Monte Carlo Computer Simulations Research Articles

The role of extended range of interactions in the dynamics of interacting molecular motors

Motor proteins, also known as biological molecular motors, play important roles in various intracellular processes. Experimental investigations suggest that molecular motors interact with each other during the cellular transport, but the nature of such interactions remains not well understood. Stimulated by these observations, we present a theoretical study aimed to understand the effect of the range of interactions on dynamics of interacting molecular motors. For this purpose, we develop a new version of the totally asymmetric simple exclusion processes in which nearest-neighbor as well as the next nearest-neighbor interactions are taken into account in a thermodynamically consistent way. A theoretical framework based on a cluster mean-field approximation, which partially takes correlations into account, is developed to evaluate the stationary properties of the system. It is found that fundamental current–density relations in the system strongly depend on the strength and the sign of interactions, as well as on the range of interactions. For repulsive interactions stronger than some critical value, a mean-field theoretical approach predicts that increasing the range of interactions might lead to a change from unimodal to trimodal dependence in the flux-density fundamental diagram. However, it is not fully supported by extensive Monte Carlo computer simulations that test theoretical predictions. Although in most ranges of parameters a reasonable agreement between theoretical calculations and computer simulations is observed, there are situations when the cluster mean-field approach fails to describe properly the dynamics in the system. Theoretical arguments to explain these observations are presented. Our theoretical analysis clarifies the microscopic picture of how the range of interactions influences the dynamics of interacting molecular motors.

How Pioneer Transcription Factors Search for Target Sites on Nucleosomal DNA.

All major biological processes start after protein molecules known as transcription factors detect specific regulatory sequences on DNA and initiate genetic expression by associating to them. But in eukaryotic cells, much of the DNA is covered by nucleosomes and other chromatin structures, preventing transcription factors from binding to their targets. At the same time, experimental studies show that there are several classes of proteins, called "pioneer transcription factors", that are able to reach the targets on nucleosomal DNA; however, the underlying microscopic mechanisms remain not well understood. We propose a new theoretical approach that might explain how pioneer transcription factors can find their targets. It is argued that pioneer transcription factors might weaken the interactions between the DNA and nucleosome by substituting them with similar interactions between transcription factors and DNA. Using this idea, we develop a discrete-state stochastic model that allows for exact calculations of target search dynamics on nucleosomal DNA using first-passage probabilities approach. It is found that the target search on nuclesomal DNA for pioneer transcription factors might be significantly accelerated while the search is slower on naked DNA in comparison with normal transcription factors. Our theoretical predictions are supported by Monte Carlo computer simulations, and they also agree with available experimental observations.

Dynamics of the protein search for targets on DNA in quorum-sensing cells

Quorum sensing is a bacterial cell-cell communication process that regulates gene expression. The search and binding of the autoinducer molecule (AHL)-bound LuxR-type proteins to specific sites on DNA in quorum-sensing cells in Gram-negative bacteria is a complex process and has been theoretically investigated based on a discrete-state stochastic approach. It is shown that several factors such as the rate of formation of the AHL-bound LuxR protein within the cells and its dissociation to freely diffusing AHL, the diffusion of the latter in and out of the cells, positive feedback loops, and the cell population density play important roles in the protein target search and can control the gene regulation processes. Physical-chemical arguments to explain these observations are presented. Our calculations of the dynamic properties are also supplemented by Monte Carlo computer simulations. Our theoretical model provides physical insights into the complex mechanisms of protein target search in quorum-sensing cells.

Optimal pathways control fixation of multiple mutations during cancer initiation

Cancer starts after initially healthy tissue cells accumulate several specific mutations or other genetic alterations. The dynamics of tumor formation is a very complex phenomenon due to multiple involved biochemical and biophysical processes. It leads to a very large number of possible pathways on the road to final fixation of all mutations that marks the beginning of the cancer, complicating the understanding of microscopic mechanisms of tumor formation. We present a new theoretical framework of analyzing the cancer initiation dynamics by exploring the properties of effective free-energy landscape of the process. It is argued that although there are many possible pathways for the fixation of all mutations in the system, there are only a few dominating pathways on the road to tumor formation. The theoretical approach is explicitly tested in the system with only two mutations using analytical calculations and Monte Carlo computer simulations. Excellent agreement with theoretical predictions is found for a large range of parameters, supporting our hypothesis and allowing us to better understand the mechanisms of cancer initiation. Our theoretical approach clarifies some important aspects of microscopic processes that lead to tumor formation.

Computer simulation investigation of the adsorption of acetamide on low density amorphous ice. An astrochemical perspective.

The adsorption of acetamide on low density amorphous (LDA) ice is investigated by grand canonical Monte Carlo computer simulations at the temperatures 50, 100, and 200K, characteristic of certain domains of the interstellar medium (ISM). We found that the relative importance of the acetamide-acetamide H-bonds with respect to the acetamide-water ones increases with decreasing temperature. Thus, with decreasing temperature, the existence of the stable monolayer, characterizing the adsorption at 200K, is gradually replaced by the occurrence of marked multilayer adsorption, preceding even the saturation of the first layer at 50K. While isolated acetamide molecules prefer to lay parallel to the ice surface to maximize their H-bonding with the surface water molecules, this orientational preference undergoes a marked change upon saturation of the first layer due to increasing competition of the adsorbed molecules for H-bonds with water and to the possibility of their H-bond formation with each other. As a result, molecules stay preferentially perpendicular to the ice surface in the saturated monolayer. The chemical potential value corresponding to the point of condensation is found to decrease linearly with increasing temperature. We provide, in analogy with the Clausius-Clapeyron equation, a thermodynamic explanation of this behavior and estimate the molar entropy of condensed phase acetamide to be 34.0 J/mol K. For the surface concentration of the saturated monolayer, we obtain the value 9.1 ± 0.8 µmol/m2, while the heat of adsorption at infinitely low surface coverage is estimated to be -67.8 ± 3.0 kJ/mol. Our results indicate that the interstellar formation of peptide chains through acetamide molecules, occurring at the surface of LDA ice, might well be a plausible process in the cold (i.e., below 50K) domains of the ISM; however, it is a rather unlikely scenario in its higher temperature (i.e., 100-200K) domains.

Influence of Nonspecific Interactions between Proteins and In Vivo Cytoplasmic Crowders in Facilitated Diffusion of Proteins: Theoretical Insights.

The binding of proteins to their respective specific sites on the DNA through facilitated diffusion serves as the initial step of various important biological processes. While this search process has been thoroughly investigated via in vitro studies, the cellular environment is complex and may interfere with the protein's search dynamics. The cytosol is heavily crowded, which can potentially modify the search by nonspecifically interacting with the protein that has been mostly overlooked. In this work, we probe the target search dynamics in the presence of explicit crowding agents that have an affinity toward the protein. We theoretically investigate the role of such protein-crowder associations in the target search process using a discrete-state stochastic framework that allows for the analytical description of dynamic properties. It is found that stronger nonspecific associations between the crowder and proteins can accelerate the facilitated diffusion of proteins in comparison with a purely inert, rather weakly interacting cellular environment. This effect depends on how strong these associations are, the spatial positions of the target with respect to the crowders, and the size of the crowded region. Our theoretical results are also tested with Monte Carlo computer simulations. Our predictions are in qualitative agreement with existing experimental observations and computational studies.

Double-Lattice Packing of Pentagonal Gold Bipyramids in Supercrystals with Triclinic Symmetry.

Pentagonal packing is a long-standing issue and a rich mathematical topic, brought to the fore by recent progress in nanoparticle design. Gold pentagonal bipyramids combine fivefold symmetry and anisotropy and their section varies along the length. In this work, colloidal supercrystals of pentagonal gold bipyramids are obtained in a compact arrangement that generalizes the optimal packing of regular pentagons in the plane. Multimodal investigations reveal a two-particle unit cell with triclinic symmetry, a lower symmetry than that of the building blocks. Monte Carlo computer simulations show that this lattice achieves the densest possible packing. Going beyond pentagons, further simulations show an odd-even effect of the number of sides on the packing: odd-sided bipyramids are non-centrosymmetric and require the double-lattice arrangement to recover inversion symmetry. The supercrystals display a facet-dependent optical response that is promising for sensing, metamaterials applications, and for fundamental studies of self-assembly processes.

MOF-801 as a Nanoporous Water-Based Carrier System for In Situ Encapsulation and Sustained Release of 5-FU for Effective Cancer Therapy.

Nanoporous metal-organic frameworks (MOFs) have been gaining a reputation for their drug delivery applications. In the current work, MOF-801 was successfully prepared by a facile, cost-efficient, and environmentally friendly approach through the reaction of ZrCl4 and fumaric acid as organic linkers to deliver 5-fluorouracil (5-FU). The prepared nanostructure was fully characterized by a series of analytical techniques including Fourier transform infrared spectroscopy, powder X-ray diffraction, field-emission scanning electron microscopy, energy-dispersive X-ray spectroscopy, UV-vis spectroscopy, 1H NMR spectroscopy, thermogravimetric analysis, high-performance liquid chromatography, and Brunauer-Emmett-Teller analysis. MOF-801 could be used for the delivery of the anticancer drug 5-FU due to its high surface area, suitable pore size, and biocompatible ingredients. Based on in vitro loading and release studies, a high 5-FU loading capacity and pH-dependent drug release behavior were observed. Moreover, the interactions between the structure of MOFs and 5-FU were investigated through Monte Carlo simulation calculations. An in vitro cytotoxicity test was done, and the results indicated that 5-FU@MOF-801 was more potent than 5-FU on SW480 cancerous cells, indicating the highlighted role of this drug delivery system. Finally, the kinetics of drug release was investigated.

Physical characterization of therapeutic proton delivery through common dental materials.

Dental fixtures are commonplace in an aging, radiation treatment population. The current, local standard of practice in particle therapy is to employ treatment geometries to avoid delivery through implanted dental fixtures. The present study aims to observe the physical effect of delivering therapeutic proton beams through common dental fixture materials as prelude to an eventual goal of assessing the feasibility of using treatment geometries not specified for avoidance of oral implants. A sampling of common dental materials was selected based on prosthodontic consult and was evaluated in terms of relative stopping power and three-dimensional (3D) dose perturbation. Amalgams, porcelain-fused-to-metal (PFM) crowns consisting of zirconia and non-noble base metals, and lithium disilicate implants were chosen for analysis. Theoretical stopping power (S) and mass stopping power (S/ρ) were calculated using the Stopping and Range of Ions in Matter (SRIM) application, basing stoichiometric compositions of each fixture on published materials data. S and S/ρ were calculated for a range of historically available compositions of amalgams from 1900 until the current era. The perturbance of S and S/ρ as a function of clinically relevant ranges of amalgam compositions for the modern era was analyzed. Water equivalent thickness (WET) and relative stopping power (Srel ) of each material was measured for a clinical spot-scanning proton beam with monoenergies of 159.9 and 228.8MeV with a multi-layer ionization chamber (MLIC). Subsequently, 3D dose perturbation was assessed by delivering proton beams through a custom phantom designed to simulate both en-face and on-edge treatment geometries through the selected materials. A treatment plan mimicking the experimental delivery was constructed in the institutional treatment planning system and calculated using TOPAS-based Monte Carlo simulation (MCS). Experimental results were used to validate the MCS. Finally, treatment planning system (TPS) outputs were compared to MCS to determine the accuracy of the dose calculation model. Historical compositions of amalgams ranged in S from 44.8 to 42.9MeV/cm, with the greatest deviation being observed for the 1900-1959 era. Deviation as a function of amalgam composition from the modern era was most sensitive to proportion of Hg, accounting for deviations up to -4.2% at the greatest clinically relevant concentration. S/ρ was not found to vary greatly between each porcelain and metal alloy material for PFM type crowns. Relative stopping powers ranged between 1.3 and 5.4 for all studied materials, suggesting substantial changes in proton range with respect to water. Film measurements of pristine spots confirm dose perturbance and shortening of proton range, with an upstream shift of each Bragg peak being observed directly behind the installed fixture. At high energies, cold spots were found in all cases directly behind each material feature with a medial fill-in of dose occurring distally. Qualitative agreement of spot perturbance was confirmed between film measurements and MCS. Finally, when comparing integrated depth doses (IDD) by summing over all axial directions, good agreement is observed between TPS and MCS. All dental materials studied substantially perturbed the dosimetry of pristine proton spots both in terms of WET/Srel as well as the spatial distribution of dose. Proton range was quantifiably shortened, and each dental material affected a cold spot directly behind the object with medial dose back-filling was observed distally. MCS and Eclipse dose calculations exhibited good agreement with measurements, suggesting that treatment planning without employing avoidance strategies may be possible with further investigation.

Atomic layer deposition precisely modified zeolite 13X: Physicochemical synergistic adsorption of space molecular contaminants

In spaceflight applications, molecular contamination control has become one of the most challenging issues. Porous zeolites are a potent molecular adsorbent with advantages of efficient adsorption at low pressure and/or high temperature, high interaction with adsorbates, and superior durability in extreme environments. Herein, zeolite 13X pellets were selected for adsorption of stearyl alcohol (C18H37OH) as a target molecular contaminant. Considering the excellent hydrophilicity of the zeolite 13X which limits the adsorption of most hydrophobic organic molecules, modification of the zeolite 13X by deposition of TiO2 via atomic layer deposition (ALD) technology was performed. Results show that ALD-grown TiO2 not only improves hydrophobicity but also renders high activity, whilst retains the hierarchical pores of the zeolites. As a result, the as-prepared zeolite 13X@TiO2 exhibits efficient adsorption toward trace stearyl alcohol under low pressure through the synergistic contribution of physisorption and chemisorption. Monte Carlo (MC) simulation, molecular dynamic (MD) and Density Functional Theory (DFT) calculations further discover that pore wall surfaces are primary adsorption sites for the physisorption while ALD-grown TiO2 provides active sites for the chemisorption.

Monte Carlo simulations of the self-assembly of hierarchically organized metal-organic networks on solid surfaces

The coordination-driven self-assembly of two-dimensional (2D) supramolecular architectures is a convenient method of rational construction of one-atom-thick nanomaterials with desired topology, intriguing physicochemical properties and high cognitive value. In this work, we use coarse-grained Monte Carlo (MC) computer simulations to study the self-assembly of functional bridging ligands with mononuclear metal centers on a triangular lattice. Particularly, we focus on the role of anisotropic, reversible ligand → metal coordinate bonds in the bottom-up formation of hierarchically organized metal-organic networks composed of star-shaped and rod-like linkers (representing real organic molecules) and trivalent metal atoms. In our model π aromatic ligands were modeled in a simplified way as a collection of flat, rigid, and interconnected segments with properly encoded short-ranged interactions. Depending on the composition of the investigated overlayers, we observed the spontaneous formation a cascade of openwork (co)crystals with a hierarchical structure, controllable chirality and scalable morphological properties like porosity, connectivity, density, etc. Our theoretical findings can pave the way for the experimental fabrication of the novel surface-confined metal-organic networks (SMONs) in which anisotropic coordinate bonds play a decisive role.

Life cycle assessment of food waste anaerobic digestion with hydrothermal and ionizing radiation pretreatment

Extensive research has been conducted on the life cycle assessment of anaerobic digestion of food waste. However, few studies have evaluated the environmental impact of anaerobic digestion from a technical perspective. This study focuses on the environmental impact of using ionization radiation pretreatment technology in the anaerobic digestion of food waste and compares it with that of traditional hydrothermal pretreatment. Model construction, environmental impact assessment, and Monte Carlo simulation calculations were performed using the OpenLCA software. Data for the analysis were obtained from an actual plant in China, experiments, literature, and databases. The results show that the introduction of the proposed ionizing radiation pretreatment causes the treatment of food waste via anaerobic digestion to have the lowest environmental impact in 14 of the 18 categories analyzed. Pretreatment was found to be the most energy-consuming unit in food waste treatment, accounting for 71–75% of the total energy consumption. This research has an important guiding role in the development and application of ionizing radiation pretreatment technology for food waste.

Theory and equation of state of two-component nonadditive hard-disks: an application in the colloidal regime

ABSTRACT We use theoretical and Monte Carlo computer simulations to study thermodynamic and structural properties of a binary mixture of nonadditive hard-disks. The nonadditivity parameter is set to assume negative values so as to favour heterocoordination between the two species. The theoretical approaches include the Rescaled Virial Expansion Equation of State, which is based on the knowledge of the virial coefficients of the mixture, and the Rogers-Young Integral-Equation Theory. The comparison with Monte Carlo data shows that the microscopic theory is able to provide a reliable prediction of both the equation of state and the radial distribution functions of the system. These results are of interest because binary mixtures of colloidal particles adsorbed at the interface exhibit a wide range of self-assembly phenomena, and achieving of a reliable fluid state theory for a simple model of these systems is an essential milestone to be able to understand their nature.

Stochastic Timed Discrete-Event Systems: Modular Modeling and Performance Evaluation Through Markovian Jumps

We are interested in a scalable, flexible, and modular methodology, for modeling and performance analysis of stochastic discrete-event systems (SDES). In this sense, we propose a modular approach for timing non-markovian SDES expressed as a parallel composition of modules that interacts with each other through events. We show how general distribution for event lifetimes can be implemented systematically by coupling timing modules to the system model. As a result, this coupling mechanism preserves modularity, leading to a compact markovian model expressed in terms of flexible modules. Therefore the methodology allows us to write the whole SDES model as a composition of the system model and the timing one, giving flexibility and scalability in modeling design, as we can modify the modules individually according to the designer’s interests. In addition, from the whole markovian SDES model, we show how to perform the model analysis through the analytic approach, as well as through Monte Carlo computer simulation. As an application, we present a numerical example of computing the abandonment rate for a service network with general service time employing both analytical and computer-simulation models.

Two surface multipactor discharge with two-frequency rf fields and space-charge effects

This paper presents two-surface multipactor discharge with two-frequency rf fields using Monte Carlo simulations and Computer Simulation Technology (CST) Particle Studio. The effects of the relative strength and phase of the second carrier mode on multipactor susceptibility and time dependent physics are studied. Compared to single-frequency rf operation, shrinkage of multipactor susceptibility regions is observed for different configurations of two-frequency rf operation. The presence of a second carrier mode in the rf field results in mixed multipactor modes in which electrons take a fixed time period to complete a round trip between the two surfaces, while the time for electrons to traverse the gap in each direction is found to be different. CST simulation reveals that the space-charge effect reduces the electron growth rate and causes shrinkage of multipactor susceptibility bands.

Separation of ethane/ethylene gas mixture by ethane-selective CAU-3-NDCA adsorbent

Ethane-selective adsorbents for separating ethane (C2H6)/ethylene (C2H4) gas mixtures have attracted considerable interest as promising alternatives to conventional cryogenic distillation because of the possibility of directly producing high-purity C2H4 (>99.95%). Herein, CAU-3-NDCA built by the coordination bond between [Al12(OCH3)24]12+ and 2,6-naphthalenedicarboxylic acid (NDCA) was evaluated for use as a C2H6-selective adsorbent for separating a C2H6/C2H4 gas mixture. The separation performance of the adsorbents was investigated using single-component gas isotherms, ideal adsorbed solution theory calculations, dynamic breakthrough experiments for gas mixture, and molecular simulations, such as Monte Carlo simulation and density functional theory calculation. CAU-3-NDCA displayed exceptional adsorption capacity (9.2–10.2 mmol g−1 at 15 bar) and good C2H6/C2H4 selectivity (1.44–1.56) in the temperature range 293–313 K. In the breakthrough experiments, the C2H6/C2H4 separation performance of CAU-3-NDCA exhibited high-purity C2H4 productivity of 6.6 and 25.7 LSTP kg−1 under a 50/50 (v/v) and 10/90 (v/v) C2H6/C2H4 gas mixture, respectively, at 298 K and 7 bar. Recyclability was evaluated by a multi-cyclic breakthrough test for five cycles with a 10/90 (v/v) C2H6/C2H4 gas mixture. Molecular simulations indicated that the preferential adsorption of C2H6 originates from the higher affinity strength of multiple C–H···π interactions of C2H6 with NDCA linkers, in addition to the stronger methyl group–gas interaction of the methanolate group than those of C2H4. Moreover, it is characterised by thermal and moisture stability. Therefore, CAU-3-NDCA is a promising candidate for pressure swing adsorption operation as a C2H6-selective adsorbent.

Requirements for the containment of COVID-19 disease outbreaks through periodic testing, isolation, and quarantine

We employ individual-based Monte Carlo computer simulations of a stochastic SEIR model variant on a two-dimensional Newman–Watts small-world network to investigate the control of epidemic outbreaks through periodic testing and isolation of infectious individuals, and subsequent quarantine of their immediate contacts. Using disease parameters informed by the COVID-19 pandemic, we investigate the effects of various crucial mitigation features on the epidemic spreading: fraction of the infectious population that is identifiable through the tests; testing frequency; time delay between testing and isolation of positively tested individuals; and the further time delay until quarantining their contacts as well as the quarantine duration. We thus determine the required ranges for these intervention parameters to yield effective control of the disease through both considerable delaying the epidemic peak and massively reducing the total number of sustained infections.

Location of the gel-like boundary in patchy colloidal dispersions: Rigidity percolation, structure, and particle dynamics

During the past decade, there has been a hot debate about the physical mechanisms that determine when a colloidal dispersion approaches the gel transition. However, there is still no consensus on a possible unique route that leads to the conditions for the formation of a gel-like state. Based on gel states identified in experiments, Valadez-Pérez etal. [Phys. Rev. E 88, 060302(R) (2013)PLEEE81539-375510.1103/PhysRevE.88.060302] proposed rigidity percolation as the precursor of colloidal gelation in adhesive hard-sphere dispersions with coordination number 〈n_{b}〉 equal to 2.4. Although this criterion was originally established to describe mechanical transitions in network-forming molecular materials with highly directional interactions, it worked well to explain gel formation in colloidal suspensions with isotropic short-range attractive forces. Recently, this idea has also been used to account for the dynamical arrest experimentally observed in attractive spherocylinders. Then, by assuming that rigidity percolation also drives gelation in spherical colloids interacting with short-ranged and highly directional potentials, we locate the thermodynamic states where gelation seems to occur in dispersions made up of patchy colloids. To check whether the criterion 〈n_{b}〉=2.4 also holds in patchy colloidal systems, we apply the so-called bond-bending analysis to determine the fraction of floppy modes at some percolating clusters. This analysis confirms that the condition 〈n_{b}〉=2.4 is a good approximation to determine those percolating clusters that are either mechanically stable or rigid. Furthermore, our results point out that not all combinations of patches and coverages lead to a gel-like state. Additionally, we systematically study the structure and the cluster size distribution along those thermodynamic states identified as gels. We show that for high coverage values, the structure is very similar for systems that have the same coverage regardless the number or the position of the patches on the particle surface. Finally, by using dynamic Monte Carlo computer simulations, we calculate both the mean-square displacement and the intermediate scattering function at and in the neighborhood of the gel-like states.

The Impacts of Battery Electric Vehicles on the Power Grid: A Monte Carlo Method Approach

Balancing energy demand and supply will become an even greater challenge considering the ongoing transition from traditional fuel to electric vehicles (EV). The management of this task will heavily depend on the pace of the adoption of light-duty EVs. Electric vehicles have seen their market share increase worldwide; the same is happening in Portugal, partly because the government has kept incentives for consumers to purchase EVs, despite the COVID-19 pandemic. The consequent shift to EVs entails various challenges for the distribution network, including coping with the expected growing demand for power. This article addresses this concern by presenting a case study of an area comprising 20 municipalities in Northern Portugal, for which battery electric vehicles (BEV) sales and their impact on distribution networks are estimated within the 2030 horizon. The power required from the grid is estimated under three BEV sales growth deterministic scenarios based on a daily consumption rate resulting from the combination of long- and short-distance routes. A Monte Carlo computational simulation is run to account for uncertainty under severe EV sales growth. The analysis is carried out considering three popular BEV models in Portugal, namely the Nissan Leaf, Tesla Model 3, and Renault Zoe. Their impacts on the available power of the distribution network are calculated for peak and off-peak hours. The results suggest that the current power grid capacity will not cope with demand increases as early as 2026. The modeling approach could be replicated in other regions with adjusted parameters.

Evaluating the Dynamic Response of the Bridge-Vehicle System considering Random Road Roughness Based on the Moment Method

The bridge-vehicle interaction (BVI) system vibration is caused by the vehicles passing through the bridge. The road roughness has a great impact on the system vibration. In this regard, poor road roughness is known to affect the comfort of the vehicle crossing the bridge and aggravate the fatigue damage of the bridge. Road roughness is usually regarded as a random process in numerical calculation. To fully consider the influence of road roughness randomness on the response of the BVI system, a random BVI model was established. Thereafter, the random process of road roughness was expressed by Karhunen–Loeve expansion (KLE), after which the moment method was used to calculate the maximum probability value of the BVI system response. The proposed method has higher accuracy and efficiency than the Monte Carlo simulation (MCS) calculation method. Subsequently, the influences of vehicle speed, roughness grade, and bridge span on the impact factor (IMF) were analyzed. The results show that the road roughness grade has a greater impact on the bridge IMF than the bridge span and vehicle speed.