Asymptotic distribution of stage-grouped population models

Matrix models are often used to predict the dynamics of size-structured or age-structured populations. The asymptotic behaviour of such models is defined by their malthusian growth rate lambda, and by their stationary distribution w that gives the asymptotic proportion of individuals in each stage. As the coefficients of the transition matrix are estimated from a sample of observations, lambda and w can be considered as random variables whose law depends on the distribution of the observations. The goal of this study is to specify the asymptotic law of lambda and w when using the maximum likelihood estimators of the coefficients of the transition matrix. We prove that lambda and w are asymptotically normal, and the expressions of the asymptotic variance of lambda and of the asymptotic covariance matrix of w are given. The convergence speed of lambda and w towards their asymptotic law is studied using simulations. The results are applied to a real case study that consists of a Usher model for a tropical rain forest in French Guiana. They permit to assess the number of trees to measure to get a given precision on the estimated asymptotic diameter distribution, which is an important information on tropical forest management.     

Fluctuation analysis of nonideal shot noise. Application to the neuromuscular junction

Procedures are described for analyzing shot noise and determining the waveform, w(t), mean amplitude, (h), and mean rate of occurrence, (r), of the shots under a variety of nonideal conditions that include: (a) slow, spurious changes in the mean, (b) nonstationary shot rates, (c) nonuniform distribution of shot amplitudes, and (d) nonlinear summation of the shots. The procedures are based upon Rice's (1944. Bell Telephone System Journal. 23: 282-332) extension of Campbell's theorem to the second (variance), lambda 2, third (skew), lambda 3, and fourth, lambda 4, semi-invariants (cumulants) of the noise. It is shown that the spectra of lambda 2 and lambda 3 of nonstationary shot noise contain a set of components that are proportional to (r) and arise from w(t), and a set of components that are independent of (r) and arise from the temporal variations in r(t). Since the latter components are additive and are limited by the bandwidth of r(t), they can be removed by appropriate filters; then (r) and (h) can be determined from the lambda 2 and lambda 3 of the filtered noise. We also show that a factor related to the ratio (lambda 3)2/(lambda 2)(lambda 4) monitors the spread in the distribution of shot amplitudes and can be used to correct the estimates of (r) and (h) for the effects of that spread, if the shape of the distribution is known and if r(t) is stationary. The accuracy of the measurements of lambda 4 is assessed and corrections for the effects of nonlinear summation of lambda 2, lambda 3, and lambda 4 are derived. The procedures give valid results when they are used to analyze shot noise produced by the (linear) summation of simulated miniature endplate potentials, which are generated either at nonstationary rates or with a distribution of amplitudes.     

A strategy to determine operating parameters in tissue engineering hollow fiber bioreactors

The development of tissue engineering hollow fiber bioreactors (HFB) requires the optimal design of the geometry and operation parameters of the system. This article provides a strategy for specifying operating conditions for the system based on mathematical models of oxygen delivery to the cell population. Analytical and numerical solutions of these models are developed based on Michaelis–Menten kinetics. Depending on the minimum oxygen concentration required to culture a functional cell population, together with the oxygen uptake kinetics, the strategy dictates the model needed to describe mass transport so that the operating conditions can be defined. If c_min ≫ K_m we capture oxygen uptake using zero‐order kinetics and proceed analytically. This enables operating equations to be developed that allow the user to choose the medium flow rate, lumen length, and ECS depth to provide a prescribed value of c_min. When , we use numerical techniques to solve full Michaelis–Menten kinetics and present operating data for the bioreactor. The strategy presented utilizes both analytical and numerical approaches and can be applied to any cell type with known oxygen transport properties and uptake kinetics. Biotechnol. Bioeng. 2011; 108:1450–1461. © 2011 Wiley Periodicals, Inc.     

Refolding of the immunoglobulin light chain.

The kinetics of the refolding reactions of type lambda Bence Jones proteins from 4 M GuHCl were studied by CD, ultraviolet absorption, and fluorescence spectrophotometry. The kinetics were complex and consisted of at least three phases, an undetectable fast phase, a detectable fast phase, and a slow phase. The slow phase followed first-order kinetics and the three experimental methods used gave similar rate constants for all the Bence Jones proteins (about 3 X 10(-3) s-1). The refolding reaction of VL fragment was too fast to be measured in the present experiments. The refolding process of CL fragment was very similar to those of Bence Jones proteins except that the detectable fast phase was less significant. The rate constant of the slow phase observed for the CL fragment was similar to those of the slow phase observed for Bence Jones proteins. The activation energy of the slow phase was the same for a Bence Jones protein and its CL fragment. These results indicate that the refolding kinetics of the CL domain are very similar to those of isolated CL fragment and that refolding of the VL domain precedes refolding of the CL domain, even though both domains have similar immunoglobulin folds. However, the results of refolding experiments on Bence Jones proteins, and VL and CL fragments in the presence of ANS, as well as the other lines of evidence, indicate that the refolding kinetics of the Bence Jones protein molecule cannot be expressed as simple sum of the refolding reactions of isolated VL and CL fragments.     

Complex spatial distribution and dynamics of an abundant Escherichia coli outer membrane protein, LamB

Advanced techniques for observing protein localization in live bacteria show that the distributions are dynamic. For technical reasons, most such techniques have not been applied to outer membrane proteins in Gram-negative bacteria. We have developed two novel live-cell imaging techniques to observe the surface distribution of LamB, an abundant integral outer membrane protein in Escherichia coli responsible for maltose uptake and for attachment of bacteriophage lambda. Using fluorescently labelled bacteriophage lambda tails, we quantitatively described the spatial distribution and dynamic movement of LamB in the outer membrane. LamB accumulated in spiral patterns. The distribution depended on cell length and changed rapidly. The majority of the protein diffused along spirals extending across the cell body. Tracking single particles, we found that there are two populations of LamB--one shows very restricted diffusion and the other shows greater mobility. The presence of two populations recalls the partitioning of eukaryotic membrane proteins between 'mobile' and 'immobile' populations. In this study, we have demonstrated that LamB moves along the bacterial surface and that these movements are restricted by an underlying dynamic spiral pattern.     

Localization accuracy in single-molecule microscopy

One of the most basic questions in single-molecule microscopy concerns the accuracy with which the location of a single molecule can be determined. Using the Fisher information matrix it is shown that the limit of the localization accuracy for a single molecule is given by, lambda(em)/2pi n(a) square root of gammaAt, where lambda(em), n(a), gamma, A, and t denote the emission wavelength of the single molecule, the numerical aperture of the objective, the efficiency of the optical system, the emission rate of the single molecule and the acquisition time, respectively. Using Monte Carlo simulations it is shown that estimation algorithms can come close to attaining the limit given in the expression. Explicit quantitative results are also provided to show how the limit of the localization accuracy is reduced by factors such as pixelation of the detector and noise sources in the detection system. The results demonstrate what is achievable by single-molecule microscopy and provide guidelines for experimental design.     

Solvent-tuning the collapse and helix formation time scales of lambda(6-85)*

The lambda(6-85)(*) pseudo-wild type of lambda repressor fragment is a fast two-state folder (k(f) approximately 35 microsec(-1) at 58 degrees C). Previously, highly stable lambda(6-85)(*) mutants with k(f) > 30 microsec(-1) have been engineered to fold nearly or fully downhill. Stabilization of the native state by solvent tuning might also tune lambda(6-85)(*) away from two-state folding. We test this prediction by examining the folding thermodynamics and kinetics of lambda(6-85)(*) in a stabilizing solvent, 45% by weight aqueous ethylene glycol at -28 degrees C. Detection of kinetics by circular dichroism at 222 nm (sensitive to helix content) and small angle X-ray scattering (measuring the radius of gyration) shows that refolding from guanidine hydrochloride denatured conditions exhibits very different time scales for collapse and secondary structure formation: the two processes become decoupled. Collapse remains a low-barrier activated process, while the fastest of several secondary structure formation time scales approaches the downhill folding limit. Two-state folding of lambda(6-85)(*) is not a robust process.     

Influence of the germline sequence on the thermodynamic stability and fibrillogenicity of human lambda 6 light chains

Light chain-associated amyloidosis is a fatal disease characterized by the aggregation and pathologic deposition of monoclonal light chain-related fragments as amyloid fibrils in organs or tissues throughout the body. Notably, it has been observed that proteins encoded by the lambda variable light chain (V(L)) gene segment 6a are invariably associated with amyloid deposition; however, the contribution of the gene to this phenomenon has not been established. In this regard, we have determined the thermodynamic stability and kinetics of in vitro fibrillogenesis of a recombinant (r) V(L) protein, designated 6aJL2, which contains the predicted sequences encoded by the 6a and JL2 germline genes. Additionally, we studied a 6a mutant (6aJL2-Arg25Gly), that is present in approximately 25% of all amyloid-associated lambda6 light chains. Remarkably, the wild-type 6aJL2 protein was more stable than were all known amyloidogenic kappa and lambda light chains for which stability parameters are available; more importantly, it was even more so (and less fibrillogenic) than the only clinically proven nonamyloidogenic lambda6 protein, Jto. Conversely, the mutated 6aJL2-R25G molecule was considerably less stable and more fibrillogenic than was the native 6aJL2. Our data indicate that the propensity of lambda6 light chains to form amyloid can not be attributed to thermodynamic instability of the germline-encoded Vlambda6 domain, but rather, is dependent on sequence alterations that render such proteins amyloidogenic.     

Laser photobleaching leads to a fluorescence grade adenosine deaminase

The enzyme adenosine deaminase (adenosine aminohydrolase EC 3.5.4.4) from calf intestinal mucosa is commercially available at high purity grade yet, at the sensitivity at which fluorescence studies may be undertaken, a nonpeptidic fluorescence is detectable at lambda exmax = 350 nm and lambda emmax = 420 nm. A sevenfold decrease of this nonpeptidic fluorescence was obtained upon irradiation by the third harmonic (355 nm) of a Nd:YAG laser for 16 min, at 5 mJ/pulse, with a pulse width of 6 ns at a repetition rate of 10 Hz. The decline of fluorescence was accompanied by a negligible loss of enzymatic activity. Moreover, the integrity of the protein was ascertained by (i) its fluorescence (lambda exmax = 305 nm, lambda emmax = 335 nm) and lifetime distribution and (ii) its kinetics in the presence of the substrate adenosine and two inhibitors, all of which remained essentially unaltered. Laser photobleaching is a simple way to achieve a fluorescence grade adenosine deaminase.     

Thermodynamic instability of human lambda 6 light chains: correlation with fibrillogenicity.

Certain types of human light chains have the propensity to deposit pathologically as amyloid fibrils as evidenced by the preferential association of monoclonal lambda 6 proteins with AL amyloidosis. However, the molecular features that render such proteins amyloidogenic have not been elucidated. Based upon the demonstrated relationship between the thermodynamic stability of light chains and their propensity to aggregate in vitro, we have initiated studies where the thermodynamic properties and fibrillogenic potential of two recombinant (r) V lambda 6 molecules were compared. The first protein was generated from cDNA cloned from marrow-derived plasma cells from a patient (Wil) who had AL amyloidosis and renal amyloid deposits; the second was from a patient (Jto) with multiple myeloma in whom the lambda 6 protein was deposited not as amyloid but in the form of renal tubular casts. The thermodynamic stabilities of rV lambda 6Wil and -Jto were determined from chaotropic and thermal denaturation studies. Based upon the Delta GH2O, Delta H, Delta G25 degrees C, Tm, and Cm values, the rV lambda 6Wil was less stable than its nonamyloidogenic counterpart, rV lambda 6Jto. Measurement of fibril formation using a novel in vitro fibril forming assay demonstrated that although both rV lambda 6 proteins formed fibrils in vitro, Wil had a shorter lag time and exhibited faster kinetics under physiologic conditions. Comparative amino acid sequence analyses of these two components and other lambda 6 amyloid-associated light chains revealed that the Jto protein had certain primary structural features that we posit contributed to its increased stability and thus rendered this protein nonamyloidogenic. Our studies provide the first evidence that stabilizing interactions within the V L domain can influence the kinetics of light chain fibrillogenicity.     

Two human genes isolated by a novel method encode DNA-binding proteins containing a common region of homology

Two cDNAs encoding new DNA-binding proteins (Dbps) have been cloned using a human placenta lambda gt11 recombinant cDNA library and DNA fragments as probes. Hybrid proteins expressed by the lambda gt11 cDNA library were blotted onto nitrocellulose filters, and incubated with three different radio-labeled DNA probes containing the human epidermal growth factor (EGF) receptor enhancer or the human c-erbB-2 promoter. Two kinds of clones, named dbpA and dbpB, showed high affinities for the DNA probes. The comparison of the nucleotide and the deduced amino acid (aa) sequences between these two cDNAs indicated that 100 of 109 aa located in the central region of these two Dbps were identical. The dbpA and dbpB-coded proteins also had an affinity for other cDNA probes such as the human c-ski gene, but not for poly(dI-dC).poly(dI-dC), suggesting that the sequence(s) recognized by the dbpA and dbpB-coded proteins may occur frequently, or that these proteins bind to DNA non-specifically in a different manner from that of histones. A simple method, described in this paper, can be used to isolate cDNA clones encoding Dbps. Strategies used for the detection of sequence-specific and non-specific Dbps are discussed.     

Using motion planning to map protein folding landscapes and analyze folding kinetics of known native structures.

We investigate a novel approach for studying the kinetics of protein folding. Our framework has evolved from robotics motion planning techniques called probabilistic roadmap methods (PRMs) that have been applied in many diverse fields with great success. In our previous work, we presented our PRM-based technique and obtained encouraging results studying protein folding pathways for several small proteins. In this paper, we describe how our motion planning framework can be used to study protein folding kinetics. In particular, we present a refined version of our PRM-based framework and describe how it can be used to produce potential energy landscapes, free energy landscapes, and many folding pathways all from a single roadmap which is computed in a few hours on a desktop PC. Results are presented for 14 proteins. Our ability to produce large sets of unrelated folding pathways may potentially provide crucial insight into some aspects of folding kinetics, such as proteins that exhibit both two-state and three-state kinetics that are not captured by other theoretical techniques.     

Folding of circular permutants with decreased contact order: general trend balanced by protein stability.

To examine the influence of contact order and stability on the refolding rate constant for two-state proteins, we have analysed the folding kinetics of the small beta-alpha-beta protein S6 and two of its circular permutants with relative contact orders of 0.19, 0.15 and 0.12. Data reveal a small but significant increase of the refolding rate constant (log k(f)) with decreasing contact order. At the same time, the decreased contact order is correlated to losses in global stability and alterations of the folding nucleus. When the differences in stability are accounted for by addition of Na2SO4 or by comparison of the folding kinetics at the transition mid-point, the dependence between log k(f) and contact order becomes stronger and follows the general correlation for two-state proteins. The observation emphasizes the combined action of topology and stability in controlling the rate constant of protein folding.     

Estimation and computation of the growth rate in Leslie's and Lotka's population models.

Leslie's or Lotka's population model has a rate of natural increase (lambda or r) which represents the growth rate of the population and characterizes the ability of the population to attain a stable age distribution. In this article are presented upper and lower bounds on that rate, primarily in terms of the net reproduction rate and other commonly used parameters of the population. Also a discussion is given of quadratically convergent numerical iterative methods of computing the growth rate.     

Kinetics analysis methods for approximate folding landscapes

MOTIVATION: Protein motions play an essential role in many biochemical processes. Lab studies often quantify these motions in terms of their kinetics such as the speed at which a protein folds or the population of certain interesting states like the native state. Kinetic metrics give quantifiable measurements of the folding process that can be compared across a group of proteins such as a wild-type protein and its mutants. RESULTS: We present two new techniques, map-based master equation solution and map-based Monte Carlo simulation, to study protein kinetics through folding rates and population kinetics from approximate folding landscapes, models called maps. From these two new techniques, interesting metrics that describe the folding process, such as reaction coordinates, can also be studied. In this article we focus on two metrics, formation of helices and structure formation around tryptophan residues. These two metrics are often studied in the lab through circular dichroism (CD) spectra analysis and tryptophan fluorescence experiments, respectively. The approximated landscape models we use here are the maps of protein conformations and their associated transitions that we have presented and validated previously. In contrast to other methods such as the traditional master equation and Monte Carlo simulation, our techniques are both fast and can easily be computed for full-length detailed protein models. We validate our map-based kinetics techniques by comparing folding rates to known experimental results. We also look in depth at the population kinetics, helix formation and structure near tryptophan residues for a variety of proteins. AVAILABILITY: We invite the community to help us enrich our publicly available database of motions and kinetics analysis by submitting to our server: http://parasol.tamu.edu/foldingserver/.     

Serologically defined V region subgroups of human lambda light chains

The availability of numerous antisera prepared against lambda-type Bence Jones proteins and lambda chains of known amino acid sequence has led to the differentiation and classification of human lambda light chains into one of five V lambda subgroups. The five serologically defined subgroups, V lambda I, V lambda II, V lambda III, V lambda IV, and V lambda VI, correspond to the chemical classification that is based on sequence homologies in the first framework region (FR1). Proteins designated by sequence as lambda V react with specific anti-lambda II antisera and are thus included in the V lambda II subgroup classification. The isotypic nature of the five V lambda subgroups was evidenced through analyses of lambda-type light chains that were isolated from the IgG of normal individuals. Based on analyses of 116 Bence Jones proteins, the frequency of distribution of the lambda I, lambda II/V, lambda III, lambda IV, and lambda VI proteins in the normal lambda chain population is estimated to be 27%, 37%, 23%, 3%, and 10%, respectively. This distribution of V lambda subgroups was comparable to that found among 82 monoclonal Ig lambda proteins. Considerable V lambda intragroup antigenic heterogeneity was also apparent. At least two sub-subgroups were identified among each of the five major V lambda subgroups, implying the existence of multiple genes in the human V lambda genome. The V lambda classification of 54 Ig lambda proteins obtained from patients with primary or multiple myeloma-associated amyloidosis substantiated the preferential association of lambda VI light chains with amyloidosis AL and the predominance of the normally rare V lambda VI subgroup in this disease.