane: the $\alpha$-carbon ($C_\alpha$), carbonyl carbon ($C$), carbonyl oxygen ($O$), amide nitrogen ($N$), amide hydrogen ($H$), and adjacent $\alpha$-carbon ($C_\alpha$).

  • Covalent bond distances:

  • $C_\alpha - C = 1.51\,\text{\AA}$

  • $C = O = 1.24\,\text{\AA}$

  • $C - N = 1.32\,\text{\AA}$

  • $N - H = 1.0\,\text{\AA}$

  • $N - C_\alpha = 1.45\,\text{\AA}$

• Trans vs. Cis Stereochemistry:

  • Peptide bonds almost exclusively adopt the trans configuration over the cis configuration.

  • In the trans arrangement, adjacent $C_\alpha$ atoms are located on opposite sides of the peptide bond, minimizing steric clash between side chains.

  • Steric overlap between groups attached to adjacent $C_\alpha$ atoms unfavorably increases free energy in the cis arrangement.

Secondary Structure Elements

• Secondary Structure Definition:

  • Spatial arrangements of amino acid residues located near one another in the linear sequence, stabilized by backbone hydrogen bonds between amide $N-H$ and carbonyl $C=O$ groups.

  • Principal secondary structures include $\alpha$ helices, $\beta$ pleated sheets, and reverse turns or loops.

• The $\alpha$ Helix:

  • A tightly coiled, rodlike helical architecture with amino acid $R$ groups extending outward.

  • Stabilized by intrachain hydrogen bonds: the carbonyl $C=O$ group of amino acid residue $i$ forms a hydrogen bond with the amide $N-H$ group of amino acid residue $i+4$

  • Structural parameters of the $\alpha$ helix:

  • Translation rise along the helix axis: $1.5\,\text{\AA}$ per amino acid residue.

  • Residues per turn: $3.6$ amino acid residues.

  • Pitch (vertical distance of one complete turn): $3.6 \times 1.5\,\text{\AA} = 5.4\,\text{\AA}$.

  • Right-handed $\alpha$ helices are energetically favored over left-handed helices due to minimal steric hindrance between side chains and backbone.

• The $\beta$ Sheet and $\beta$ Strands:

  • $\beta$ pleated sheets are formed by hydrogen bonding between individual, fully extended polypeptide segments called $\beta$ strands.

  • Distance between adjacent amino acids along a $\beta$ strand is $3.5\,\text{\AA}$ (compared to $1.5\,\text{\AA}$ in an $\alpha$ helix), yielding a structural repeat distance of $7\,\text{\AA}$.

  • Side chains ($R$ groups$) project alternately above and below the plane of the $\beta$ strand.

• Structural Classifications of $\beta$ Sheets:

  • Antiparallel $\beta$ Sheet:

  • Adjacent $\beta$ strands run in opposite N-to-C chemical directions.

  • The $N-H$ group and $C=O$ group of each residue on one strand are hydrogen bonded to the $C=O$ group and $N-H$ group of a single corresponding residue on the adjacent strand.

  • Parallel $\beta$ Sheet:

  • Adjacent $\beta$ strands run in the same N-to-C direction.

  • The $N-H$ group of residue $i$ on one strand forms a hydrogen bond with the $C=O$ group of residue $j$ on the adjacent strand; the $C=O$ group of residue $i$ forms a hydrogen bond to the $N-H$ group of residue $j+2$.

  • Mixed and Twisted $\beta$ Sheets:

  • $\beta$ sheets can combine parallel and antiparallel arrangements and often adopt a right-handed twisted conformation.

• Reverse Turns and Loops:

  • Polypeptide chains undergo reversals in direction via reverse turns ($\beta$ turns or hairpin turns) and surface loops.

  • In a standard $\beta$ turn, the carbonyl $C=O$ group of residue $i$ is hydrogen-bonded to the amide $N-H$ group of residue $i+3$, stabilizing sharp directional changes.

  • Loops lack strict periodic symmetry but are well-defined structural features located on protein surfaces that facilitate interactions with other molecules.

Tertiary Structure, Supersecondary Motifs, and Fibrous Proteins

• Tertiary Structure Principles:

  • Tertiary structure refers to the three-dimensional folding of an entire single polypeptide chain.

  • Globular Proteins:

  • Highly compact, asymmetric structures that are soluble in water.

  • Myoglobin is an $\alpha$-helical globular protein containing a non-polypeptide heme prosthetic group centered around an iron atom.

• Thermodynamics of Hydrophobic Residue Distribution:

  • Water-soluble globular proteins sequester nonpolar hydrophobic residues (such as Leu, Val, Phe, Met) within their interior core, away from aqueous solvent.

  • Polar and charged residues (such as Asp, Glu, Lys, Arg) reside predominantly on the exterior surface in contact with water.

• Membrane Protein Structural Distribution:

  • Membrane-embedded proteins display an inverted spatial arrangement.

  • For example, porins possess a hydrophobic outer surface in contact with the nonpolar membrane lipid fatty acid chains.

  • Porin interiors contain a water-filled hydrophilic channel lined with charged and polar amino acids.

• Supersecondary Structures (Motifs):

  • Common combinations of secondary structures present across structurally distinct proteins.

  • The helix-turn-helix motif consists of two $\alpha$ helices joined by a short turn, serving as a primary structural element in DNA-binding proteins.

• Protein Domains:

  • Compact, modular regions of a single polypeptide chain that fold independently into functional units.

  • Domains are connected by short, flexible linker sequences.

  • The cell-surface protein CD4 contains four distinct extracellular immunoglobulin-like domains.

• Fibrous Structural Proteins:

  • Fibrous proteins form extended structural components featuring repeating primary sequences.

  • $\alpha$-Keratin:

  • Composed of two right-handed $\alpha$ helices wrapped around each other to form a left-handed superhelical coiled coil.

  • Member of the coiled-coil structural protein superfamily.

  • Interchain interactions are stabilized by van der Waals forces, ionic interactions, and covalent disulfide cross-links.

• Heptad Repeat Sequence Pattern:

  • Coiled-coil proteins feature a central domain consisting of imperfect seven-residue repeats designated as heptad repeats: $(a-b-c-d-e-f-g)_n$

  • Position $a$ and position $d$ contain hydrophobic residues, resulting in every seventh residue being a leucine (Leu).

  • These leucine residues align on one face of each $\alpha$ helix to form a hydrophobic stripe that drives dimerization.

• Collagen:

  • Primary structural protein of connective tissue, tendons, cartilage, and bone.

  • Composed of three left-handed helical polypeptide strands intertwined to form a tight, right-handed superhelical cable.

  • Primary sequence motif: Repeating $Gly-Pro-Hyp$ or $Gly-X-Y$ sequences.

  • Glycine occurs at every third position because no other amino acid side chain can fit into the restricted inner core of the triple-helical cable.

• Pathological Collagen Mutations:

  • Substitution of the invariant internal glycine residue by bulkier amino acids impairs triple-helix assembly.

  • Mutations replacing internal glycine residues cause osteogenesis imperfecta (brittle bone disease).

Quaternary Structure and Multisubunit Assemblies

• Quaternary Structure Definition:

  • Quaternary structure describes the spatial organization and interactions of multiple polypeptide chains (subunits) in a protein complex.

  • Subunits associate via noncovalent interactions (hydrophobic interactions, hydrogen bonds, salt bridges) and optional disulfide bonds.

• Homodimeric Assemblies:

  • Structural complexes formed by two identical polypeptide chains.

  • Example: Regulatory homodimeric DNA-binding proteins.

• Heterotetrameric Assemblies:

  • Structural complexes containing distinct, non-identical polypeptide subunits.

  • Example: Hemoglobin, an $\alpha_2\beta_2$ heterotetramer composed of two $\alpha$-globin subunits and two $\beta$-globin subunits.

Determinants and Thermodynamics of Protein Folding

• The Anfinsen Ribonuclease Experiment:

  • Christian Anfinsen investigated the folding mechanism of bovine pancreatic ribonuclease, an enzyme composed of $124$ amino acids cross-linked by four disulfide bonds ($Cys26-Cys84$, $Cys40-Cys95$, $Cys58-Cys110$, $Cys65-Cys72$).

• Denaturation of Ribonuclease:

  • Ribonuclease was denatured in a solution containing $8\,M$ urea and excess $\beta$-mercaptoethanol.

  • Urea disrupts all noncovalent interactions (hydrogen bonds, hydrophobic contacts).

  • $\beta$-mercaptoethanol reduces covalent disulfide bonds to free sulfhydryl ($-SH$) groups.

  • The resulting unfolded protein was enzymatically inactive and existed as a randomly coiled polypeptide chain.

• Renaturation and Refolding:

  • Slow removal of urea and $\beta$-mercaptoethanol by dialysis in the presence of molecular oxygen ($O_2$) yielded active enzyme identical to native ribonuclease.

  • This demonstrated that the primary amino acid sequence contains all necessary information to specify the native three-dimensional structure of a protein.

• Disulfide Bond Shuffling and Scrambled Ribonuclease:

  • When $\beta$-mercaptoethanol was removed before urea was removed, oxidized disulfide bonds reformed randomly while the backbone remained denatured, producing an inactive "scrambled" ribonuclease (~1% native activity).

  • Trace amounts of $\beta$-mercaptoethanol added back to scrambled ribonuclease catalyzed the cleavage and re-formation of disulfide bonds (disulfide shuffling) until the lowest-energy, native conformation was fully restored.

• Secondary Structure Propensities of Amino Acids (Table 2.3):

  • Amino acid residues exhibit distinct conformational preferences for forming $\alpha$ helices, $\beta$ sheets, or reverse turns.

• Relative Frequencies of Residues in Secondary Structures:

  • $\alpha$ Helix Preferences: Glu ($1.59$), Ala ($1.41$), Leu ($1.34$), Met ($1.30$), Gln ($1.27$), Lys ($1.23$), Arg ($1.21$).

  • $\beta$ Sheet Preferences: Val ($1.87$), Ile ($1.67$), Tyr ($1.45$), Cys ($1.40$), Trp ($1.35$), Phe ($1.33$).

  • Reverse Turn Preferences: Gly ($1.77$), Asn ($1.34$), Pro ($1.32$), Ser ($1.22$), Asp ($1.24$).

  • Local sequence preferences alone are insufficient to predict 3D fold completely; for example, the hexapeptide sequence $VDLLKN$ forms an $\alpha$ helix in one protein environment and a $\beta$ sheet in another.

• Cooperative Nature of Protein Folding:

  • Protein folding and unfolding operate via an "all-or-none" cooperative transition.

  • Intermediate states are unstable relative to fully folded or unfolded states; at $50\%$ denaturant concentration, the solution consists of a 1:1 mixture of fully folded and fully unfolded molecules.

• Cumulative Selection and Levinthal's Paradox:

  • Levinthal's paradox states that if an unfolded protein searched all possible conformations randomly, folding a 100-residue protein would take $10^{77}$ years.

  • Protein folding occurs rapidly via cumulative selection: partially correct intermediates are thermodynamically retained because they are slightly more stable than unfolded states.

  • This process is illustrated by the typing monkey analogy, where keeping correct letters reduces search iterations from astronomical numbers to thousands.

• Nucleation-Condensation Mechanism:

  • Local secondary structures form early (nucleation) and rapidly collapse around a hydrophobic core (condensation).

  • Simulated in model proteins like Chymotrypsin Inhibitor.

• The Folding Funnel Theory:

  • Depicts the thermodynamics of protein folding.

  • The top of the funnel represents high conformational entropy and high free energy (unfolded polypeptide).

  • As folding proceeds, conformational entropy decreases while hydrophobic interactions reduce free energy, directing the protein down the funnel toward the global minimum (native state).

• Computational Structure Prediction and AlphaFold:

  • Structure prediction utilizes ab initio methods (folding from primary sequence without template structures) or knowledge-based methods (homology modeling).

  • The AlphaFold deep learning platform achieved over $90\%$ accuracy in predicting complex folds, such as the ORF8 protein from SARS-CoV-2, matching experimental structures.

Protein Misfolding, Pathologies, and Post-Translational Modifications

• Amyloid Aggregates and Disease:

  • Misfolding of soluble proteins leads to the accumulation of insoluble amyloid fibrils rich in $\beta$ sheets.

  • Pathological conditions linked to amyloid plaque deposition include Alzheimer disease, Parkinson disease, Huntington disease, and transmissible spongiform encephalopathies (prion diseases).

  • Amyloid fibrils feature a cross-$\beta$ spine structure oriented perpendicular to the fibril growth axis.

• In Vivo Visualization of Amyloid Aggregates:

  • Positron Emission Tomography (PET) scanning utilizes radiotracer ligands to visualize amyloid plaque accumulation in patients with Alzheimer disease.

• Covalent Post-Translational Modifications (PTMs):

  • Covalent modifications alter amino acid side chains after protein translation, modifying functionality and regulatory control.

  • Hydroxyproline: Proline hydroxylation stabilizes collagen triple helices; catalyzed by prolyl hydroxylase, an enzyme requiring Vitamin C (ascorbic acid). Deficiency causes scurvy.

  • $\gamma$-Carboxyglutamate: Glutamate carboxylation introduces a second carboxyl group, enabling calcium binding in blood-clotting proteins like prothrombin; dependent on Vitamin K.

  • Carbohydrate-Asparagine Adducts: N-linked glycosylation attaches oligosaccharides to asparagine side chains, enhancing solubility and extracellular recognition.

  • Phosphoserine: Reversible phosphorylation of serine (or threonine/tyrosine) by protein kinases regulates enzyme activity and cellular signaling.

• Autocatalytic Fluorophore Assembly in Green Fluorescent Protein (GFP):

  • GFP contains a 11-stranded $\beta$-barrel structure surrounding a central chromophore.

  • Chromophore formation occurs autocatalytically through the internal cyclization and oxidation of tripeptide sequence $Ser65-Tyr66-Gly67$

  • Engineered variants of GFP are widely utilized in dual-color fluorescence imaging to track protein localization and tumor cell invasion.