A mathematical model of single target site location by Brownian movement in subcellular compartments

The location of distinct sites is mandatory for many cellular processes. In the subcompartments of the cell nucleus, only very small numbers of diffusing macromolecules and specific target sites of some types may be present. In this case, we are faced with the Brownian movement of individual macromolecules and their "random search" for single/few specific target sites, rather than bulk-averaged diffusion and multiple sites. In this article, I consider the location of a distant central target site, e.g. a globular protein, by individual macromolecules executing unbiased (i.e. drift-free) random walks in a spherical compartment. For this walk-and-capture model, the closed-form analytic solution of the first passage time probability density function (p.d.f.) has been obtained as well as the first and second moment. In the limit of a large ratio of the radii of the spherical diffusion space and central target, well-known relations for the variance and the first two moments for the exponential p.d.f. were found to hold with high accuracy. These calculations reinforce earlier numerical results and Monte Carlo simulations. A major implication derivable from the model is that non-directed random movement is an effective means for locating single sites in submicron-sized compartments, even when the diffusion coefficients are comparatively small and the diffusing species are present in one copy only. These theoretical conclusions are underscored numerically for effective diffusion constants ranging from 0.5 to 10.0 microm(2) s(-1), which have been reported for a couple of nuclear proteins in their physiological environment. Spherical compartments of submicron size are, for example, the Cajal bodies (size: 0.1-1.0 microm), which are present in 1-5 copies in the cell nucleus. Within a small Cajal body of radius 0.1 microm a single diffusing protein molecule (with D=0.5 microm(2) s(-1)) would encounter a medium-sized protein of radius 2.5 nm within 1 s with a probability near certainty (p=0.98).     

Interactions between lac repressor protein and site-specific bromodeoxyuridine-substituted operator DNA. Ultraviolet footprinting and protein-DNA cross-link formation

Specific contacts between the lac repressor and operator have been explored using 5-bromodeoxyuridine-substituted DNA. Substitution of BrdU for single thymidine positions in a synthetic 40-base pair operator provides substrate for ultraviolet irradiation; upon irradiation, strand scission occurs at the BrdU residues. When bound, lac repressor protein provides protection against UV-induced breakage depending on the nature of the sites and type of interaction. We have confirmed 13 unique sites of inducer-sensitive protection along the operator sequence using this method compared to complete substitution with BrdU; differences were observed at two positions for singly substituted versus completely substituted DNAs (Ogata, R., and Gilbert, W. (1977) Proc. Natl. Acad. Sci. U.S.A. 74, 4973-4976). The ability of these photosensitive DNAs to form short range cross-links to bound protein has been used to determine the efficiency with which cross-linked protein-DNA complexes are generated at each individual site of BrdU substitution. Five sites of high efficiency cross-linking to the repressor protein have been identified. At one site, cross-linking without protection from strand scission was observed; this result suggests an unusual mechanism of strand scission and/or cross-linking at this site. Comparison of the UV protection results and the cross-linking data show that these processes provide complementary tools for identifying and analyzing individual protein-DNA contacts.     

Intracellular antibody capture: A molecular biology approach to inhibitors of protein–protein interactions

Many proteins of interest in basic biology, translational research studies and for clinical targeting in diseases reside inside the cell and function by interacting with other macromolecules. Protein complexes control basic processes such as development and cell division but also abnormal cell growth when mutations occur such as found in cancer. Interfering with protein–protein interactions is an important aspiration in both basic and disease biology but small molecule inhibitors have been difficult and expensive to isolate. Recently, we have adapted molecular biology techniques to develop a simple set of protocols for isolation of high affinity antibody fragments (in the form of single VH domains) that function within the reducing environment of higher organism cells and can bind to their target molecules. The method called Intracellular Antibody Capture (IAC) has been used to develop inhibitory anti-RAS and anti-LMO2 single domains that have been used for target validation of these antigens in pre-clinical cancer models and illustrate the efficacy of the IAC approach to generation of drug surrogates. Future use of inhibitory VH antibody fragments as drugs in their own right (we term these macrodrugs to distinguish them from small molecule drugs) requires their delivery to target cells in vivo but they can also be templates for small molecule drug development that emulate the binding sites of the antibody fragments. This article is part of a Special Issue entitled: Recent advances in molecular engineering of antibody.     

Kinetics and mechanism in the reaction of gene regulatory proteins with DNA

We have measured the kinetic properties of the Escherichia coli cAMP receptor protein (CAP) and lac repressor interacting with lac promoter restriction fragments. Under our reaction conditions (10 mM-Tris X HCl (pH 8.0 at 21 degrees C), 1 mM-EDTA, 10 microM-cAMP, 50 micrograms bovine serum albumin/ml, 5% glycerol), the association of CAP is at least a two-step process, with an initial, unstable complex formed with rate constant kappa a = 5(+/- 2.5) X 10(7) M-1 s-1. Subsequent formation of a stable complex occurs with an apparent bimolecular rate constant kappa a = 6.7 X 10(6) M-1 s-1. At low total DNA concentration, the dissociation rate constant for the specific CAP-DNA complex is 1.2 X 10(-4) s-1. The ratio of formation and dissociation rate constants yields an estimate of the equilibrium constant, Keq = 5 X 10(10) M-1, in good agreement with static results. We observed that the dissociation rate constant of both CAP-DNA and repressor-DNA complexes is increased by adding non-specific "catalytic" DNA to the reaction mixture. CAP dissociation by the concentration-dependent pathway is second-order in added non-specific DNA, consistent with either the simultaneous or the sequential participation of two DNA molecules in the reaction mechanism. The results imply a role for distal DNA in assembly-disassembly of specific CAP-DNA complexes, and are consistent with a model in which the subunits in the CAP dimer separate in the assembly-disassembly process. The dissociation of lac repressor-operator complexes was found to be DNA concentration-dependent as well, although in contrast to CAP, the reaction is first-order in catalytic DNA. Added excess operator-rich DNA gave more rapid dissociation than equivalent concentrations of non-specific DNA, indicating that the sequence content of the competing DNA influences the rate of repressor dissociation. The simplest interpretation of these observations is that lac repressor can be transferred directly from one DNA molecule to another. A comparison of the translocation rates calculated for direct transfer with those predicted by the one-dimensional sliding model indicates that direct transfer may play a role in the binding site search of lac repressor.     

Specific binding of lac repressor to linear versus circular polyoperator molecules

Gel shift assays were used to examine the binding of the lactose (lac) repressor to polyoperator DNA molecules. Specific binding was differentiated from nonspecific DNA association by (i) equilibrating repressor-operator complexes below the nonspecific association constant and (ii) demonstrating the effects of the inducer isopropyl beta-D-thiogalactoside (IPTG) on the formation of repressor-operator complexes. With the linear polyoperator molecules, all eight operator sites could be simultaneously bound by distinct repressors. However, with circular molecules, the eight operator sites were saturable by repressor only in the nicked circular state and not in the covalently closed circular form. Under the experimental conditions used, there was no evidence of bifunctional repressor binding or loop formation. The results suggest that the conformational perturbation of DNA that occurs upon specific repressor binding was retained in topologically closed molecules and could modify other operator sites so as to make them unavailable for specific binding.     

Sliding and target location of DNA-binding proteins:an NMR view of the lac repressor system

In non-specific lac headpiece-DNA complexes selective NMR line broadening is observed that strongly depends on length and composition of the DNA fragments. This broadening involves amide protons found in the non-specific lac-DNA structure to be interacting with the DNA phosphate backbone, and can be ascribed to DNA sliding of the protein along the DNA. This NMR exchange broadening has been used to estimate the 1D diffusion constant for sliding along non-specific DNA. The observed 1D diffusion constant of 4×10^?12 cm²/s is two orders of magnitude smaller than derived from previous kinetic experiments, but falls in the range of values determined more recently using single molecule methods. This strongly supports the notion that sliding could play at most a minor role in the association kinetics of binding of lac repressor to lac operator and that other processes such as hopping and intersegment transfer contribute to facilitate the DNA recognition process.     

Targeting the Escherichia coli lac repressor to the mammalian cell nucleus

We have previously shown that about 90% of total Escherichia coli lac repressor synthesized in mammalian cells is located in the cytoplasm [Hu and Davidson, Cell 48 (1987) 555-566]. To target a functional lac repressor to the nucleus, we mutated 10 nucleotides at the 3' end of the coding sequence, thus adding the nuclear localization signal of the simian virus 40 large-T antigen to the C terminus of the repressor. The mutant lacI gene and the wild-type (wt) gene, both in standard animal cell expression vectors, driven by the promoter of the Rous sarcoma virus long terminal repeat, were stably transfected into three rodent cell lines. In confirmation of our previous results, only about 10% of the wt repressor, but all of the mutant protein, was localized in the nucleus. DNase I footprint analyses showed that the mutant repressor retained the same operator DNA-binding specificity as wt repressor. Furthermore, both repressor-operator complexes could be dissociated by addition of isopropyl-beta-D-thiogalactopyranoside in vitro. However, the ratio of number of repressor molecules per nucleus that, by in vitro assay, could bind to the operator sequence to the number of monomer repressor polypeptides per nucleus, as determined by Western blotting, was about 1:4 for the wt repressor and about 1:30 for the mutant repressor. This suggests that: (a) the mutant repressor assembles into tetramers inefficiently; and/or (b) it has reduced binding affinity to the operator sequence; and/or (c) it has higher binding affinity to nonspecific DNA.     

The lac repressor

Few proteins have had such a strong impact on a field as the lac repressor has had in Molecular Biology. Over 40 years ago, Jacob and Monod [Genetic regulatory mechanisms in the synthesis of proteins, J. Mol. Biol. 3 (1961) 318] proposed a model for gene regulation, which survives essentially unchanged in contemporary textbooks. It is a cogent depiction of how a set of 'structural' genes may be coordinately transcribed in response to environmental conditions and regulates metabolic events in the cell. In bacteria, the genes required for lactose utilization are negatively regulated when a repressor molecule binds to an upstream cis activated operator. The repressor and its operator together form a genetic switch, the lac operon. The switch functions when inducer molecules alter the conformation of the repressor in a specific manner. In the presence of a particular metabolite, the repressor undergoes a conformational change that reduces its affinity for the operator. The structures of the lac repressor and its complexes with operator DNA and effector molecules have provided a physical platform for visualizing at the molecular level the different conformations the repressor and the molecular basis for the switch. The structures of lac repressor, bound to its operator and inducer, have also been invaluable for interpreting a plethora of biochemical and genetic data.     

Recombination by resolvase is inhibited by lac repressor simultaneously binding operators between res sites

The Tn3 resolvase requires that the two recombination (res) sites be aligned as direct repeats on the same molecule for efficient recombination to occur. To test whether resolvase must contact the DNA between res sites as predicted by tracking models, we have determined the sensitivity of recombination to protein diffusion blockades. Recombination between two res sites is unaffected either by lac repressor or bacteriophage T7 RNA polymerase being bound between them. Yet recombination is inhibited by lac repressor if the res site is bounded by a lac operator on both sides. We demonstrate that lac repressor will bind to more than one DNA site under the conditions used to assay recombination. This result suggests that lac repressor can inhibit resolvase by forming a DNA loop that isolates a res site topologically. These results do not support a tracking model for resolvase but suggest that the structure and topology of the DNA substrate is important in the formation of a synapse between res sites.     

How Lac repressor finds lac operator in vitro.

Filter-binding and gel mobility shift assays were used to analyse the kinetics of the interaction of Lac repressor with lac operator. A comparison of the two techniques reveals that filter-binding assays with tetrameric Lac repressor have often been misinterpreted. It has been assumed that all complexes of Lac repressor and lac operator DNA bind with equal affinity to nitrocellulose filters. This assumption is wrong. Sandwich or loop complexes where two lac operators bind to one tetrameric Lac repressor are not or are only badly retained on nitrocellulose filters under normal conditions. Taking this into account, dimeric and tetrameric Lac repressor do not show any DNA-length dependence of their association and dissociation rate constants when they bind to DNA fragments smaller than 2455 base-pairs carrying a single symmetric ideal lac operator. A ninefold increased association rate to ideal lac operator on lambda DNA is observed for tetrameric but not dimeric Lac repressor. It is presumably due to intersegment transfer involving lac operator-like sequences.     

Construction, isolation and implications of repressor-galactosidase - beta-galactosidase hybrid molecules.

Escherichia coli heterogenotes, which produce hybrid molecules between the chimaeric protein repressor-galactosidase and the enzyme beta-galactosidase, were constructed. Repressor-galactosidase in which fully active lac repressor is covalently linked to active beta-galactosidase, is an aggregate with a core structure of four beta-galactosidase parts and two peripheral lac repressor dimers. The lac repressor dimers, which are separated by tetrameric beta-galactosidase, retain all the biological activities of tetrameric lac repressor. Substitution of repressor-galactosidase subunits with beta-galactosidase subunits leads to hybrid molecules with y beta-galactosidase subunits aggregated with (4-y) repressor-galactosidase subunits (where y = 1, 2 or 3). A 2:2 hybrid, i.e. a tetrameric beta-galactosidase core with one lac repressor dimer grafted to it, binds at least 100 times less strongly to 32P-labelled lambdaplac DNA than pure lac repressor or repressor-galactosidase. The data suggest a model in which lac repressor binds with two subunits to lac operator and with the other two subunits elsewhere on the DNA, possibly on sequences like the lac operator.     

Genetic studies of the lac repressor. XIII. Extensive amino acid replacements generated by the use of natural and synthetic nonsense suppressors

We have altered the amino acid sequence of the lac repressor one residue at a time by utilizing a collection of nonsense suppressors that permit the insertion of 13 different amino acids in response to the amber (UAG) codon, as well as an additional amino acid in response to the UGA codon. We used this collection to suppress nonsense mutations at 141 positions in the lacI gene, which encodes the 360 amino acid long lac repressor, including 53 new nonsense mutations which we constructed by oligonucleotide-directed mutagenesis. This method has generated over 1600 single amino acid substitutions in the lac repressor. We have cataloged the effects of these replacements and have interpreted the results with the objective of gaining a better understanding of lac repressor structure, and protein structure in general. The DNA binding domain of the repressor, involving the amino-terminal 59 amino acids, is extremely sensitive to substitution, with 70% of the replacements resulting in the I- phenotype. However, the remaining 301 amino acid core of the repressor is strikingly tolerant of substitutions, with only 30% of the amino acids introduced causing the I- phenotype. This analysis reveals the location of sites in the protein involved in inducer binding, tighter binding to operator and thermal stability, and permits a virtual genetic image reconstruction of the lac repressor protein.     

Characterization of the lac repressor species produced by limited tryptic cleavage

Tryptic cleavage of native lac repressor under very mild conditions has been found to yield preparations suitable for detailed physical and chemical analysis. Sephadex G-200 chromatography of the digest produces one main protein peak followed by small peptides. The protein from the main peak was analyzed by automated Edman degradation and revealed two unique cleavage sites, one at residue 51 and the other at 59. The tryptic core protein under native conditions is tetrameric and exhibits a circular dichroism spectrum similar to that of native lac repressor.     

lac repressor acts by modifying the initial transcribing complex so that it cannot leave the promoter

RNA polymerase engaged in the joint complex with the lac repressor at the lac UV5 promoter cannot escape into elongation but generates abortive RNA oligomers. The joint complex actively transcribes a few initial base pairs in a reaction unusually sensitive to a decrease in the substrate concentration. The joint complex, however, fails to traverse a point in the initial transcribed sequence that normally requires a high concentration of the elongating substrate. Thus, the repressor acts by augmenting a natural high "kNTP" site (pause site) embedded in the promoter. A lethal RNA polymerase mutation that mimics the effect of the repressor leads to an analogous block of promoter clearance and shortened abortive product pattern on several promoters, reflecting the widespread occurrence of high kNTP sites in promoters.     

31P NMR spectra of oligodeoxyribonucleotide duplex lac operator-repressor headpiece complexes: importance of phosphate ester backbone flexibility in protein-DNA recognition.

The 31P NMR spectra of various 14-base-pair lac operators bound to both wild-type and mutant lac repressor headpiece proteins were analyzed to provide information on the backbone conformation in the complexes. The 31P NMR spectrum of a wild-type symmetrical operator, d(TGTGAGCGCTCACA)2, bound to the N-terminal 56-residue headpiece fragment of a Y7I mutant repressor was nearly identical to the spectrum of the same operator bound to the wild-type repressor headpiece. In contrast, the 31P NMR spectrum of the mutant operator, d(TATAGAGCGCTCATA)2, wild-type headpiece complex was significantly perturbed relative to the wild-type repressor-operator complex. The 31P chemical shifts of the phosphates of a second mutant operator, d(TGTGTGCGCACACA)2, showed small but specific changes upon complexation with either the wild-type or mutant headpiece. The 31P chemical shifts of the phosphates of a third mutant operator, d(TCTGAGCGCTCAGA)2, showed no perturbations upon addition of the wild-type headpiece. The 31P NMR results provide further evidence for predominant recognition of the 5'-strand of the 5'-TGTGA/3'-ACACT binding site in a 2:1 protein to headpiece complex. It is proposed that specific, strong-binding operator-protein complexes retain the inherent phosphate ester conformational flexibility of the operator itself, whereas the phosphate esters are conformationally restricted in the weak-binding operator-protein complexes. This retention of backbone torsional freedom in strong complexes is entropically favorable and provides a new (and speculative) mechanism for protein discrimination of different operator binding sites. It demonstrates the potential importance of phosphate geometry and flexibility on protein recognition and binding.     

Interlocking of plasmid DNAs due to Lac repressor-operator interaction.

The presence of a single lac repressor binding sequence on plasmid DNAs is shown to mediate the formation of interlocked dimers in E. coli. The presence of both homo- and hetero-interlocked dimers suggests that the lac repressor complex can bring together randomly two plasmid DNA molecules to facilitate gyrase-mediated interlocking. The exclusive formation of multiply intertwined dimers also suggest that the lac repressor complex may bind simultaneously to a pair of replicated daughter plasmid molecules prior to their segregation. The formation of interlocked plasmid DNAs can be indicative of interaction between two DNA bound proteins in vivo.