Investigating the two regimes of fibrin clot lysis: an experimental and computational approach

It has been observed in vitro that complete clot lysis is generally preceded by a slow phase of lysis during which the degradation seems to be inefficient. However, this slow regime was merely noticed, but not yet quantitatively discussed. In our experiments, we observed that the lysis ubiquitously occurred in two distinct regimes, a slow and a fast lysis regime. We quantified extensively the duration of these regimes for a wide spectrum of experimental conditions and found that on average, the slow regime lasts longer than the fast one, meaning that during most of the process, the lysis is ineffective. We proposed a computational model in which the properties of the binding of the proteins change during the lysis: first, the biochemical reactions take place at the surface of the fibrin fibers, then in the bulk, resulting in the observed fast lysis regime. This simple hypothesis appeared to be sufficient to reproduce with a great accuracy the lysis profiles obtained experimentally.     

A combined experimental and mathematical approach for molecular-based optimization of irinotecan circadian delivery

Circadian timing largely modifies efficacy and toxicity of many anticancer drugs. Recent findings suggest that optimal circadian delivery patterns depend on the patient genetic background. We present here a combined experimental and mathematical approach for the design of chronomodulated administration schedules tailored to the patient molecular profile. As a proof of concept we optimized exposure of Caco-2 colon cancer cells to irinotecan (CPT11), a cytotoxic drug approved for the treatment of colorectal cancer. CPT11 was bioactivated into SN38 and its efflux was mediated by ATP-Binding-Cassette (ABC) transporters in Caco-2 cells. After cell synchronization with a serum shock defining Circadian Time (CT) 0, circadian rhythms with a period of 26 h 50 (SD 63 min) were observed in the mRNA expression of clock genes REV-ERBα, PER2, BMAL1, the drug target topoisomerase 1 (TOP1), the activation enzyme carboxylesterase 2 (CES2), the deactivation enzyme UDP-glucuronosyltransferase 1, polypeptide A1 (UGT1A1), and efflux transporters ABCB1, ABCC1, ABCC2 and ABCG2. DNA-bound TOP1 protein amount in presence of CPT11, a marker of the drug PD, also displayed circadian variations. A mathematical model of CPT11 molecular pharmacokinetics-pharmacodynamics (PK-PD) was designed and fitted to experimental data. It predicted that CPT11 bioactivation was the main determinant of CPT11 PD circadian rhythm. We then adopted the therapeutics strategy of maximizing efficacy in non-synchronized cells, considered as cancer cells, under a constraint of maximum toxicity in synchronized cells, representing healthy ones. We considered exposure schemes in the form of an initial concentration of CPT11 given at a particular CT, over a duration ranging from 1 to 27 h. For any dose of CPT11, optimal exposure durations varied from 3h40 to 7h10. Optimal schemes started between CT2h10 and CT2h30, a time interval corresponding to 1h30 to 1h50 before the nadir of CPT11 bioactivation rhythm in healthy cells.     

A theory of contraction and a mathematical model of striated muscle

A theory of contraction and an associated model of striated muscle are presented, based on the assumption that chemical energy is being converted into electrical energy which, in turn, is being converted into mechanical energy and heat.The model, set up for the frog sartorius muscle, is able to predict the “rowing” motion of the cross-bridges, the force-velocity relation, the tension-length curve, the isometric force, all energy rates (heat and work rates), the metabolic rates and all known features of the stretched, stimulated muscle (no ATP-splitting, stretching tension higher than isometric tension, etc.). It also offers an alternative explanation for Hill's thermoelastic effect. The significance of Hill's force-velocity equation in the context of this theory is also discussed in detail.     

Effects of forskolin and cilostazol on clot retraction

We examined the effects of two inhibitors of aggregation of human platelets the, Forskolin and Cilostazol on clot retraction. Both substances suppressed clot retraction in a dose-dependent way. Both suppress platelet aggregation because of an increase in intercellular cyclic AMP, but there was no close correlations were shown between suppression rate for clot retraction and cyclic-AMP content in platelets in the clot in each substance. Furthermore, although it has been considered that actomyosin in platelets is a major contractile source for clot retraction and that failure of actin polymerization results suppression of clot retraction. As it was difficult to obtain active actin from platelets of the reagents on the polymerization. Cilostazol accelerated actin polymerization, whereas Forskolin did not. From these findings, it was considered that the effects of both substances on clot retraction could not be interpreted directly just by the increasing effect for intracellular cyclic-AMP. Clot retraction is consider to be a in vitro model of hemostasis and its contractile force is supplied from platelets (1,2,3). Experiments used prostaglandin E-1 revealed that elevation of cyclic-AMP (c-AMP) would regulate the clot retraction, and experiments used cytochalasin B demonstrated that actomyosin is responsible to the retraction (4,5). Many date demonstrate that elevation of c-AMP level suppresses platelet aggregation (6,7). c-AMP, therefore, should play a key role on platelet activation. Forskolin and Cilostazol are newly-developed reagents as a suppress for platelet functions. Pharmacological action of these substances have been interpreted to process increase effect for intracellular c-AMP of platelets(8,9). If so, both substances should show some effect on clot retraction. Under this assumption, we examined the effects.     

A mathematical approach to cytoskeletal assembly

The cytoskeleton is a fundamental and important part of cell's structure, and is known to play a large role in controlling the shape, function, division, and motility of the cell. In recent years, the traditional biological and biophysical experimental work on the cytoskeleton has been enhanced by a variety of theoretical, physical and mathematical approaches. Many of these approaches have been developed in the traditional frameworks of physico-chemical and statistical mechanics or equilibrium thermodynamic principles. An alternative is to use kinetic modelling and couch the analysis in terms of differential equations which describe mean field properties of cytoskeletal networks or assemblies. This paper describes two such recent efforts. In the first part of the paper, a summary of work on the kinetics of polymerization, fragmentation, and dynamics of actin and polymers in the presence of gelsolin (which nulceates, fragments, and caps the filaments) is given. In the second part, some of the kinetic models aimed at elucidating the spatio-angular density distribution of actin filaments interacting via crosslinks is described. This model given insight into effects that govern the formation of clusters and bundles of actin filaments, and their spatial distribution. Received: 7 January 1998 / Revised version: 4 March 1998 / Accepted: 7 March 1998     

Quantitative analysis of electrophoretograms: A mathematical approach to super-resolution

A mathematical method is presented for the quantitative analysis of overlapping spots or bands taken from digitized gel patterns. The procedure is applied to both one- and two-dimensional gel electrophoretic separations.     

Effects of functional diversity and salinization on zooplankton productivity: an experimental approach

Hydrobiologia - Quantifying the interactions between functional diversity and environmental change is important for understanding the effects of biodiversity on ecosystem processes. This study aims...     

A mathematical model of protein degradation by the proteasome

The proteasome is the major protease for intracellular protein degradation. The influx rate of protein substrates and the exit rate of the fragments/products are regulated by the size of the axial channels. Opening the channels is known to increase the overall degradation rate and to change the length distribution of fragments. We develop a mathematical model with a flux that depends on the gate size and a phenomenological cleavage mechanism. The model has Michaelis-Menten kinetics with a V(max) that is inversely related to the length of the substrate, as observed in the in vitro experiments. We study the distribution of fragment lengths assuming that proteasomal cleavage takes place at a preferred distance from the ends of a protein fragment, and find multipeaked fragment length distributions similar to those found experimentally. Opening the gates in the model increases the degradation rate, increases the average length of the fragments, and increases the peak in the distribution around a length of 8-10 amino acids. This behavior is also observed in immunoproteasomes equipped with PA28. Finally, we study the effect of re-entry of processed fragments in the degradation kinetics and conclude that re-entry is only expected to affect the cleavage dynamics when short fragments enter the proteasome much faster than the original substrate. In summary, the model proposed in this study captures the known characteristics of proteasomal degradation, and can therefore help to quantify MHC class I antigen processing and presentation.     

On immunotherapies and cancer vaccination protocols: A mathematical modelling approach

In this paper we develop a new mathematical model of immunotherapy and cancer vaccination, focusing on the role of antigen presentation and co-stimulatory signaling pathways in cancer immunology. We investigate the effect of different cancer vaccination protocols on the well-documented phenomena of cancer dormancy and recurrence, and we provide a possible explanation of why adoptive (i.e. passive) immunotherapy protocols can sometimes actually promote tumour growth instead of inhibiting it (a phenomenon called immunostimulation), as opposed to active vaccination protocols based on tumour-antigen pulsed dendritic cells. Significantly, the results of our computational simulations suggest that elevated numbers of professional antigen presenting cells correlate well with prolonged time periods of cancer dormancy.     

A mathematical model for experimental gene evolution

The purpose of this paper is to determine the optimal mutation rate for random mutagenesis procedures used to make mutant libraries for subsequent screening. When the mutation rate is low, the probability of achieving a rare beneficial mutation is low. When the mutation rate is high, the probability of producing lethal mutations which result in loss of function is also high. We demonstrate that between these two extremes, an optimal mutation rate exists for experimental gene improvement. This rate depends strongly on the number of simultaneous mutations required for a beneficial change of the gene, but only weakly on the number of possible lethal mutations. This model predicts that when mutagenesis is performed at the optimum mutation rate, at least 63% (1--e(-1)) of the cloned genes in a mutant library will be non-functional.     

On a simple way to verify the experimental agreement of any two-state mathematical model of muscle contraction

In the usual theories of muscular contraction, the crossbridges are considered to be the force generators leading to the sliding of the thick and the thin filaments past each other. The first mathematical treatment of such models was that of Huxley (1957) and since this date the formalism has been continuously improved. Here we have obtained a relation identifiable to the mathematical expression of the Fenn effect. This relation leads to a new expression of the tension P(V), which must be compared with that directly obtained from mechanical considerations. These two expressions do not fit in the currently accepted two-state models.     

A mathematical approach to multiple genetic relationships

A fundamental concept in the treatment of genetic relationships is that of gene identity which first was introduced by Cotterman (1940). Based on this notion several measures of relationship evolved such as the inbreeding coefficient, the coefficient of kinship, and the identity coefficients; by means of these quantities joint and conditional phenotype probabilities could be derived. This paper is an attempt at a general mathematical treatment of genetic relationships: Identity states are defined for any number of individuals, a method is given for the calculation of the corresponding identity coefficients by means of generalized coefficients of kinship, and applications are emphasized.     

A mathematical model of the coupled mechanisms of cell adhesion,contraction and spreading

Recent research has shown that cell spreading is highly dependent on the contractility of its cytoskeleton and the mechanical properties of the environment it is located in. The dynamics of such process is critical for the development of tissue engineering strategy but is also a key player in wound contraction, tissue maintenance and angiogenesis. To better understand the underlying physics of such phenomena, the paper describes a mathematical formulation of cell spreading and contraction that couples the processes of stress fiber formation, protrusion growth through actin polymerization at the cell edge and dynamics of cross-membrane protein (integrins) enabling cell-substrate attachment. The evolving cell’s cytoskeleton is modeled as a mixture of fluid, proteins and filaments that can exchange mass and generate contraction. In particular, besides self-assembling into stress fibers, actin monomers able to polymerize into an actin meshwork at the cell’s boundary in order to push the membrane forward and generate protrusion. These processes are possible via the development of cell-substrate attachment complexes that arise from the mechano-sensitive equilibrium of membrane proteins, known as integrins. After deriving the governing equation driving the dynamics of cell evolution and spreading, we introduce a numerical solution based on the extended finite element method, combined with a level set formulation. Numerical simulations show that the proposed model is able to capture the dependency of cell spreading and contraction on substrate stiffness and chemistry. The very good agreement between model predictions and experimental observations suggests that mechanics plays a strong role into the coupled mechanisms of contraction, adhesion and spreading of adherent cells.     

Mechanism of bone-conducted hearing: mathematical approach

For better understanding of bone-conducted (BC) hearing, a mechanical BC model is formulated using the Wentzel–Kramers–Brillouin (WKB) method. The BC hearing can be generally described by three main mechanisms: (1) cochlear fluid inertia, (2) in-phase motion of the outer bony shell, and (3) out-of-phase motion of the outer bony shell. Specifically, the second and third mechanisms can be identically explained by symmetric pressure compression–expansion and anti-symmetric compression–expansion, respectively. In this study, simulation results show that both the symmetric and anti-symmetric compression–expansion modes become significant at frequencies above 7 kHz while the fluid inertial mode is dominant at lower frequencies. The density difference between the scala fluid and soft cells of basilar membrane and the amplitude of the anti-symmetric compression–expansion input are identified as the difference between the air conduction and bone conduction. The natural frequency of the cochlear duct wall determines the magnitudes between the three mechanism and is approximated to be in the order of 10 MHz and above.     

A mathematical and experimental study of ant foraging trail dynamics

In this article, we present a mathematical model coupled to an experimental study of ant foraging trails. Our laboratory experiments on Tetramorium caespitum do not find a strong relationship between ant densities and velocities, a common assumption in traffic modeling. Rather, we find that higher order effects play a major role in observed behavior, and our model reflects this by including inertial terms in the evolution equation. A linearization of the resulting system yields left- and right-moving waves, in agreement with laboratory measurements. The linearized system depends upon Froude numbers reflecting a ratio of the energy stored in the foraging trail to the kinetic energy of the ants. The model predicts and the measurements support the existence of two distinct phase velocities.     

Substrate deformation determines actin cytoskeleton reorganization: A mathematical modeling and experimental study

A mathematical model has been developed to define the relationship between the actin cytoskeleton reorganization of a cell and substrate deformation acting on the cell. The model is based on the following major assumptions: (a) normal substrate strain, not the shear substrate strain, determines the actin cytoskeleton reorganization; (b) the normal substrate strain is transmitted to individual actin filaments; (c) each actin filament has a basal strain energy (BSE) when the cell adheres to the substrate without stretching; and (d) the actin filaments undergo disassembly when their strain energies are decreased to zero or increased to twice their BSEs. The resulting model predicts that the actin filaments are formed in the direction where their BSEs are minimally altered. This direction is therefore the one without normal substrate strain. The prediction was confirmed by experiments conducted on both fibroblasts and endothelial cells. The present model may be relevant for understanding better the effects of mechanical stimuli on the cells.     

The comparability of pharmacokinetics of creatinine in rabbit and man: A mathematical approach

A model simulating the kinetics of creatinine displacement in rabbit is investigated. The model is validated by comparing the predicted renal clearance and production rate constant with observed values and those reported previously in the literature. By applying steady state conditions to the model, a simple equation for prediction of creatinine clearance from serum creatinine is obtained. This is the first equation for predicting clearance which is not based on empirical relationships. The equation is then tested on a set of data from 61 patients with various degrees of renal impairment and a wide variation in weights and ages. It is found that good correlation (r = 0·93) exists between predicted and observed creatinine clearances. This comparability is attributed to the similarities in disposition of a non-threshold substance, like creatinine, in rabbits and man. Thus, it is suggested that more confidence can be placed on the use of rabbit as animal model in creatinine investigations.