Exploration of the Parameter Space of an Ion Channel Kinetic Model by a Markov-Chain-Based Methodology.

In this work, we propose a methodology based on Monte Carlo Markov chains to explore the parameter space of kinetic models for ion channels. The methodology allows the detection of potential parameter sets of a model that are compatible with experimentally obtained whole-cell currents, which could remain hidden when methods focus on obtaining the parameters that provide the best fit. To show its implementation and utility, we considered a four-state kinetic model proposed in the literature to describe the activation of the voltage-gated proton channel (Hv1), Biophysical Journal, 2014, 107, 1564. In that work, a set of values for the rate transitions that describe the channel kinetics at different intracellular H+ concentration (pHi) were obtained by the Simplex method. With our approach, we find that, in fact, there is more than one parameter set for each pHi, which renders the same open probability temporal course within the experimental error margin for all of the considered voltages. The large differences that we obtained for the values of some rate constants among the different solutions show that there is more than one possible interpretation of this channel behavior as a function of pHi. We also simulated a proposed new experimental condition where it is possible to observe that different sets of parameters yield different results. Our study highlights the importance of a comprehensive analysis of parameter space in kinetic models and the utility of the proposed methodology for finding potential solutions.

Immunity acquired by a minority active fraction of the population could explain COVID-19 spread in Greater Buenos Aires (June-November 2020).

The coronavirus disease 2019 (COVID-19) pandemic had an uneven development in different countries. In Argentina, the pandemic began in March 2020 and, during the first 3 months, the vast majority of cases were concentrated in a densely populated region that includes the city of Buenos Aires (country capital) and the Greater Buenos Aires (GBA) area that surrounds it. This work focuses on the spread of COVID-19 between June and November 2020 in GBA. Within this period of time there was no vaccine, basically only the early wild strain of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) was present, and the official restriction and distancing measures in this region remained more or less constant. Under these particular conditions, the incidences show a sharp rise from June 2020 and begin to decrease towards the end of August until the end of November 2020. In this work we study, through mathematical modelling and available epidemiological information, the spread of COVID-19 in this region and period of time. We show that a coherent explanation of the evolution of incidences can be obtained assuming that only a minority fraction of the population got involved in the spread process, so that the incidences decreased as this group of people was becoming immune. The observed evolution of the incidences could then be a consequence at the population level of lasting immunity conferred by SARS-CoV-2.

La no obligatoriedad de la vacunación y su potencial impacto en la epidemiología de coqueluche / Non-mandatory immunization and its potential impact on pertussis epidemiology

En este trabajo, se analizan cuantitativamente las consecuencias a corto plazo que tendría sobre coqueluche la sanción del Proyecto de Ley de Consentimiento Informado en Materia de Vacunación presentado en Argentina, en 2017, el cual contempla la no obligatoriedad de la aplicación de las vacunas del Calendario Nacional a los menores de edad. Se utiliza un modelo matemático para la transmisión de pertusis, desarrollado previamente en nuestro grupo. Se considera que la sola presentación del proyecto provoca una disminución en las coberturas por generar desconfianza sobre los beneficios del programa de vacunación. Asumiendo 5 % anual de reducción de las coberturas durante 4 años a partir de 2018, en el siguiente brote, los casos graves en menores del año se incrementarían en más del 100 % respecto del último brote, y se estiman 101 fallecidos. Con una reducción del 10 % anual por 4 años, el siguiente brote superaría al previo en más del 200 %, con 163 decesos.

In this study, we performed a quantitative analysis of the potential short-term consequences on pertussis of the draft bill on Informed Consent for Immunization proposed in Argentina in 2017, which considers a non-mandatory immunization schedule for minors. We used a mathematical model of pertussis transmission, which had been previously developed by our group. It is considered that the mere presentation of the project causes a reduction in coverage because it creates suspicion on the benefits of immunization. Assuming a 5 % annual reduction in coverage for 4 years as of 2018, in the next outbreak, severe cases in infants younger than 1 year will increase more than 100 % compared to the latest outbreak, with an estimated 101 deaths. With a 10 % annual reduction in the coverages for 4 years, the next outbreak would result in an increase of number of cases of more than 200 %, with 163 deaths.

Non-mandatory immunization and its potential impact on pertussis epidemiology. / La no obligatoriedad de la vacunación y su potencial impacto en la epidemiología de coqueluche.

In this study, we performed a quantitative analysis of the potential short-term consequences on pertussis of the draft bill on Informed Consent for Immunization proposed in Argentina in 2017, which considers a non-mandatory immunization schedule for minors. We used a mathematical model of pertussis transmission, which had been previously developed by our group. It is considered that the mere presentation of the project causes a reduction in coverage because it creates suspicion on the benefits of immunization. Assuming a 5 % annual reduction in coverage for 4 years as of 2018, in the next outbreak, severe cases in infants younger than 1 year will increase more than 100 % compared to the latest outbreak, with an estimated 101 deaths. With a 10 % annual reduction in the coverages for 4 years, the next outbreak would result in an increase of number of cases of more than 200 %, with 163 deaths.

En este trabajo, se analizan cuantitativamente las consecuencias a corto plazo que tendría sobre coqueluche la sanción del Proyecto de Ley de Consentimiento Informado en Materia de Vacunación presentado en Argentina, en 2017, el cual contempla la no obligatoriedad de la aplicación de las vacunas del Calendario Nacional a los menores de edad. Se utiliza un modelo matemático para la transmisión de pertusis, desarrollado previamente en nuestro grupo. Se considera que la sola presentación del proyecto provoca una disminución en las coberturas por generar desconfianza sobre los beneficios del programa de vacunación. Asumiendo 5 % anual de reducción de las coberturas durante 4 años a partir de 2018, en el siguiente brote, los casos graves en menores del año se incrementarían en más del 100 % respecto del último brote, y se estiman 101 fallecidos. Con una reducción del 10 % anual por 4 años, el siguiente brote superaría al previo en más del 200 %, con 163 decesos.

Potential Impact of Changes in the Schedule for Primary Diphtheria-Tetanus Toxoids-Pertussis Immunization as Control Strategy for Pertussis.

BACKGROUND: Pertussis is a vaccine-preventable respiratory disease that may cause death mainly in infants. The schedules for primary pertussis vaccination are set in each country by the local health authorities. Several different schedules meet World Health Organization recommendations, 2-4-6 months, 6-10-14 weeks, 2-3-4 months and 3-4-5 months being the most commonly used worldwide. In this work, we analyze the benefits of changing the vaccination schedule to control the disease. METHODS: We used an age-structured deterministic mathematical model for pertussis transmission to compute the incidences for the 4 above-mentioned schedules. Different vaccination coverages and vaccine effectiveness levels were considered. Immunization data from Argentina and Belgium were used. RESULTS: The highest reduction in incidence was obtained by adopting the 6-10-14 weeks schedule, reaching about a 36% reduction of 0-1-year incidence with respect to the 2-4-6 months schedule. We show the dependence of this reduction on both vaccine effectiveness and coverage. The severe pertussis incidence decreased significantly when the first dose of the 2-4-6 months schedule was accelerated to 6 weeks. Finally, we estimated that the communication campaign adopted in Flanders (Belgium) to improve compliance with the vaccine schedule could lead to a reduction of 16% in severe pertussis incidence and about 7% in total incidence in infants. CONCLUSIONS: Our work highlights the use of mathematical modeling to quantify the benefits of the existing vaccination schedules and the strategies that could be implemented to improve their compliance. Our results indicated that the 6-10-14 weeks is the best schedule option and that the Belgium vaccination campaign significantly reduced the incidence of severe cases.

SIR model with local and global infective contacts: A deterministic approach and applications.

An epidemic model with births and deaths is considered on a two-dimensional L×L lattice. Each individual can have global infective contacts according to the standard susceptible-infected-recovered (SIR) model rules or local infective contacts with their nearest neighbors. We propose a deterministic approach to this model and, for the parameters corresponding to pertussis and rubella in the prevaccine era, verify that there is a close agreement with the stochastic simulations when epidemic spread or endemic stationarity is considered. We also find that our approach captures the characteristic features of the dynamic behavior of the system after a sudden decrease in global contacts that may arise as a consequence of health care measures. By using the deterministic approach, we are able to characterize the exponential growth of the epidemic behavior and analyze the stability of the system at the stationary values. Since the deterministic approximation captures the essential features of the disease transmission dynamics of the stochastic model, it provides a useful tool for performing systematic studies as a function of the model parameters. We give an example of this potentiality by analyzing the likelihood of the endemic state to become extinct when the weight of the global contacts is drastically reduced.

Assessment of pertussis vaccination strategies using a mathematical model of disease transmission.

Pertussis or whooping cough is a vaccine-preventable respiratory disease that has reemerged in the past decades. A higher morbidity and mortality has been recorded in infants, although cases have also been reported in adolescents and adults. The epidemiological scenario for this condition has urged to review and implement new strategies aimed at improving its control. However, many of these strategies have not been investigated in depth so as to be established as universal. In this context, mathematical models of disease transmission are useful decision-making tools. Using a mathematical model of pertussis, this study assessed the possible impact of the different control measures on the most vulnerable population (0-1 year old infants). In particular, the analysis focused on the impact of including a booster vaccination at 11 years old, the effect of improving the coverage provided by primary doses, and the reduction of any delay in their administration. The assessment also estimated the effect of immunizing pregnant women. Results show that including a booster dose at 11 years reduces the incidence of pertussis by 3% in infants younger than 1 year old. In addition, administering primary doses in compliance with the schedule (with no delays) reduces pertussis incidence by 16%. Increasing coverage from 80% to 95% results in a signifcantly decreased incidence in the vulnerable population (38%). If the percentage of immunized pregnant women reaches 50%, the reduction of the most severe infant cases could be more than 43% (0-2 month-old infants).

Assessment of pertussis vaccination strategies using a mathematical model of disease transmission / Evaluación de las estrategias de vacunación contra la tos convulsa mediante un modelo matemático de transmisión de la enfermedad

Pertussis or whooping cough is a vaccine-preventable respiratory disease that has reemerged in the past decades. A higher morbidity and mortality has been recorded in infants, although cases have also been reported in adolescents and adults. The epidemiological scenario for this condition has urged to review and implement new strategies aimed at improving its control. However, many of these strategies have not been investigated in depth so as to be established as universal. In this context, mathematical models of disease transmission are useful decision-making tools. Using a mathematical model of pertussis, this study assessed the possible impact of the different control measures on the most vulnerable population (0-1 year old infants). In particular, the analysis focused on the impact of including a booster vaccination at 11 years old, the effect of improving the coverage provided by primary doses, and the reduction of any delay in their administration. The assessment also estimated the effect of immunizing pregnant women. Results show that including a booster dose at 11 years reduces the incidence of pertussis by 3% in infants younger than 1 year old. In addition, administering primary doses in compliance with the schedule (with no delays) reduces pertussis incidence by 16%. Increasing coverage from 80% to 95% results in a signifcantly decreased incidence in the vulnerable population (38%). If the percentage of immunized pregnant women reaches 50%, the reduction of the most severe infant cases could be more than 43% (0-2 month-old infants).

La tos convulsa o coqueluche es una enfermedad respiratoria inmunoprevenible que ha resurgido en las últimas décadas. La mayor morbimortalidad se registra en los lactantes, aunque también se detectan casos en adolescentes y adultos. La situación epidemiológica de la enfermedad ha obligado a revisar e implementar nuevas estrategias para mejorar su control. Sin embargo, muchas de estas estrategias aún no cuentan con un sustento experimental que permita su universalización. En este contexto, los modelos matemáticos de transmisión de enfermedades resultan herramientas útiles en la toma de decisiones. En este trabajo se evaluó, mediante un modelo matemático para coqueluche, el impacto que tendrían distintas medidas de control en la población más vulnerable (0 a 1 año). En particular, se analizó el impacto de la inclusión de un refuerzo a los 11 años, el efecto de la mejora en las coberturas de las dosis primarias y la disminución del retraso en la aplicación de estas. También se estimó el efecto de la vacunación a embarazadas. Los resultados muestran que la inclusión de un refuerzo a los 11 años disminuye un 3% la incidencia en los menores de 1 año. Por su parte, la aplicación de las dosis primarias a tiempo calendario (sin retrasos) la reduce un 16%. Al aumentar la cobertura del 80% al 95%, la incidencia en la población vulnerable se reduce signifcativamente (38%). Cuando el porcentaje de las embarazadas inmunizadas alcanza el 50%, la reducción de los casos más graves en los infantes superaría el 43% (0 - 2 meses).

Assessment of pertussis vaccination strategies using a mathematical model of disease transmission / Evaluación de las estrategias de vacunación contra la tos convulsa mediante un modelo matemático de transmisión de la enfermedad

Pertussis or whooping cough is a vaccine-preventable respiratory disease that has reemerged in the past decades. A higher morbidity and mortality has been recorded in infants, although cases have also been reported in adolescents and adults. The epidemiological scenario for this condition has urged to review and implement new strategies aimed at improving its control. However, many of these strategies have not been investigated in depth so as to be established as universal. In this context, mathematical models of disease transmission are useful decision-making tools. Using a mathematical model of pertussis, this study assessed the possible impact of the different control measures on the most vulnerable population (0-1 year old infants). In particular, the analysis focused on the impact of including a booster vaccination at 11 years old, the effect of improving the coverage provided by primary doses, and the reduction of any delay in their administration. The assessment also estimated the effect of immunizing pregnant women. Results show that including a booster dose at 11 years reduces the incidence of pertussis by 3% in infants younger than 1 year old. In addition, administering primary doses in compliance with the schedule (with no delays) reduces pertussis incidence by 16%. Increasing coverage from 80% to 95% results in a signifcantly decreased incidence in the vulnerable population (38%). If the percentage of immunized pregnant women reaches 50%, the reduction of the most severe infant cases could be more than 43% (0-2 month-old infants).(AU)

La tos convulsa o coqueluche es una enfermedad respiratoria inmunoprevenible que ha resurgido en las últimas décadas. La mayor morbimortalidad se registra en los lactantes, aunque también se detectan casos en adolescentes y adultos. La situación epidemiológica de la enfermedad ha obligado a revisar e implementar nuevas estrategias para mejorar su control. Sin embargo, muchas de estas estrategias aún no cuentan con un sustento experimental que permita su universalización. En este contexto, los modelos matemáticos de transmisión de enfermedades resultan herramientas útiles en la toma de decisiones. En este trabajo se evaluó, mediante un modelo matemático para coqueluche, el impacto que tendrían distintas medidas de control en la población más vulnerable (0 a 1 año). En particular, se analizó el impacto de la inclusión de un refuerzo a los 11 años, el efecto de la mejora en las coberturas de las dosis primarias y la disminución del retraso en la aplicación de estas. También se estimó el efecto de la vacunación a embarazadas. Los resultados muestran que la inclusión de un refuerzo a los 11 años disminuye un 3% la incidencia en los menores de 1 año. Por su parte, la aplicación de las dosis primarias a tiempo calendario (sin retrasos) la reduce un 16%. Al aumentar la cobertura del 80% al 95%, la incidencia en la población vulnerable se reduce signifcativamente (38%). Cuando el porcentaje de las embarazadas inmunizadas alcanza el 50%, la reducción de los casos más graves en los infantes superaría el 43% (0 - 2 meses).(AU)

Assessment of pertussis vaccination strategies using a mathematical model of disease transmission. / Assessment of pertussis vaccination strategies using a mathematical model of disease transmission.

Pertussis or whooping cough is a vaccine-preventable respiratory disease that has reemerged in the past decades. A higher morbidity and mortality has been recorded in infants, although cases have also been reported in adolescents and adults. The epidemiological scenario for this condition has urged to review and implement new strategies aimed at improving its control. However, many of these strategies have not been investigated in depth so as to be established as universal. In this context, mathematical models of disease transmission are useful decision-making tools. Using a mathematical model of pertussis, this study assessed the possible impact of the different control measures on the most vulnerable population (0-1 year old infants). In particular, the analysis focused on the impact of including a booster vaccination at 11 years old, the effect of improving the coverage provided by primary doses, and the reduction of any delay in their administration. The assessment also estimated the effect of immunizing pregnant women. Results show that including a booster dose at 11 years reduces the incidence of pertussis by 3

in infants younger than 1 year old. In addition, administering primary doses in compliance with the schedule (with no delays) reduces pertussis incidence by 16

. Increasing coverage from 80

to 95

results in a signifcantly decreased incidence in the vulnerable population (38

). If the percentage of immunized pregnant women reaches 50

, the reduction of the most severe infant cases could be more than 43

(0-2 month-old infants).

Modelos matemáticos sobre la transmisión de coqueluche y estrategias de vacunación en Argentina / Mathematical models about pertussis transmission and vaccination strategies in Argentina

INTRODUCCION: La tos convulsa o pertussis es una enfermedad respiratoria que es más severa en los lactantes. Antes de que la vacunación infantil se introdujera en la década de 1950, la tos convulsa era una de las principales causas de mortalidad infantil en el mundo. La enfermedad hoy es reconocida como una infección frecuente, no sólo para los niños sino también para los adultos. Las razones de esta situación epidemiológica y las estrategias de control para la enfermedad son objeto de debate en la comunidad científica. En este contexto, los modelos matemáticos se utilizan cada vez más como un herramienta no sólo para el análisis, sino también para predicciones con el fin de contribuir al conocimiento de este complejo problema.OBJETIVO: En este estudio se presenta un modelo compartamentalizado, que de manera simplificada permite describir la propagación de la tos convulsa en la Argentina y evaluar el impacto de los cambios en el calendario de vacunación en el control de la enfermedad.METODOS: El modelo epidemiológico aplicado considera que la exposición a la tos convulsa a través de la infección natural o vacunación induce una respuesta inmune que previene la enfermedad grave. Además, se considera que estos efectos protectores son temporales debido a la disminución de la inmunidad.RESULTADOS: El estudio señala que la dosis administrada a los 11 años (recientemente introducidos en el esquema de vacunación de Argentina) disminuye la incidencia de la enfermedad en el grupo etario de 11 a 13 años de edad en una proporción de alrededor del 40%. Sin embargo, este refuerzo podría tener un impacto mucho menor (menos del 5%) para los niños menores de 1 año de edad que son el grupo más vulnerable.CONCLUSIONES: Nuestro estudio sugiere que un esfuerzo dirigido a la mejora de la cobertura de las primeras dosis tendrá un impacto mucho mayor que el refuerzo de los 11 en lo que se refiere a la reducción de la incidencia de tos convulsa en los niños más pequeños.

INTRODUCTION: Whooping cough, or pertussis, is a respiratory disease that is mose severe in infants. Before childhood vaccination was introduced in the 1950s, pertussis was a major cause of infant mortality worldwide. The disease is now recognized as a frequent infection not only for infants but also for adults. The reasons for this epidemiological situation and strategies for disease control are matters of debate in the scientific community. In this context, the mathematical models are being used increasingly as a tool not only for analysis but also for predictions in order to contribute to the knowledge of this complex problem.OBJECTIVE: The study has a compartmental model that, in a simplistic way, allows to describe the propagation of pertussis in Argentina and to assess the impact of changes in the vaccination schedule on the disease control.METHODS: The model here presented considers that pertussis exposure through natural infection or vaccination induces an immune response that prevents severe disease and assumes that these protective effects are temporary due to waning of immunity.RESULTS: The study points out that the dose given at 11 years of age (recently introduced in Argentica vaccination schedule) would decrease around 40% the incidence of the disease in the age group from 11 to 13 years old. However, this reinforcement would have a much lower impact (less than 5%) in children under 1 year, who are the most vulnerable group.CONCLUSIONS: It would be important to make an effort towards vigilance, so as to improve the coverage of the primary close and then significantly reduce the incidence of pertussis in the youngest children.

Modelos matemáticos sobre la transmisión de coqueluche y estrategias de vacunación en Argentina / Mathematical models about pertussis transmission and vaccination strategies in Argentina

INTRODUCCION: La tos convulsa o pertussis es una enfermedad respiratoria que es más severa en los lactantes. Antes de que la vacunación infantil se introdujera en la década de 1950, la tos convulsa era una de las principales causas de mortalidad infantil en el mundo. La enfermedad hoy es reconocida como una infección frecuente, no sólo para los niños sino también para los adultos. Las razones de esta situación epidemiológica y las estrategias de control para la enfermedad son objeto de debate en la comunidad científica. En este contexto, los modelos matemáticos se utilizan cada vez más como un herramienta no sólo para el análisis, sino también para predicciones con el fin de contribuir al conocimiento de este complejo problema.OBJETIVO: En este estudio se presenta un modelo compartamentalizado, que de manera simplificada permite describir la propagación de la tos convulsa en la Argentina y evaluar el impacto de los cambios en el calendario de vacunación en el control de la enfermedad.METODOS: El modelo epidemiológico aplicado considera que la exposición a la tos convulsa a través de la infección natural o vacunación induce una respuesta inmune que previene la enfermedad grave. Además, se considera que estos efectos protectores son temporales debido a la disminución de la inmunidad.RESULTADOS: El estudio señala que la dosis administrada a los 11 años (recientemente introducidos en el esquema de vacunación de Argentina) disminuye la incidencia de la enfermedad en el grupo etario de 11 a 13 años de edad en una proporción de alrededor del 40%. Sin embargo, este refuerzo podría tener un impacto mucho menor (menos del 5%) para los niños menores de 1 año de edad que son el grupo más vulnerable.CONCLUSIONES: Nuestro estudio sugiere que un esfuerzo dirigido a la mejora de la cobertura de las primeras dosis tendrá un impacto mucho mayor que el refuerzo de los 11 en lo que se refiere a la reducción de la incidencia de tos convulsa en los niños más pequeños.

INTRODUCTION: Whooping cough, or pertussis, is a respiratory disease that is mose severe in infants. Before childhood vaccination was introduced in the 1950s, pertussis was a major cause of infant mortality worldwide. The disease is now recognized as a frequent infection not only for infants but also for adults. The reasons for this epidemiological situation and strategies for disease control are matters of debate in the scientific community. In this context, the mathematical models are being used increasingly as a tool not only for analysis but also for predictions in order to contribute to the knowledge of this complex problem.OBJECTIVE: The study has a compartmental model that, in a simplistic way, allows to describe the propagation of pertussis in Argentina and to assess the impact of changes in the vaccination schedule on the disease control.METHODS: The model here presented considers that pertussis exposure through natural infection or vaccination induces an immune response that prevents severe disease and assumes that these protective effects are temporary due to waning of immunity.RESULTS: The study points out that the dose given at 11 years of age (recently introduced in Argentica vaccination schedule) would decrease around 40% the incidence of the disease in the age group from 11 to 13 years old. However, this reinforcement would have a much lower impact (less than 5%) in children under 1 year, who are the most vulnerable group.CONCLUSIONS: It would be important to make an effort towards vigilance, so as to improve the coverage of the primary close and then significantly reduce the incidence of pertussis in the youngest children.

From particles to spins: Eulerian formulation of supercooled liquids and glasses.

The dynamics of supercooled liquid and glassy systems are usually studied within the Lagrangian representation, in which the positions and velocities of distinguishable interacting particles are followed. Within this representation, however, it is difficult to define measures of spatial heterogeneities in the dynamics, as particles move in and out of any one given region within long enough times. It is also nontransparent how to make connections between the structural glass and the spin glass problems within the Lagrangian formulation. We propose an Eulerian formulation of supercooled liquids and glasses that allows for a simple connection between particle and spin systems, and that permits the study of dynamical heterogeneities within a fixed frame of reference similar to the one used for spin glasses. We apply this framework to the study of the dynamics of colloidal particle suspensions for packing fractions corresponding to the supercooled and glassy regimes, which are probed via confocal microscopy.

Fickian crossover and length scales from two point functions in supercooled liquids.

Particle motion of a Lennard-Jones supercooled liquid near the glass transition is studied by molecular dynamics simulations. We analyze the wave vector dependence of relaxation times in the incoherent self-scattering function and show that at least three different regimes can be identified and its scaling properties determined. The transition from one regime to another happens at characteristic length scales. The length scale associated with the onset of Fickian diffusion corresponds to the maximum size of heterogeneities in the system, and the characteristic time scale is several times larger than the alpha relaxation time. A second crossover length scale is observed, which corresponds to the typical time and length of heterogeneities, in agreement with results from four point functions. The different regimes can be traced back to the behavior of the van Hove distribution of displacements, which shows a characteristic exponential regime in the heterogeneous region before the crossover to Gaussian diffusion and should be observable in experiments. Our results show that it is possible to obtain characteristic length scales of heterogeneities through the computation of two point functions at different times.

Distance between inherent structures and the influence of saddles on approaching the mode coupling transition in a simple glass former.

We analyze through molecular dynamics simulations of a Lennard-Jones (LJ) binary mixture the statistics of the distances between inherent structures sampled at temperatures above the mode coupling transition temperature T(MCT). After equilibrating at T>T(MCT) we take equilibrated configurations and randomly perturb the coordinates of a given number of particles. After that we find the nearby inherent structures (IS) of both the original and perturbed configurations and evaluate the distance between them. This distance presents an inflection point at T(li) approximately 1 with a strong decrease below this temperature which goes to a small but nonzero value on approaching T(MCT). In the low-temperature region we study the statistics of events which give zero distance, i.e., dominated by minima, and find evidence that the number of saddles decreases exponentially near T(MCT). This implies that saddles continue to exist even at T