We conceptualize protein folding as motion in a large dimensional dihedral angle space. We use Lagrangian mechanics and introduce an unspecified Lagrangian to study the motion. The fact that we have reliable folding leads us to conjecture the totality of paths forms caustics that can be recognized by the vanishing of the second variation of the action. There are two types of folding processes: stable against modest perturbations and unstable. We also conjecture that natural selection has picked out stable folds. More importantly, the presence of caustics leads naturally to the application of ideas from catastrophe theory and allows us to consider the question of stability for the folding process from that perspective. Powerful stability theorems from mathematics are then applicable to impose more order on the totality of motions. This leads to an immediate explanation for both the insensitivity of folding to solution perturbations and the fact that folding occurs using very little free energy. The theory of folding, based on the above conjectures, can also be used to explain the behavior of energy landscapes, the speed of folding similar to transition state theory, and the fact that random proteins do not fold.

Walter Simmons

Joel L. Weiner

The Principle of Stationary Action in Biophysics: Stability in Protein Folding

It is known that secondary transporters, which utilize transmembrane ionic gradients to drive their substrates up a concentration gradient, can reverse the uptake and instead release their substrates. Unfortunately, the <i>Michaelis-Menten</i> kinetic scheme, which is popular in transporter studies, does not include transporter reversal, and it completely neglects the possibility of equilibrium between the substrate concentrations on both sides of the membrane. We have developed a complex two-substrate kinetic model that includes transport reversal. This model allows us to construct analytical formulas allowing the calculation of a &#x201c;heteroexchange&#x201d; and &#x201c;transacceleration&#x201d; using standard Michaelis coefficients for respective substrates. This approach can help to understand how glial and other cells accumulate substrates without synthesis and are able to release such substrates and gliotransmitters.

V. Makarov

L. Kucheryavykh

Y. Kucheryavykh

A. Rivera

M. J. Eaton

S. N. Skatchkov

M. Inyushin

Transport Reversal during Heteroexchange: A Kinetic Study

The Flory-Stockmayer theory for the polycondensation of branched polymers, modified for finite systems beyond the gel point, is applied to the connection (synapses) of neurons, which can be considered highly branched &#x201c;monomeric&#x201d; units. Initially, the process is a linear growth and tree-like branching between dendrites and axons of nonself-neurons. After the gel point and at the maximum &#x201c;tree&#x201d; size, the tree-like model prescribes, on average, one pair of twin synapses per neuron. About 13&#x25; of neurons, &#x201c;unconnected&#x201d; to the maximum tree, migrate to the surface to form cortical layers. The number of synapses in each neuron may reach 10000, indicating a tremendous amount of flexible, redundant, and neuroplastic loop-forming linkages which can be preserved or pruned by experience and learning.

Benjamin C. Yan

Johnson F. Yan

A Tree-Like Model for Brain Growth and Structure

Extracellular matrix (ECM) remodeling is a critical step of many biological and pathological processes. However, most of the studies to date lack a quantitative method to measure ECM remodeling at a scale comparable to cell size. Here, we applied image spatial correlation to collagen second harmonic generation (SHG) images to quantitatively evaluate the degree of collagen remodeling by cells. We propose a simple statistical method based on spatial correlation functions to determine the size of high collagen density area around cells. We applied our method to measure collagen remodeling by two breast cancer cell lines (MDA-MB-231 and MCF-7), which display different degrees of invasiveness, and a fibroblast cell line (NIH/3T3). We found distinct collagen compaction levels of these three cell lines by applying the spatial correlation method, indicating different collagen remodeling ability. Furthermore, we quantitatively measured the effect of Latrunculin B and Marimastat on MDA-MB-231 cell line collagen remodeling ability and showed that significant collagen compaction level decreases with these treatments.

Chi-Li Chiu

Michelle A. Digman

Enrico Gratton

Cell Matrix Remodeling Ability Shown by Image Spatial Correlation

Polycystin-1 is a large transmembrane protein, which, when mutated, causes autosomal dominant polycystic kidney disease, one of the most common life-threatening genetic diseases that is a leading cause of kidney failure. The REJ (receptor for egg lelly) module is a major component of PC1 ectodomain that extends to about 1000 amino acids. Many missense disease-causing mutations map to this module; however, very little is known about the structure or function of this region. We used a combination of homology molecular modeling, protein engineering, steered molecular dynamics (SMD) simulations, and single-molecule force spectroscopy (SMFS) to analyze the conformation and mechanical stability of the first &#x7e;420 amino acids of REJ. Homology molecular modeling analysis revealed that this region may contain structural elements that have an FNIII-like structure, which we named REJd1, REJd2, REJd3, and REJd4. We found that REJd1 has a higher mechanical stability than REJd2 (&#x7e;190 pN and 60 pN, resp.). Our data suggest that the putative domains REJd3 and REJd4 likely do not form mechanically stable folds. Our experimental approach opens a new way to systematically study the effects of disease-causing mutations on the structure and mechanical properties of the REJ module of PC1.

Meixiang Xu

Liang Ma

Paul J. Bujalowski

Feng Qian

R. Bryan Sutton

Andres F. Oberhauser

Analysis of the REJ Module of Polycystin-1 Using Molecular Modeling and Force-Spectroscopy Techniques

The effect of high or low levels of trace metals in human tissues has been studied widely. There have been detectable significant variations in the concentrations of trace metals in normal and cancerous tissues suggesting that these variations could be a causative factor to various cancers. Even though essential trace metals play an important role such as stabilizers, enzyme cofactors, elements of structure, and essential elements for normal hormonal functions, their imbalanced toxic effects contribute to the rate of the reactive oxygen species (ROS) and formation of complexities in the body cells which may lead to DNA damage. The induction of oxidative-induced DNA damage by ROS may lead to isolated base lesions or single-strand breaks, complex lesions like double-strand breaks, and some oxidative generated clustered DNA lesions (OCDLs) which are linked to cell apoptosis and mutagenesis. The difference in published works on the level of variations of trace metals in different cancer tissues can be attributed to the accuracy of the analytical techniques, sample preparation methods, and inability of taking uniform samples from the affected tissues. This paper reviews comparative trace elemental concentrations of cancerous and noncancerous tissues using PIXE that has been reported in the published literature.

Stephen Juma Mulware

Comparative Trace Elemental Analysis in Cancerous and Noncancerous Human Tissues Using PIXE

Most models developed to represent transport across epithelia assume that the cell interior constitutes a homogeneous compartment, characterized by a single concentration value of the transported species. This conception differs significantly from the current view, in which the cellular compartment is regarded as a highly crowded media of marked structural heterogeneity. Can the finding of relatively simple dynamic properties of transport processes in epithelia be compatible with this complex structural conception of the cell interior? The purpose of this work is to contribute with one simple theoretical approach to answer this question. For this, the techniques of model reduction are utilized to obtain a two-state reduced model from more complex linear models of transcellular transport with a larger number of intermediate states. In these complex models, each state corresponds to the solute concentration in an intermediate intracellular compartment. In addition, the numerical studies reveal that it is possible to approximate a general two-state model under conditions where strict reduction of the complex models cannot be performed. These results contribute with arguments to reconcile the current conception of the cell interior as a highly complex medium with the finding of relatively simple dynamic properties of transport across epithelial cells.

Julio A. Hern&#xe1;ndez

Reduced Dynamic Models in Epithelial Transport

Ghrelin is a growth hormone (GH) secretagogue (GHS) and GHRP-6 is a synthetic peptide analogue; both act through the GHS receptor. GH secretion depends directly on the intracellular concentration of Ca<sup  >2+</sup>; this is determined from the intracellular reserves and by the entrance of Ca<sup  >2+</sup> through the voltage-dependent calcium channels, which are activated by the membrane depolarization. Membrane potential is mainly determined by K<sup  >+</sup> channels. In the present work, we investigated the effect of ghrelin (10&#x2009;nM) or GHRP-6 (100&#x2009;nM) for 96&#x2009;h on functional expression of voltage-dependent K<sup  >+</sup> channels in rat somatotropes: GC cell line. Physiological patch-clamp whole-cell recording was used to register the K<sup  >+</sup> currents. With Cd<sup  >2+</sup> (1&#x2009;mM) and tetrodotoxin (1&#x2009;<i  >&#x3bc;</i>m) in the bath solution recording, three types of currents were characterized on the basis of their biophysical and pharmacological properties. GC cells showed a K<sup  >+</sup> current with a transitory component <svg     style="vertical-align:-3.276pt;width:28.1625px;" id="M1" height="16.275" version="1.1" viewBox="0 0 28.1625 16.275" width="28.1625"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg> sensitive to 4-aminopyridine, which represents  &#x7e;40&#x25; of the total outgoing current; a sustained component named delayed rectifier <svg     style="vertical-align:-3.276pt;width:27.950001px;" id="M2" height="16.275" version="1.1" viewBox="0 0 27.950001 16.275" width="27.950001"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg>, sensitive to tetraethylammonium; and a third type of K<sup  >+</sup> current was recorded at potentials more negative than &#x2212;80&#x2009;mV, permitting the entrance of K<sup  >+</sup> named inward rectifier (K<sub  >IR</sub>). Chronic treatment with ghrelin or GHRP-6 did not modify the functional expression of K<sup  >+</sup> channels, without significant changes (<svg     style="vertical-align:-0.1638pt;width:58.712502px;" id="M3" height="11.375" version="1.1" viewBox="0 0 58.712502 11.375" width="58.712502"  xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg">
	
		
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</svg>) in the amplitudes of the three currents observed; in addition, there were no modifications in their biophysical properties and kinetic activation or inactivation.

Belisario Dom&#xed;nguez Mancera

Eduardo Monjaraz Guzman

Jorge L. V. Flores-Hern&#xe1;ndez

Manuel Barrientos Morales

Jos&#xe9; M. Mart&#xed;nez Hernandez

Antonio Hern&#xe1;ndez Beltran

Patricia Cervantes Acosta

Potassium Current Is Not Affected by Long-Term Exposure to Ghrelin or GHRP-6 in Somatotropes GC Cells

The thermal aggregation of the biopharmaceutical protein recombinant protective antigen (rPA) has been explored, and the associated kinetics and thermodynamic parameters have been extracted using optical and environmental scanning electron microscopies (ESEMs) and ultraviolet light scattering spectroscopy (UV-LSS). Visual observations and turbidity measurements provided an overall picture of the aggregation process, suggesting a two-step mechanism. Microscopy was used to examine the structure of aggregates, revealing an open morphology formed by the clustering of the microscopic aggregate particles. UV-LSS was used and developed to elucidate the growth rate of these particles, which formed in the first stage of the aggregation process. Their growth rate is observed to be high initially, before falling to converge on a final size that correlates with the ESEM data. The results suggest that the particle growth rate is limited by rPA monomer concentration, and by obtaining data over a range of incubation temperatures, an approach was developed to model the aggregation kinetics and extract the rate constants and the temperature dependence of aggregation. In doing so, we quantified the susceptibility of rPA aggregation under different temperature and environmental conditions and moreover demonstrated a novel use of UV spectrometry to monitor the particle aggregation quantitatively, <i>in situ</i>, in a nondestructive and time-resolved manner.

Daniel J. Belton

Aline F. Miller

Thermal Aggregation of Recombinant Protective Antigen: Aggregate Morphology and Growth Rate

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Journal of Biophysics